Fundamentals of Strength of Materials and FEM

METHODS TO SOLVE ANY ENGINEERING PROBLEMS ANALYTICAL METHODNUMERICAL METHODEXPERIMENTAL METHOD

-CLASSICAL APPROACH -100% ACCURATE RESULTS-CLOSED FORM SOLUTION- PL/3EI- APPLICABLE ONLY FOR SIMPLE PROBLEMS LIKE CANTILEVER & SIMPLY SUPPORTED BEAMS ETC-MATHEMATICALREPRESENTATION -APPROXIMATE , ASSUMPTIONS MADE-APPLICABLE EVEN IF PHYSICAL PROTOTYPE NOT AVAILABLE - REAL LIFE COMPLICATED PROBLEMS -RESULTS CANNOT BE BLINDLY BELIEVED

-ACTUAL MEASUREMENTS -TIME CONSUMING AND NEEDS EXPENSIVE SET UP - APPLICABLE ONLY IF PHYSICAL PROTOTYPES ARE AVAILABLE

THOUGH ANALYTICAL METHODS COULD ALSO GIVE APPROXIMATE RESULTS IF THE SOLUTION IS NOT IN CLOSED FORM , BUT IN GENERAL AND BROAD SENSE ANALYTICAL METHODS ARE CONSIDERED AS CLOSED FORM SOLUTIONS I.E. 100% ACCURATE FINITE ELEMENT METHOD - LINEAR , BUCKLING , THERMAL , DYNAMIC AND FATIGUE ANALYSIS BOUNDARY ELEMENT METHOD ACOUSTICS / NVH FINITE VOLUME METHOD CFD AND ELECTROMAGNETICS FINITE DIFFERENCE METHOD THERMAL AND FLUID FLOW ANALYSIS -STRAIN GUAGE -PHOTO ELASTICITY-VIBRATION MEASUREMENTS -SENSORS FOR TEMP. & PRESSURE -FATIGUE TEST

How does numerical methods solve the problem?This is achieved by discretization of problems . All real life objects are continuous . Means there is no physical gap between two consecutive particles . As per material science any object is made of small particles , particles of molecules , molecules of atoms and so on and are bonded together by attraction . Solving a real life problems with continuous material approach is difficult and basic of all numerical methods is to simplify the problem by discretizing( discountinuation ) it . In simple words nodes work like atoms and gap in between them is filled by entity called as element . Calculations are made at nodes and results are interpolated for entire elements. FEMFinite Any continuous object has infinite degrees of freedom & its just not possible to solve the problem in this format . Finite Element Method reduces degrees of freedom from Infinite to Finite with the help of discretization i.e. meshing (nodes & elements ).Element All the calculations are made at limited number of points known as nodes . Entity joining nodes and forming a specific shape such as quadrilaterals or triangular is known as element .Method There are three methods to solve any engineering problem . FEM belongs to one of them.

ADVANTAGES OF FEM1> Improved visualization2> Lesser design cycle time3> Lesser number of prototypes4> Lesser no. of testing required 5> Decrease in cost of production

VISUALIZATION OF RESULTS : For simple geometries such as simply supported beams or cantilever beams it is easy to visualize point of maximum stress and displacement . But in real life for parts or assemblies with complex geometrical shapes , made up of different materials with many discontinuities subjected to flexible constraints , complex loading conditions it is not easy to predict failure location . Here CAE softwares gives you stresss contours for any complex loading case which helps you to easily determine failure location .

STAGES OF ANALYSIS

STAGE 1: PRE-PROCESSINGCAD&MESHING There are specialized softwares for CAD , Meshing & Analysis . CAD and meshing consumes most of the time .BOUNDARY CONDITIONS Consumes least time but the most important step

STAGE 2: SOLUTION Software carries out matrix formulations , inversions , multiplications and solutions for unknown for eg: displacements and then stress and strain for static analysis .

STAGE 3 : POST-PROCESSING Post processing is viewing results , verifications , conclusions and thinking about what steps be taken to improve the design .

BASICS OF STATICS AND STRENGTH OF MATERIALS STRESS Internal resistance to external force . In simple words it is defined as force per unit area .

S.I. unit of stress is N/m2 . But the results are in very small numerical figure & hence N/mm2 (or MPa , Mega Pascal ) is more popular among CAE engineersTypes of StressHow many types of stresses are there in engineering world?Only two- Normal and Shear i.e. normal and shear . Bending , torsion , tension , compression , max. principal , von-mises etc. are forms of Normal and Shear stresses. Normal Stress: Acts perpendicular to cross section and causes elongation / compressionShear Stress: Acts parallel to cross section , causes distortion (changes original shape)

Types of Forces in engineering world1> Based on direction of force:There are 3 types of forces Fx,Fy,Fz and 3 types of moments Mx,My,Mz in the world . All the loading conditions like concentrated load , distributed loads , pressure , traction , gravity , torsion etc are forms of Fx,Fy,Fz, Mx,My & Mz

FORCEFX FY FZ

2> Based on region of force application FORCES Point Area Line Volume

If perpendicular If inclined or parallel Gravitational force Centrifugalcalled pressure called traction force

Types of moments in engineering worldMx Torsion , Shear stress

My Bending Normal Stress

Mz Bending Normal Stress

What is torque ? Is it force or moment.Torque is moment acting along the axis of shaft/object eg. In above fig. is Mx . Torque causes shear stress while other 2 moments causes normal stress.

Basic assumptions for nature of stress

Uni-axial Bi-axial Triaxial 1-D 2-D

By default all the post processors gives von-mises stress plot ? What is von mises stress & max. principal stress ?

The stress-strain diagram is plotted from standard uniaxial tensile test . This curve is helpful in designing dimensions of component if tensile force is known , based on yield stress one can easily determine safe area of c/s (Area=Force/yield stress). But when component is subjected to multi-axial loading (i.e. normal and shear stress together) nature of stress-strain curve will not be same . It indicates for different combinations for loading (FX,FY,FZ,MX,MY,MZ) different graphs should be referred to . Therefore it is just not practical to conduct so many tests. Here we use different theories of failure which gives us equivalent max. normal or max. shear stress or energy of component subjected to multiaxial loading . It is then equated with respective value at yield point(uniaxial tensile test)

vonMises Stress: Based on distortion energy or shear strain energy theory

FAILURE CRITERIA Shear strain energy (multiaxial loading) = shear strain energy at yield point (uniaxial tensile test)RECOMMENDED for ductile materials i.e. steel , aluminium components

Why vonmises stress is recommended for ductile and Principal stresses for brittle materials?

BRITTLE Failure of cast iron rod subjected to uniaxial test is along a plane perpendicular to axis of loading . Clearly the failure is due to normal stress . Out of different theories of failure max. principal stress theory is the one which is based on normal stress . Hence for brittle material component Max. Principal stress is used Mild steel fails at a plane inclined at 450 to axis of loading . Normal stress cant act on this plane and the only other possibility is shear stress . Out of different theories of failure its max. shear stress and vonMises stress which are based on shear stress. Von mises gives better correlation with experimental results and hence preferable for ductile materials .

Types of analysis 1> Linear static analysis

Equation of motion is given by f=kx where F is forceK is stiffness constant X is displacement Linear means straight line .Static:There are 2 conditions for static analysis 1> Force is static i.e. no variation with respect to time ( dead weight) Df/dt=0

2> Equilibrium condition - forces (Fx,Fy,Fz) and Moments (Mx,My,Mz) =0 . Finite Element model fulfils this condition at each and every node .

Practical Application : Most commonly used analysis in aerospace , automobile , offshore and civil engineering industries perform linear static analysis 2> NONLinear static analysis Non- Linearity

Geometrical Material Contact Force(stress) vs Displacement(strain) curve is non linear Stiffness K varies and is not constant as in the case of linear analysis Deals with true stress & true strain (unlike engineering stress & engineering strain in linear static analysis)

A> Geometric Non LinearityThough component is within the elastic limit but due to very large length even small force causes large deformation . Regular formulas of strength of materials like deflection PL3 /3EI not applicable as these are based on small displacement assumption . Example : Fishing Rod

B> Material Non LinearityStress strain diagram along with hardening rule for material is required as Input data . Metallic non linearity applications: Automobiles , aerospace , ship industries . To know exact value of stress/strain when it crosses yield point . For low cycle fatigue analysis this data is considered as input for strain life approach.Nonmetallic non linearity applications : Automobile , aerospace industry , analysis of rubber , plastic , asbestos , fibre components .Creep At elevated temperatures even small magnitude of foce if kept alive over long time period say for months and years would cause failure . Application Nuclear / Thermal power plants , Civil engineering etc.

C> Contact Non Linearity To simulate physical gap between two parts eg. Bearing and shafts or press fit between two cylinders

3> Dynamic analysis DYNAMIC ANALYSIS

FREE VIBRATION FORCED VIBRATION

Practical Applications: Natural frequency is characteristic and basic design property of any component while forced vibrations are applicable for components subjected to force/displacement/velocity/acceleration varying with respect to time/frequency.

4> LINEAR BUCKLING ANALYSIS

Applicable for only compressive loads Slender beams & sheet metal parts Bending stiffness fatigue ANALYSIS Calculations for life of structure when subjected to repetitive loads S-N curve(alternating stress vs cycles) or (alternating strain vs reversals) is the base for fatigue calculations

Damage=n/N Endurance Factor of Safety(EFS)= =No. of cycles / life Endurance strength/FE stress Damage < 1 safe Damage >1 fail EFS1 safeHigh cycle fatigue

Static and dynamic analysis can not tell how long component will survive for given load . Also there is no consideration for factors like surface finish, heat treatment , decarburizing , alloying elements .

7> optimization Optimization

Geometrical Parameters Shape optimization Optimization for geometry - Usually restricted to only linear static Parameters , work well at individual and normal mode dynamicsComponent level rather than Complicated assemblies - Good tool for innovative kind of Products

Software cant add or remove geometries - Software can give hint for addition On its own but can play with only or removal of geometriesPredefined parameters within specified limits.

Practical Applications: Applicable to any component which is over or under designed

8> Cfd-computational fluid dynamicsCFD is the branch of fluid mechanics which uses numerical methods to analyse fluid dynamics problems . It is based on Navier-Stokes equation(mass, moment and energy conservation equilibrium equations)

Practical Applications: Drag prediction and streamlining of a car, combustion chamber design to check an optimum fuel-air mixing , airplane design etc.

9> Crash analysis

STRUCTUTAL CRASHWORTHINESS/IMPACT SIMULATIONSDROP TEST SIMULATIONS OCCUPANT SAFETY

To find deformation, stress and energy absorbing capacity of various structural components of vehicle hitting a stationary or moving object . The component is said to be crashworthy(safe) if it meets the plastic strain and energy targets .

Applications: Frontal, side , Rear , Roof crush , car hitting pole.etc.

Drop test is a free fall test carried out to check the structural integrity of component.

Application: Blackbox of an aircraft, mobile phone , consumer goods , TV Fridge etc.To find the effects of crash on human body and making the ride safe for driver as well as passengers .

Several regulations have come across different countries to ensure proper certifications e.g.FMVSS(Federal Motor vehicle safety standards) in USA

In india ARAI has set up standard procedures for automotive industry and called as AIS(Automotive Industry Standard)

10> Noise vibration and harshness (nvh) analysisSOUND RADIATION OR SCATTERING COUPLED OR VIBROACOUSTICS PROBLEMS

Predicts how much sound pressure level is felt by a vibrating source at a certain distance as a function of solid angle . Ex. Sound felt due to horn or silencer vibrating at a certain distance

These are solved by Boundary Element MethodThere is a clear interaction of a structure and fluid cavity . A typical example is noise level felt at drivers right ear due to engine vibration in idle condition .

These are solved by Finite Element Method

Ansys Ansys is a complete FEA package used by engineers worldwide in virtually all fields of engineering.

ANSYS workbench complete environment for geometry modeling , mesh manipulation , structural / thermal analysis , and optimization , which is tightly integrated with CAD packages

CFX- state of the art CFD solvers , including the coupled , parallel CFX-5 solver

ICEM CFD Powerful meshing tools with general pre and post processing features

ANSYS MULTIPHYSICS provides the analysis capabilities for industrys most comprehensive coupled physics tool combining structural, thermal , CFD , acoustics and electro-magnetic simulation capabilities into a single software prouct . It is the flagship product of ANSYS which includes analysis capabilities in all engineering disciplines . It has two GUI ANSYS classic environment for exposure of all functionality ANSYS workbench environment for tight integration with CAD ANSYS Mechanical Structural and Thermal analysis tool which includes a full compliment of nonlinear and liner elements , material laws ranging from metal to rubber and the most comprehensive sets of solvers available

ANSYS Structural Provides the power of ANSYS non linear structural capabilities as well as linear capabilities to deliver highest quality, most reliable structural simulation results possible

ANSYS Professional Inexpensive, easy to use program for structural/thermal analysis projects

ANSYS Design Space An easy to use package that gives designers the tool to conceptualize, design and validate ideas right on desktop.

ANSYS LS-DYNA This tool helps engineers to understand elaborate combinations of non-linear phenomena found in crash tests , metal forging , stamping and catastrophic failures .

List of industries using ansys Aerospace Automotive Biomedical Bridges and buildings Electronics and appliances Heavy equipment and machinery MEMS- Micro Electromechanical systems Sporting goods

Description of ANSYS Menus and WindowsWhen using the ANSYS program in Interactive Mode, the Graphical UserInterface (GUT) is activated. The GUI has six distinct components:

Utility Menu: Contains functions that are available throughout theANSYS session, such as file controls, selecting, graphic controls, andparameters. The ANSYS Help System is also accessible through thismenu.Main Menu: Contains the primary ANSYS functions organized byprocessors (Preprocessor, Solution, General Postprocessor, etc.).Toolbar: Contains push-buttons for executing commonly used ANSYScommands and functions. Customized buttons can be created.Input Field: Displays a text field for typing commands. All previouslytyped commands are stored in a pull-down menu for easy reference andaccess.Graphics Window: Displays the graphical representation of the models/meshes created within ANSYS. Also, the related results are reviewed inthis window.Output Window: Receives text output from the program. This windowis usually positioned behind other windows and can be raised to thefront when necessary.

UTILITY MENU RAISE HIDDEN INPUT LINE

ANALYZING BEAMS

Beams are structural members subjected to transverse loading .

GRAPHICS AREA USER PROMPT INFO MODEL CONTROL TOOL BAR

ANSYS memory management ANSYS executable memory is the memory required for ANSYS program. ANSYS workspace is the memory required to run in addition to the ANSYS executable memory . Real memory is the amount of actual , physical memory (RAM) available through memory chips on your machine . System virtual memory is simply a portion of computers hard disk used by the system to supplement physical memory .

Workspace is the memory ANSYS needs to run. Default is 512 MB in Windows and UNIX machines . Database space is used to work with ANSYS database . For example model geometry , material properties , loads etc. Defaults to 256 MB on windows and UNIX machines . Scratch space is where all internal calculations are done . For example element matrix formulation , frontal solution , Boolean calculations and so on .

ANSYS basics PICKING AND PLOTTING It is often advantageous to plot only certain entities in the model .Within the utility menu > plot , you will see geometric , finite element and other entities can be plotted .

The plot ctrls menu is used to control how the plot is to be displayed : Plot orientation , zoom , colors , symbols , annotation , animation etc

Mouse clicks Ctrl + left mouse button pans the model Ctrl + middle mouse button zooms the model and spins the model Ctrl + right mouse button rotates the model .PICKINGPicking allows you to identify model entities or locations in the graphics window . Picking operation typically involves the use of the mouse and picker menu .

Left mouse button picks or unpicks the entity or location closest to mouse pointer . Middle mouse button does an apply and saves time . Right mouse button toggles between pick and unpick mode

COORDINATE SYSTEMS

The ANSYS program has several types of coordinate systems, each used for a different reason: Globalandlocalcoordinate systems are used to locate geometry items (nodes, keypoints, etc.) in space. Thedisplaycoordinate system determines the system in which geometry items are listed or displayed. Thenodalcoordinate system defines the degree of freedom directions at each node and the orientation of nodal results data. Theelementcoordinate system determines the orientation of material properties and element results data. Theresultscoordinate system is used to transform nodal or element results data to a particular coordinate system for listings, displays, or general postprocessing operations (POST1).

GLOBAL COORDINATE SYSTEM The global reference system for the model May be cartisian (0) , cylindrical (1) , spherical (2)

LOCAL COORDINATE SYSTEM A user defined system at a desired location , with ID number 11 or greater May be cartisian , cylindrical or spherical May be rotated about X,Y,Z axis

DISPLAY COORDINATE SYSTEM Can be changed to show and list entities in multiple coordinate systems Default is global Cartesian Used mostly for listing and plotting models in non-cartesian systems Active coordinate system in ANSYS is default to global Cartesian SELECT LOGIC FUNCTION Suppose you want to do the following: Plot all areas located in the second quadrant Delete all arcs of radius 0.2 to 0.3 units Apply a convection load on all exterior lines Write out all nodes at Z=3.5 to a file They all operate on a subset of a model . Select logic allows you to select a subset of entities and operate only on those entities .Utility menu > select > entities

Criteria by which to select :By num/pick: to select based on entity numbers or by pickingAttached to : to select based on attached entities . For example select all lines attached to the current subset of areas .By location : to select based on x,y,z location . For example select all nodes at X=2.5 . X,Y,Z are interpreted in active coordinate systems By attributes : to select based on material number , real constants set number etc Different attributes are available for different entities Exterior : to select entities lying on exterior By results : to select entities by results data e.g. nodal displacements

TYPE OF SELECTION From full : selects a subset from the full set of entities Reselect: select a subset from current subset Also select: adds another subset to current subset Unselect: deactivates a portion of current subset Invert: toggles the active and inactive subsets Select none : deactivates the full set of entities Select all: reactivates the full set of entities

REACTIVATING THE FULL SETUtility menu > select everything

COMPONENT MANAGER Components are user named subsets of entities . The name can be used in dialogue boxes or commands in place of entity numbers .A group of nodes , elements or key points , or lines , or volumes can be defined as a component . Only one entity type is associated with component .Components can be selected or unselected . When you select a component , you are actually selecting all of the entities in that component .Component manager is used to create , display , list and select components and assemblies Utlity menu > select > component manager

Creating a component could be done by Utility menu > select > component manager Click on create component icon All of the currently selected entities will be included in the component , or you can select the desired entities at this step Enter a name upto 32 characters letters , numbers and _(underscores) are allowedCreating an assembly Highlight the components for the assembly Click on the create assembly icon and enter a name Checking the box next to a component under the assembly number will also put a component in a assembly

General analysis procedure Every analysis involves four major steps

1> Preliminary decisions -Which analysis type ?- What to model ?-Which element type ?

Depending on the physics of the problem analysis type should be decided , the loads involved and output desired .For example if load is pressure on bodies , or contact of two bodies then analysis type will be structural . If loads applied is heat , temperature than analysis type will be thermal.

Modeling may not necessary be full geometry . Depending upon symmetry in geometry and loading conditions we can model or model . Or model can be imported from other CAD modules also .

Selection of element type is very important step . Selection of element depends upon shape function of element which depicts the behavior of element . Lower order element gives less accuracy and low computational time . Higher order element gives higher accuracy and higher computational time .

2> Preprocessing -Define element type-Defining material properties-Create or import the geometry model-Mesh the geometry

Defining element type ANSYS has library of more than 180 elements . To select right element type we need to know the element shape function and behavior .

Defining material properties

Defining material properties : We dont need to define system of units in which we are working . Simply decide units you will use , then make sure all of your input is consistent .

-for example , if the model geometry is in inches , make sure that all other input data material properties , real constants , loads etc are in inches .

Creating geometry

There are 2 approaches for modeling in ANSYS top down approach and bottom up approach .

In this method, first keypoints are created, and then other higher order entities such as lines, areas, and volumes are created by using these keypoints, refer to Figure 1, 2, 3, and 4.

In this method, the model is created using the geometric primitives such as fully-definedkeypoints, lines, areas, and volumes. Figure 5 shows the frustum of a cone created using the top-down construction method.

For analysing a model, you do not need the same model as the actual component. So, before creating the model, you need to consider the following points to decide which features to be modeled and which ones to be ignored while performing an analysis

The minor details that are not important to the analysis can be avoided in the model.

For symmetric models, you need not to create the complete model. The main advantages of symmetric model are that you can create the model easily and generating the finer mesh to get better results.

There are four types of symmetrical models that are discussed next

Axisymmetric models are symmetric about their central axes; for example, cylinders, cones, bulbs, and so on,

In a rotational symmetric model, the repetitive segments are arranged about the central axis

In a repetitive symmetric model, the repeated segments are arranged in a straight line

Keypoints are created in the active coordinate system. Keypoints are the base points for creating other geometric entities such as line, area, and volume

This option is used to create keypoints using the X, Y, and Z coordinates. To do so, choose this option; the Create Keypoints in Active Coordinate System

Modeling > create > keypoints > in active cs

This option is used to create a keypoint on a line in ratio

This option is used to create a keypoint at any existing node To create a keypoint, choose the On Nodes option from the Keypoints node; the Create KP on Node dialog box will be displayed and you will be prompted to select the node on which you want to create the keypoint

Lines are used to define areas. Some of the line elements; for example, beams are defined by lines

This option is used to create a straight line between two keypoints using the global cartesian coordinate system

This option is used to create a straight line between two keypoints using the active coordinate system

This option is used to create the straight line between two keypoints on an area

This option is used to create a line tangent to an existing line. To create a tangent line,choose the Tangent to Line option from the Lines node; the Line Tangent to Line dialog box will be displayed and you will be prompted to select a line that will be tangent to a new line

This option is used to create a line that will be tangent to two existing lines

This option is used to create a straight line that will be normal (at 90-degree) to the existing line

This option is used to create a straight line that will be normal (at 90-degree) to two existing lines

This option is used to create a straight line that will be at a specified angle to the existing line

You can create an arc by choosing Preprocessor > Modeling > Create > Lines > Arcs from the Main Menu; the options to create arcs will be displayed under the Arcs node

This option is used to create an arc using three keypoints

This option is used to create circular arcs using center point and radius

To create a fillet between two intersecting lines, choose Preprocessor > Modeling >Create > Lines > Line Fillet from the Main Menu; the Line Fillet dialog box will be displayed

You can create an area by connecting keypoints or lines. To do so, choose Preprocessor > Modeling > Create > Areas from the Main Menu; the options to create areas will be displayed

To create arbitrary using the Arbitrary option, choose Preprocessor > Modeling > Create > Areas > Arbitrary from the Main Menu

This option is used to create an area by specifying keypoints

This option is used to create an area using the shape of an existing area

Area created using the Through KPs The overlaid area created option1

This option is used to create an area using the existing lines

This option is used to create an area by skinning a surface through guiding lines

Area created using the By Lines options Area created using the By Skinning opt

This option is used to create an area offset to an existing area

The Create Area by Offset From Base Area dialog boxAn offset area created

Figure shows the rectangular areas. Its various options are discussed next

This option is used to create a rectangular area on a workplane by specifying two opposite corners

The Rectangle by 2 Corners The rectangular area created

This option is used to create a rectangular area on a workplane

This option is used to create a rectangular area on a workplane by specifying the X andY coordinates of two diagonal points of a rectangle

The Create Rectangle by Dimensions dialog box

Figure shows the circular areas and its various options

Options for creating the circular areas

This option is used to create a solid circular area on a workplane

This option is used to create a annular circular area on a workplane

This option is used to create a partial annulus circular area on a workplane

The partial annulus circular area

This option is used to create a solid circular area on a workplane

This option is used to create a solid circular area on a workplane by specifying the outerradius, inner radius, starting angle, and ending angle in the graphics area

The Circular Area by Dimensions dialog box

This option is used to create a triangular area on a workplane

The options to create polygon The Triangular Area dialog box The triangular area

Meshing in ansys

Element order Element order refers to the polynomial order of the elements shape functions.

What is shape function ? It is a mathematical function that gives the shape of results within the element . Since FEA solves for DOF values only at nodes we need the shape function to map the nodal DOf values to points within the element . The shape function represents the assumed behavior for a given element How well each assumed shape function matches the true behavior directly affects the accuracy of solution .When you choose an element type you are implicitly choosing and accepting the element shape function assumed for that element type . Therefore check the element shape function before selecting the element .

Linear elements Quadratic elements

Linear variation of quantities

Highly sensitive to element distortion

Acceptable if you are interested in nominal stress results Quadratic variation of quantities

Can represent curved edges and surfaces more accurately than linear elements . Not as sensitive to element distortion

Recommended if you are interested in highly accurate results

Mesh densityThe fundamental premise of FEA is that as the number of elements(mesh density ) is increased , the solution gets more and more accurate , however solution time and CPU usage also dramatically increases .

Controlling Mesh densityAnsys provides many tools to control mesh density both on local and global level .

Global controls Smart sizing Global element sizing Default sizing

Smart sizing This option determines element sizes by assigning divisions on all lines , taking into account curvature of line , its proximity to holes and other features and element order .To use smart sizing Goto > mesh tool > turn on smart sizing > manage meshing density ( 1-10)

Global element sizing This option allows you to specify a maximum element edge length for the entire model Main menu> preprocessor> meshing > mesh tool > size controls > global Using this option with ( smartsizing off) will result in a uniform element size throughout the volume ( or area ) being meshed With smartsizing on , this option acts a guide but specified sizes may be overridden to accommodate line curvature or proximity to features

default element sizing If you dont specify any controls , ANSYS uses default sizing , whih assigns minimum and maximum line divisions , aspect ratio , etc based on element order .

Local controls

Keypoint sizing Line sizing Area sizing

Keypoint sizing Controls element size at keypoints Main menu > preprocessor > meshing > mesh tool > size controls set keypoint and set

Setting up different keypoints with different sizes we find useful to contemplate stress concentration regions . Line sizing Controls element size at lines Main menu > preprocessor > meshing > mesh tool ; then select size controls lines and set

Area sizing Controls element size in the interior of areas .

Main menu > preprocessor > meshing > mesh tool ; select size controls , areas and set

Types of meshing methods

Free mesh Have no element shape restrictions Suitable for complex shapes and geometries Smart sizing is preferred Tria and quad shape for 2d elements and tetra for 3d elements

Mapped mesh Follows regular pattern Not suitable for complex shapes Smartsizing is not preferred and should be off For areas no. of edges should be 3 or 4 For volumes no. areas should be 4,5 or 6. Concatenation This option creates a new line that is combination of two or more lines . Main menu > preprocessor > concatenate > lines concatenate

Tri and quad shape for 2d element and brick for 3d elements

Sweep mesh Smart sizing is preferred Only for solids Only brick shape is available

Volume must be toppologically consistent for sweep meshing eg. Plate with a hole Tet mesh option for non sweepable volumes Go to meshing > mesh > volume sweep > sweep options Check the option tet mesh option for non sweepable volumes

3> Solution-loading and solution

Solution You must first define a Load Step containing set of boundary conditions as stated above.Then for solution part

Goto solution > solve > current LSWhen you click on solve , ANSYS performs matrix formulations , multiplications , inversions . For this purpose there are various solvers in ANSYS

Solvers

The function of solver is to solve the system of linear simultaneous equations representing the structures degree of freedom. The solution could take anywhere from a few seconds to several hours depending primarily on the size of model , the solver selected and speed of your computer .

A linear static analysis with one load step requires only one such solution , but a non linear or transient analysis may require tens , thousands or even thousands of solutions.Therefore the type of solver you select is very important .

The solvers available in ANSYS can be categorized into four types-1> Direct Elimination2> Iterative3> Distributed domain4> Distributed ANSYS

How does solver calculate solution ?The calculation takes place as shown in following steps

1> Formulate individual element matrices2> Assemble global stiffness matrix3> Sparse direct solver factorizes the stiffness matrix , and then calculates DOF solution from backward-substitution.4> Iterative solver starts with an assumed zero value for all DOF and iterate to convergence (based on an input tolerance on residual force )

5> Use element matrices to calculate the element solution

Formulate element matrices

Assemble global matrix .full fie

Solve matrix equation .rst/.rth fie

Follow the guidelines below to choose the solver Main Menu > Solution > Analysis type > Solution Controls then choose solution options tab

Direct Elimination solvers are further classified into Sparse (default) FrontalIf the linear static case of [k]{x}={F} ,Direct solvers factorizes [K] to solve for [k]-1.Then {x}=[k]-1{F}This factorization is expensive but is done once .

Iterative solvers further classified into PCG ( Pre-conditioned Conjugate Gradient ) ICCG ( Incomplete Cholesky Conjugate Gradient ) JCG ( Jacobi Conjugate Gradient ) AMG ( Algebraic Multigrid )

Iterative solvers use a preconditioner [Q] to solve the equation [Q][K]{x}=[Q]{F} .Assume that [Q]=[K]-1 . In the trivial case , [I]{x}=[K]-1{F} . However the preconditioner is not usually [K]-1 . The closer [Q] is to [K]-1 , the better preconditioning is .However the preconditioner is not usually [K]-1 , so this process is repeated hence the name , iterative solver .

For iterative solvers , matrix multiplication is performed . This is much faster than matrix inversion if done entirely in RAM , so as long as the number of iterations is not very high iterative solvers can be more efficient than sparse solvers . The main difference between the iterative solvers in ANSYS namely PCG , JCG , ICCG is the type of pre-conditioner used .

Multiple load steps

By using multiple load steps , you can :isolate the structures response to each loading condition Combine these responses in desired fashion during post processing , allowing you to study different what-if scenarios .

There are 2 ways to define and solve multiple load steps : Multiple solve method Load step file method

Multiple solve methodAn extension of single load step solution , where you solve each load step sequentially without leaving the solution processor Best suited for batch mode When used in interactive mode this method is useful only for models that solve quickly

Load step file methodIn this case instead of solving each load step , you write the load step information to a file called load step file : Main menu > solution > load step opts > Write LS file

After writing all load step files you can solve it by Mein menu > solution > solve > from LS files to read in each file sequentially and solve

4> Post processing-Review results and check the validity of solution

Plotting results :ANSYS provides contour plot , vector plot of results example stresses , strains , deflection , thermal temperature , flux and so on .General posrproc > plot results > contour plot > nodal solution >stress von mises

DMX- Maximum displacement SMX- Maximum stress SMN-Minimum stress

Query picking Query picking allows you to probe the model for stresses , displacements or other results quantities at any picked location You can also quickly locate the maximum and minimum values of the item being queried . Available only through GUI General postproc > query results > element or sub grid solution >ok

Path operations Path operations allows you to : Map results data onto an arbitrary path through the model Perform mathematical operations along the path , including integration and differentiation Display a path plot 1>Define a path Points defining a path you can use existing nodes or locations on the working plane Path curvature , determined by active coordinate systems (CSYS) A name for the path General postproc > path operations > define path > by nodes Pick nodes from desired path and O.K. Choose a path name

2>Map data onto a path General postproc > path operations > map onto path Choose desired quantity , such as SEQV Enter a label for quantity 3>Plot the data General postproc > path operations > plot path item > on graph Besides plots and listings there are many other path capabilities Stress linearization used in the pressure vessel industry to decompose stress along a path into its membranes and bending components Calculus functions used in fracture mechanics to calculate J-integrals and stress concentration fctors . Dot products and cross products used in electromagnetic analyses to operate on vector quantities

Error estimations

Variable viewer Variable viewer is a specialized tool allowing you to post results with respect to time The variable viewer can be started by simply opening the Time History Postprocessor Main menu > time history postproc > variable viewer

Go to add data > select desired node > list data / graph data

Results viewer The results viewer is a specialized postprocessing menu and graphic system Fast graphics for large models Easy to use menu system for quick results viewing General postproc > write PGR file

Module 1 Structural analysis of beams

TYPES OF BEAMS & TYPES OF LOADINGS

Beam:-A structural member which is acted upon by a system of external loads at right angles to its axis is known as beam.

TYPES OF BEAMS:-There are five types of beams as under:-

1.Cantilever Beam:-Acantilever beamis one whose one end is fixed and the other end carries a point or concentrated load.

2.Simply Supported Beam:-A simply supported beam is one which carries two reaction forces at its two ends & a point load at its mid-point

3.Overhanging Beam:-It is a type of simply supported beam which overhangs from its supports.An overhanging beam may overhang on one side only or on both sides of the supports

5.Continuous Beam:-It is a type of overhanging beam which consists of a numerous reaction forces and point loads

SOLVED EXAMPLE

1> Defining element typesPreprocessor> element type > add/edit/delete > add > BEAM 188 The BEAM188 element is suitable for analyzing slender to moderately stubby/thick beam structures. This element is based on Timoshenko beam theory. The degrees of freedom at each node include translations in x,y, and z directions, and rotations about the x,y, and z directions.

2> Define material properties Preprocessor> material properties > material model > structural > linear > elastic > isotropic EX=2E5 ( 2*105) PRXY=.33

3> Define section properties Preprocessor> sections > beam > common sections B=60H=40

4> Modelling keypoints and lines Modelling > Create > Keypoints > In active c/s Create Keypt No.1 at (1,0,0)

Create Keypt No.2 at (400,0,0)

Modeling > Create > Lines > In active c/s > Select Keypt. 1 and Keypt 2

5> Meshing Meshing > Mesh tool > Global > Set No. of element divisions NDIV. = 10 > Mesh > Select line > OK

6> Viewing Elements Utility Menu > Plot Ctrls > Style > Size & Shape > Check display of element

7> Applying Loads & Boundary Conditions

Solution>Define Loads> apply > structural> displacement > on keypoins > select leftmost key point > DOFs to be constrained > all DOF

8> Applying Loads & Boundary Conditions Solution>Define Loads> apply > structural> force/moments > on keypoins > select rightmost keypoint >direction of force moment Fy ,value of force -2500

9> SolutionSolution> solve > current LS(Load Step)>OK

10> Postprocessing Generalpostproc > Plot Results > Deformed Shape > Deformed+undeformed

11> Postprocessing Generalpostproc > Plot Results > Contour plot>nodal solution > stress > Von-Mises stress

12> Animating Utility Menu > Plot Ctrls > Animate > Deformed Results > Stress > Von Mises

No of Frames to create = 20

To be performed by students

Analytical methodFem solution in ansys

Beam orientation theory

The cross section of beam is different from section created in ANSYS s/w . The main reason for this is difference in orientation of nodal coordinate system and World Coordinate System . To rectify this problem we need to orient the orientation keypoint to global Y axis .

Create a third keypoint i.e. keypt no.3 for orientation at 0,40,0

Go to meshing > mesh tool > element attributes > line > select line > tick on orientation keypoint to yes

Then continue from step no. 5

Practice questions 1:

F = 5000NEX= 2*105 N/mm2PRXY=.33

Practice questions 2:

Modulus of elasticity = 30 * 106 psiPoisons ratio = .33

Practice questions 3:

EX=1*10^7 psiPrxy=.33

Simply supported beams

Determine reaction loads at A & B and also create Shear force and Bending Moment Diagrams

Modelling > Create > Keypoints > Keypoint no. 1 at (0,0,0) and keypoint no. 2 (2.5,0,0) and Keypoint no. 3 (5,0,0)

Modelling > Create lines > From Keypoint 1 to 2 and from Keypoint 2 to 3

Applying Boundary Conditions Solution > Define Loads > Apply Structural> Displacement > On keypoints > Select keypoint no. 1 and 2 > restrict Ux,Uy,Uz,Rotx ,Roty degrees of freedom

Solution Define Loads > Apply > Structural > Force > On keypoint no. 2 > Fy=-10000

Viewing reaction loads and S.F. and B.M diagrams

General Postproc > List Results > Reaction Solutions > All Items

General Postproc > Element Table> Define Table > By sequence num > SMISC 6 > APPLY > SMISC 19

General Postproc > Plot results > Line Element Results > SMISC 6 , SMISC 19

How to apply Uniformily distributed loads (udl) ?After meshing goto utility menu > Plot lines You will see 4 lines with elements (dashed lines)

Go to apply> structural > pressure on beams > select line all dashed lines of line 3 > okAfter selection colour will change to dark yellow

Remaining steps are same from step no. 9

Assignment questions

Ex = 1e11 N/mm^2 Prxy =.33

Ex = 1e11 N/m^2 Prxy =.33

Ex = 1e5psi Prxy =.33

How to apply uniformly varying loads ?

Pressure value at node I = 0Pressure value at node j = 5000

Module 2 Structural analysis of trusses

Trussis astructure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to asnodes. External forces and reactions to those forces are considered to act only at the nodes and result in forces in the members which are eithertensile orcompressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated asrevolutes.

In truss members the forces on the members are axial (that is, they act along the axis of the member), putting them in either pure tension or pure compression.The members are joined together by pins.Top of Form

Bottom of FormIn trusses loaded by downward forces, the members along the top (the top chord) are in compression and the members along the bottom (the bottom chord) are in tension. The members connecting the top and bottom chords (the web members) may be tension or compression, depending on their angles and the distribution of the loads.Top of Form

Bottom of FormThe forces in the members can be calculated in several ways. The traditional by hand methods are themethod of jointsand themethod of sections. For truss analysis via computer, thefinite element methodis the standard technique.

Element type selection LINK 180

DEFINING REAL CONSTANTS Preprocessor > Real Constants > Add /Edit/Delete > Add > ok > Area= .1

MESHING ( 1 divisions / line )Preprocessor > meshing > mesh tool > global size > NDIV = 1

OUTPUT defining element table General postproc > element table > define table > add SMISC ,1 > apply > LS,1 >ok > close

a> Loads on each member SMISC , 1b> Stresses on each member LS,1

LISTING RESULTS General postproc > list results > element table date > select SMISC 1 and LS1 > ok

Assignment questions

Cross section is .01m^2Ex=2e11 n/mm^2Prxy=.33

Cross section is .01m^2Ex=2e11 n/mm^2 Prxy=.33Analyzing bicycle frame

Module 3 Analyzing Plane stress , symmetricity

Plane stress analysis

The normal stresses (x'andy') and theshear stress(x'y') vary smoothly with respect to therotationangle, in accordance with thecoordinate transformationequations. There exist acoupleof particular angles where the stresses take on special values.First, there exists an anglepwhere the shear stressx'y'becomes zero. That angle is found by settingx'y'to zero in the above shear transformation equation and solving for(set equal top). The result is,

The anglepdefines theprincipal directionswhere the only stresses are normal stresses. These stresses are calledprincipal stressesand are found from the original stresses (expressed in thex,y,zdirections) via,

The transformation to the principal directions can be illustrated as:

Maximum Shear Stress Direction

Another important angle,s, is where the maximum shear stress occurs. This is found by finding the maximum of the shear stress transformation equation, and solving for. The result is,

The maximum shear stress is equal to one-half the difference between the two principal stresses,

The transformation to the maximum shear stress direction can be illustrated as:

ELEMENT TYPE : PLANE 182 , 183

Plane 182 shape

Plane 183 shape

Element behavior k3 to plane stress with thickness

Case study1Analyze the geometry given below first without hole and then with hole , plot von-mises stress and conclude .

Defining real constants Preprocessor>real constants > add/edit/delete > add > thickness=.001

Creating areas Modeling > create > areas > rectangle > by dimensions >

MESHING Meshing> mesh tool > turn smart sizing to 5 > mesh > select area Note = you can select either tri shape or quad shape for mesh

Applying loads and boundary conditions Loads > apply > structural > displacement > on lines > select leftmost line > restrict all DOFLoads > apply > structural > pressure > on lines > select rightmost line > Load pressure value=-1

Output Generalpostproc > plot results > contour plot > stress > von mises

Creating rectangular geometry with hole

First create rectangle of 300,100 After creating rectangle goto modeling > create > circle >solid circle > assign following values

Boolean operation Booleans > operate > subtract > areas > select rectangle > apply > select circle > ok

Perform the remaining steps of meshing , loads , solution and postprocessing COMPARISON OF CONTOUR PLOTS WITHOUT HOLE WITH HOLE

How to create vector plots of stress ?Plot results > vector plot > predefined > stress > principal s

COMPARISON OF CONTOUR PLOTS

COMPARISON OF vector PLOTS

Conclusion of analysis STRESS CONCENTRATION FACTOR (SCF)Failures such as fatigue brittle cracking and plastic deformation frequently occur at points of stress concentration. It is for this reason that stress concentration factors play an important role in design. The value of SCFs depend on the shape and dimensions of the component being designed and can be calculated using finite element methods. Stress concentrations arise from any abrupt change in the geometry of a specimen under loading. As a result, the stress distribution is not uniform throughout the cross-section.

Stress concentration factor k in this example may be defined as:

(1)0

where x is maximum stress appears around stress concentration point and 0 is nominal applied stress. For linear-elastic material behaviour SCF has constant value for any nominal loading. Its value is varying only with the changing of radius of roundness.

Using reflective symmetry in ansys Consider a rectangular plate with a hole that is symmetrically loaded and has geometrical symmetricity about line AB . Here we dont need to model whole geometry instead we can model half of geometry about AB and apply symmetric boundary condition about line AB .

Applying symmetric boundary condition

Model half geometry as shown above

First create the half geometry as shown above .Goto loads > apply > structural > symmetric B.C > on lines > select line ABApply > structural > pressure > on lines > select rightmost line > -2000

Remaining steps are same as given in above examples Assignment questions MODULUS OF ELASTICITY = 2E5 N/MM^2POISONS RATIO=.33The bracket is loaded uniformily over 150mm line with load of 2625 N/mm

The bracket is loaded with a point load of 2000N at center point P

axisymmetry

Axisymmetric elements are 2-D elements that can be used to model axisymmetric geometries with axisymmetric loads These convert a 3-D problem to a 2-D problem Smaller models Faster execution Easier postprocessing We only model the cross section, and ANSYS accounts for the fact that it is really a 3-D, axisymmetric structure (no need to change coord. Systems)

Modeling To model this We just need this: Modeling To model this We need this

Note: Axisymmetry is always about Y-axis

To model this

We need this

Note: Axisymmetry is always about Y-axis

The pressure vessel shown below is made of cast iron (E = 2e5 N/mm^2, = 0.33) and contains an internal pressure of P = 35 N/mm^2 . You need to apply symmetric B.Cs to solve this problem . You may create model or model and apply symmetric boundary conditions .

Note: Axisymmetry is always about Y-axis Radial stress is SXAxial Stress is Sy Hoops stress is SZ

Analytical results Ansys results

Radial stress (SX) = 35 N/mm^2Axial stress(SY)= 45 N/mm^2Hoops Stress(SZ)= 125 N/mm^2Deflection = .0458 mm

Thin Cylinders Subjected to Internal Pressure:When a thin walled cylinder is subjected to internal pressure, three mutually perpendicular principal stresses will be set up in the cylinder materials, namely Circumferential or hoop stress The radial stress Longitudinal stressnow let us define these stresses and determine the expressions for themHoop or circumferential stress:This is the stress which is set up in resisting the bursting effect of the applied pressure and can be most conveniently treated by considering the equilibrium of the cylinder.

In the figure we have shown a one half of the cylinder. This cylinder is subjected to an internal pressure p.i.e. p = internal pressured = inside diameter L = Length of the cylindert = thickness of the wallTotal force on one half of the cylinder owing to the internal pressure 'p'= p x Projected Area= p x d x L=p .d. L-------(1)The total resisting force owing to hoop stressesHset up in the cylinder walls=2 .H.L.t---------(2)BecauseH.L.t. is the force in the one wall of the half cylinder.the equations (1) & (2) we get2 .H. L . t=p . d . L H=(p . d) / 2tCircumferentialor hoop Stress(H)=(p .d)/ 2t

Longitudinal Stress:Consider now again the same figure and the vessel could be considered to have closed ends and contains a fluid under a gage pressure p.Then the walls of the cylinder will have a longitudinal stress as well as a ciccumferential stress.

Total force on the end of the cylinder owing to internal pressure= pressure x area= p xd2/4Area of metal resisting this force =d.t. (approximately)becaused is the circumference and this is multiplied by the wall thickness

Module 3 analysis of tri-axial stress system

Analyzing 3d geometries

3D ElementsElement type : solid 185

Element type : solid 186

Modeling block Modeling > create > volumes Block > by dimensions Give values for x1,y1,z1 and x2,y2,z2

Modeling solid cylinders Modeling > create > volumesCylinder > solid cylinder

WP X ,WP Y are center point of base

Modeling hollow cylinders / annulus Modeling > create > volumesHollow Cylinder > by dimensions

Offsetting workplanes

Utility menu > workplane > offset workplane by increments

We are required to place WP at (5,5,10) location from (0,0,0)Specify increment value along x,y,z directions

rotating workplane

1> Set angle to 90 degrees by scrolling bar to right

2> Rotate clockwise or anticlockwise by using these icons

3> Create solid cylinder

Performing Boolean operations Modeling > operate Booleans > subtract > select bigger volume > ok >select smaller volume > ok

Similarly you can perform add operation Modeling > operate > Booleans > add > volumes > pick all

Modeling assignments

Importing files in ansys Utility menu > file > import > iges

Goto browse > select file

Import cutter.igs file and bracket.igs file from B1 workshop input files for practice

ASSIGNMENT QUESTIONS 3-D BracketDescriptionApply loads to the 3-D bracket model below and solve using the Sparse iterative solver. The model has already been meshed with SOLID95 20-noded bricks, and Youngs Modulus has been set to 30e6 psi

The meshed model is already provided

Connecting RodDescription Apply loads to the connecting rod (half-symmetry) model below and solve using the SPARSE solver. The model has already been meshed with SOLID95 20-noded bricks, and Youngs Modulus has been set to 30e6 psi.

Meshed model is already provided

Module 4 Dynamic analysis

Dynamic analysis Why dynamic analysis ? Static analysis doesnt take into account variation of load w.r.t time . Output in the form of stress , displacement etc w.r.t time could be predicted by dynamic analysis In static analysis velocity and acceleration are always zero . Dynamic analysis can predict these variables w.r.t time/frequency . To determine natural frequency of components . It is the basic design property and is useful for avoiding resonance , reducing noise .

STATIC ANALYSIS DYNAMIC ANALYSIS

Force is static ( dead wt )Force varies w.r.t. time /frequency

Displacement is static Displacement is function of time/frequency

No velocity and acceleration due to constant or fixed displacement F=KX

Velocity and acceleration develops due to variation of displacement Damping force , inertia force due to velocity & acceleration

Dx/dt=0

D2x/dt2=0

Hence x and x terms are zero and equation reduces to F=Kx

Solution time is less Solution time is high

Output- stress , displacement Output stress , displacement, velocity , acceleration w.r.t. time /frequency

MODAL ANALYSISThe purpose of conducting modal analysis is to determine natural frequency and corresponding mode shapes .

0

FUNDAMENTAL FREQUENCY Fundamental frequency is the first natural frequency of component .

NATURAL FREQUENCY Natural frequency is the frequency with which an object once disturbed will vibrate on its own without any external excitation.

Circular frequency

Where k is constant M is mass Cyclic frequency

After solving k/m we get as EI / ALl4

Engineering application of modal analysis 1> To avoid resonance When natural frequency of component becomes equal to frequency of external excitation , it results in amplitude build up , this phenomenon is known as resonance and causes failure .

2> Physical significance of mode shape Suppose natural frequency we got is 30 Hz and mode shape is in y direction . If an external excitation is applied at 30Hz along y direction then resonance will occur but if external excitation of 30 Hz is applied along x direction then no resonance will occur .

How to avoid resonance ? To avoid resonance either external excitation frequency should be changed or natural frequency of component . Generally we do not have any control on external excitation frequency and hence practical approach is to alter natural frequency.

Natural frequency depends on mass (inversely proportional) and stiffness (directly proportional ) . In practice natural frequency is altered by changing stiffness rather than mass.

How to change stiffness?

1> Changing the support ( boundary conditions )

Additional support of shaft by one or more bearing increases stiffness and results in higher natural frequency .2> Add ribs/stiffners , change thickness , use stiffer material etcWhen changing the boundary conditions is not possible , other alternatives like adding ribs , increasing thickness or to use stiffer materials ( higher E).

Steps involved :-

Preprocessor > material properties > material models > specify density

Solution > analysis type > new analysis > modal

Solution > analysis options Mode extraction method BLOCK LANCOZNo. of modes to extract 10No. of modes to expand - 10

When asked for frequency range leave blank as we dont know about upper and lower limits START FREQUENCY=0END FREQUENCY=0

Several mode extraction methods are available in ANSYS: Block Lanczos (default) Subspace PowerDynamics Reduced Unsymmetric Damped (full) QR Damped Which method you choose depends primarily on the model size (relative to your computer resources) and the particular application.

CASE STUDY 1

EX=2e5MpaPRXY=.33Density=7830e-9 100mm

300mm

Determine the first 10 natural frequencies of rectangular plate with 30mm thickness . There are 3 cases 1> Only left end fixed2> Both end fixed 3> Take E=5e5 Mpa

S.No CASE 1 CASE 2 CASE 3

1

2

3

4

5

6

7

8

9

10

Conclusion :

CASE STUDY 2

Extract the first ten modes of the u-bracket model using the Block Lanczos method. List the frequencies and plot the von Mises stress for all the modes. Next, plot the mode shape for the first mode and then animate it.Material Properties: EX = 30,023,280 psi PRXY = 0.29 DENS = 7.346344e-3Boundary Conditions: Fix topmost area (area 17)

Material Selected Structural SteelYoungs Modulus(E) 2.0e+005MpaPoissons Ratio 0.3Density 7.85e-006Kg/mm^3Tensile Ultimate Strength 460 MpaTensile Yield Strength 250 MpaCompressive Yield Strength 250 Mp

Determine first 10 natural frequencies of above given components .

Module 5thermal analysis

Thermal analysis Heat transfer is defined as energy in transit . Analysis of a system using the laws of heat transfer is named as Thermal Analysis . Thermal analysis is investigation of the part or system to calculate heat transfer rate and temperature distribution .

Element types available in ansys

1-d 2-d 3-d

Link 31Plane 55Brick 8 node 278

Link 33Plane 7720 node 279

All thermal elements have 1 dof/node i.e. temperature .

Thermal loads Convection Heat flux Temperature Heat flow Heat generation

Output Temperature distribution Thermal flux Thermal gradient

Types of heat transfer

1> Pure ConductionThe transfer of heat is from a high temperature to lower temperature . In solids heat transfer is due to lattice vibration ( translational and rotational ) Fouriers law governs conduction heat transfer

The temperature gradient been assigned with negative sign as temperature gradient vector is in opposite direction of heat flow . The direction of heat transfer will be opposite to temperature gradient , since net energy is transferred from high temperature to low temperature .

Heat fluxHeat flux is defined as the amount of heat transferred per unit area per unit time from or to a surface.

Temperature gradient Atemperature gradientis aphysical quantity that describes in which direction and at what rate thetemperature changes the most rapidly around a particular location

Pure conduction case Determine the temperature distribution and vector plots of heat flux and thermal gradient for the following fig. Thermal conductivity k=10 W/m K

T=200oc

T=10o0c

T=1000c 20m

10m t=100oc

Selecting element type:Preprocessor > element type > plane 77

Defining material propertiesPreprocessor > material properties > material models > thermal > conductivity > isotropic ; KXX=10

Defining loads Loads > define loads > apply > thermal temperature > on lines ; select 3 lines and apply temperature of 373 (100+273)k and top line with 473 (200+273)

Postprocessing ( plotting temperature plot , thermal flux and thermal gradient )General postproc > plot results > contour plot > nodal solution > dof solution > nodal temperature

Vector plot > predefined > flux and gradient > Thermal flux

Vector plot > predefined > flux and gradient > Thermal gradient

Postprocessing ( path operations )1. Defining a path General postproc > path operations > define path > By nodes Click 2 nodes and choose a path name

Map onto path > dof solution > temperature

Plot path items > on graph > temp

2> Convection Convection heat transfer is due to molecular movement of fluid such as air or water , when the fluid is caused to move away from source of heat , carrying energy with it .

Many industrial thermal problems are convective in nature . Basic governing equation is for convection is Newtons law of cooling

mixed conduction/convection)Mixed convection/conduction/insulated boundary condition example is constrained as shown below . Determine the temperature distribution and vector plots of heat flux and thermal gradient .

Applying convection Loads > define loads > apply thermal > convection > on lines/areas > Film coefficient=10Bulk temperature=100

Problem 3Temperature distribution in a fin cooled electronic component .This analysis involves heat generation , conduction and convection Physical prolemAll electronic items generate heat during the course of their operation . To ensure optimal working of component , the generated heat needs tobe removed and thus the electronic component be cooled . This is done by attaching fins to the device which aid in rapid heat removal .Problem definition For the sake of simplicity we assume tht electronic circuit is made of copper with thermal conductivity of 386 W/mK . Also it generates heat at the rate of 10e6 W. The enclosing container is made of steel with thermal conductivity of 20 W/m K . The fins are made of thermal aluminium with thermal conductivity 180 W/m K . There is convection along all boundaries except the bottom which is insulated . the film coefficient is 50W/m2 k and Bulk temperature is 200C .

Glue operationIt attaches 2 or more entities creating common boundary between them

Without fin with fins

CONCLUSION The vector plot of geometry with fins shows that heat is dissipates through fins and serves as a channel for heat dissipation with increased surface area .

transient thermal analysis

Transient thermal analysis determines temperatures and other thermal quantities that vary over time. Engineers commonly use temperatures that a transient thermal analysis calculates as input to structural analyses for thermal stress evaluations. Many heat transfer applications-heat treatment problems, nozzles, engine blocks, piping systems, pressure vessels, etc.-involve transient thermal analyses.A transient thermal analysis follows basically the same procedures as a steady-state thermal analysis. The main difference is that most applied loads in a transient analysis are functions of time. To specify time-dependent loads, you first divide the load-versus-time curve into load steps.

O/P DESIRED : 1> TEMP VS TIME GRAPH 2> ANIMATION OF TEMP DISTRIBUTION OVER TIME

STEPS involved :DEFINING element typePreprocessor > element type > add/edit > thermal mass > solid > 20 node 279

The element is defined by 20 nodes with a temperature degree of freedom at each node. DEFINING MATERIAL PROPERTIES Preprocessor > material properties > material models > thermal conductivity =10 ; density = 7830 ;specific heat = 2.01

Solution New analysis > transient > full

Solution > solution controls ; make following settings Time at end of load step=5000No. of sub steps=100Automatic time stepping is OFFIn frequency write every Nth substep

In non-linear tab set line search to ON

Defining thermal loads and initial conditions

Solution > define loads > settings > reference temperature > 300

Solution > define loads > apply > thermal > temperature > on areas > select left most area > 500

Solution > define loads > apply > thermal > convection >on areas > select all area except leftmost Film coefficient=10Bulk temperature = 305

Solution > solve > current LS

PostprocessingGeneral postproc > results summary

Here we have got collection of 100 result sets as we have assigned no. of substeps to be 100 , the S/W has performed this by breaking load step into 100 substeps . Result summary shows all the results at different time intervals Read results > by pick > select any of result set > read

Plot results > contour plot > nodal solution > dof solution > nodal temperature

Plotting temperature vs time graph Goto timehistory postproc > add > select any node > graph data

Temp vs time plot

Module 6Structural non analysis

Non linear analysis

A nonlinear analysis is needed if the loading on a structure causes significant changes in stiffness. Typical reasons for stiffness to change significantly are: Material non linearity Strains beyond the elastic limit (plasticity) Geometric non linearity Large deflections, such as with a loaded fishing rod

Contact non linearity Contact between two bodies

When a load causes significant changes in stiffness, the load-deflection curve becomes nonlinear. The challenge is to calculate the nonlinear displacement response using a linear set of equations.

One approach is to apply the load gradually by dividing it into a series of increments and adjusting the stiffness matrix at the end of each increment. The problem with this approach is that errors accumulate with each load increment, causing the final results to be out of equilibrium.

ANSYS uses the Newton-Raphson algorithm: Applies the load gradually, in increments. Also performs equilibrium iterations at each load increment to drive the incremental solution to equilibrium. Solves the equation [KT]{Du} = {F} - {Fnr} [KT]= tangent stiffness matrix{u}= displacement increment{F} = external load vector{Fnr} = internal force vector Iterations continue until {F} - {Fnr} (difference between external and internalloads) is within a tolerance.Some nonlinear analyses have trouble converging. Advanced analysis techniques are available in such cases

This process is repeated for each load increment until the full external load has been applied. One or more load steps to apply the external loads and boundary conditions. (This is true of linear analyses too.) Multiple substeps to apply the load gradually. Each substep represents one load increment. (A linear analysis needs just one substep per load step.) Equilibrium iterations to obtain equilibrium (or convergence) at each substep. (Does not apply to linear analyses.)

Time and Time Step

Each load step and substep is associated with a value of time.Time in most nonlinear static analyses is simply used as a counter and does not mean actual, chronological time

By default, time = 1.0 at the end of load step 1, 2.0 at the end of load step 2, and so on. For rate-independent analyses, you can set it to any desired value for convenience. For example, by setting time equal to the load magnitude, you can easily plot the load-deflection curve.

The "time increment" between each substep is the time step Dt. Time step Dt determines the load increment DF over a substep. The higher the value of Dt, the larger the DF, so Dt has a direct effect on the accuracy of the solution. ANSYS has an automatic time stepping algorithm that predicts and controls the time step size for all substeps in a load step.

Solved Example In this example, we will investigate the behavior of a cantilever beam under largerdeflection. When the model undergoes larger deflection, the basic analysis that is oftenused in ANSYS is no longer sufficient. The load has to be broken down in to small steps(load steps) and the stiffness matrix is then updated each tim using the the result from theprevious load step. Theoretical details on geometric nonlinearity can be found in the classhandout, hence, we will only focus on how to perform such analysis using ANSYS here.The model to be analyzed in this example is illustrated in Figure 1.

Material properties Geometric propertiesLoading

E = 1 x 106 psi

L=100inB=2inH=2.5P=400lb

Loading , meshing , modeling steps will be same as in case of linear analysis

Goto solution > solution controls

Analysis options : large displacement staticAutomatic time stepping :ONNumber of substeps : 100Maximum number of substeps:1000Min. number of substeps :1

Goto nonlinear tab > line search on

ANSYS File StructureSeveral files are created during a typical ANSYS analysis. Some of thesefiles are in ASCII format while the others are binary. Brief descriptions ofcommon file types are given below.

2.5.1 Database FileDuring a typical ANSYS analysis, input and output data reside in memoryuntil they are saved in a Database File, which is saved in the WorkingDirectory. The syntax for the name of the Database File isjobname,db. Thisbinary file includes the element type, material properties, geometry (solidmodel), mesh (nodal coordinates and element connectivity), and the resultsif a solution is obtained. Once the Database File is saved, the user canresume from this file at any time. There are three distinct ways to save andresume the Database File: Use the Utility Menu. Click on SAVE JOB or RESUMJDB button on the ANSYS Toolbar. Issue the command SAVE or RESUME in the Input Field.

2.5.2 Log FileThe Log File is an ASCII file, which is created (or resumed) immediatelyupon entering ANSYS. Every action taken by the user is stored sequentiallyin this file in command format (ANSYS Parametric Design Language(APDL)). The syntax for the name of the Log File, which is also saved inthe Working Directory, isjobname.log. If jobname.log already exists in theWorking Directory, ANSYS appends the newly executed actions instead ofoverwriting the file. The Log File can be utilized to: Understand how an analysis was performed by another user. Learn the command equivalents of the actions taken within ANSYS.

2.5.3 Error FileSimilar to the Log File, the Error File is an ASCII file, which is created (orresumed) immediately upon entering ANSYS. This file captures all warningand error messages issued by ANSYS during a session. It is saved in theWorking Directory with the following syntax for the name: jobname.err. Ifjobname.err already exists in the Working Directory, ANSYS appends thenewly issued warning and error messages instead of overwriting the file.This file is particularly important when ANSYS issues several warning anderror messages too quickly during an interactive session. The user can thenconsult the Error File to discover the exact cause(s) of each of the warningsor errors.

2.5.4 Results FilesThe results of an ANSYS analysis are stored in a separate Results File. Thisfile is a binary file and, depending upon the Analysis Type, the file'sFUNDAMENTALS OF ANSYS 29extension takes a different form. The following syntax applies to the ResultsFile name for the selected Analysis Type:Structural analysis: jobname.rstThermal analysis: jobname.rthFluids analysis: jobname,rfl

Module 7 Ansys workbench

ANSYS workbench developed by ANSYS Inc. USA is a computer aidedFinite Element Modeling and Finite Element Analysis tool . In the GUI of ANSYS workbench user can generate 3D and FEA models perform analysis and generate results of analysis .You can perform variety of tasks ranging from Design Assessment to Finite Element Analysis too complete product optimization Analysis by using ANSYS workbench .

STARTING ANSYS WORKBENCH To start ANSYS workbench choose Start > Programs /All programs > ANSYS 14.0> Workbench

The workbench window helps streamline an entire project to be carried out in ANSYS workbench . In this wwindow one can create , manage and view the workflow of the entire project created by using standard analysis systems

The workbench window mainly consists of Menu Bar , Standard tool bar , tool box window , project schematic window and status bar .

Toolbox window This is located on left in workbench window . The toolbox window lists standard and customized templates or the individual analysis components that can be used to create projects . To create a project drag a particular analysis or component systems from toolbox indow and drop it into the project schematic window .

Analysis system toolboxThis is displayed expanded in the toolbox window by default . It contains pre-defined templates for different types of analysis that can be carried out in ANSYS workbench . Each predefined component consists of all the components that are used to perform a particular type of analysis .

Different types of analysis systems are discussed below .Design assessment : This analysis system is used to perform a combined solution for static and transient structural analysis . It also performs post-processing through a script using additional data associated with geometry

Electric: This analysis system is used to analyze steady state electric conduction

Explicit Dynamics This analysis system is used to identify the dynamic response of a component under stress wave propogation , or time-dependent loads or impacts .

Fluid flow (CFX) This system allows users to carry out flow analysis of compressible and incompressible fluids .It is also used to analyze heat transfer in fluids Fluid flow (FLUENT) Like CFX FLUENT is also used to carry out fluid flow analysis of compressible and incompressible fluids and their heat transfer analysis .

Harmonic Response Harmonic response is the response of a system under a sustained cyclic load . This is used to analyze a system working under periodic or sinusoidal loads . This analysis helps in determining whether a particular structure will be withstanding resonance , fatigue , and other effects of forced civration .

IC engine This analysis systems helps to determine the performance of the whole system of an IC engine . It takes into consideration the various fluid properties , moving components , and electric and electronic components inside an engine .

Linear Buckling This analysis systems is used to evaluate the buckling strength of a system under external loads .

Magnetostatics This analysis system is used to analyze the magnetic field developed due to the presence of a temporary or permanent magnet .

Modal This analysis system is used to study the dynamic properties of model , subjected to vibration , determines frequency and mode shapes .

Random vibration This analysis system is used to determine reaction of a structure or a component to changing frequencies of vibrations . Many components experience vibrations which are random in nature . This analysis systems is used to determine the response of structure that are exposed to such random vibrations

Random vibration This analysis system is similar to random vibration analysis system and is used after transient analysis is done .

Rigid dynamics This analysis system is used to determine the response of a rigid bodies or mechanisms consisting of rigid bodies . Response of a robot mechanism is an example of rigid dynamics .

Static structural This analysis system is used to determine the response of a structure subjected to static loading conditions . The loads in this case are assumed to produce no or negligible time based loading characteristics . Using this type of analysis displacement , stresses and deformation of structures under static loading conditions can be determined .

Steady state thermalThis analysis system is used to determine temperature , thermal gradient , heat flow rates and heat fluxes under the influence of thermal loading which remains constant with time and are static in nature .

Thermal electric This analysis system is used to simulate thermal and electric fields .

Transient structural This analysis system is used to determine response of structures under the action of time dependent variable . Using this analysis , time-varying displacement , stresses and strains can be determined .

Transient thermalThis analysis system is used to determine the temperature and other thermal variables of a structure that vary over time .

Component system toolboxThis toolbox is displayed in the collapsed state in the toolbox window . To expand component system toolbox , click on (+) sign located on the left of the component systems title bar . The components displayed in the component system are basic blocks of a project and form only a part of analysis system such as geometry , mesh etc .

Custom system toolboxBy default custom system toolbox is also displayed in collapsed state in toolbox. To expand this node (+) sign displayed on left of custom system title bar . the system is used to carry out standard coupled analysis in which the input and output data of one analysis are used as input for the next analysis . For example pre-stressed modal system is used to carry static tructural analysis followed by a modal analysis . Similarly FSI:Fluid flow (CFX) -> static structural custom system is used to carry out a fluid flow analysis in CFX followed by a static structural analysis.

Design exploration toolboxBy default design exploration toolbox is displayed in collapsed manner in the toolbox window . Expand this toolbox by following the procedure discussed earlier . The options in the design exploration toolbox are used to explore a component , so that the design of component can be further optimized by changing the design variables based on performance of the product .

Project schematic windowThe project schematic window helps manage an entire project . It displays the workflow of entire analysis project . To add an analysis system into the project schematic window , drag the analysis system from the toolbox window and drop it into the green-colored box displayed in the project schematic window .Alternatively double-click on an analysis systems in toolbox indo to include it in the project schematic window .

Each time you drag and drop an analysis system or an item into project schematic window a system is formed . Each system consists of cells which are used to carry out various tasks within a system . You can add more than one systems in project schematic window and can even share data available in cells from one system to other system .

Menu bar Menu bar is located on top of the workbench window and contains various options such as file , view , tools and so on . This option enable you to control and manage the files of the current project .

Standard tool bar The standard toolbar is collection of the frequently used tools in ANSYS workbench . The various tools available in the standard toolbar are New , open , save , save as , import , reconnect , refresh project , update project .

Contact analysis

While working on assemblies, the first question would be whether or not the contact stresses are important. If not, then we can just bond the surfaces together and can have coarse mesh and be done with it. But if contact stresses are important and more over surfaces are opening and closing then we need to look more into other types (NL) of contacts and finer meshing techniques. The following types are available in ANSYSMechanical

1. Bonded

2. No Separation

3. Rough

4. Frictionless

5. Frictional

1. Bonded:Both surfaces are bonded like glue. They are not allowed to separate. Not allowed to Slide. Surfaces will be together irrespective of gap, penetration, loading and behavior of other parts/ contacts. We always have some tolerance in our designs. For example you may have five thousands of gap between two parts. But if you do not want to move those parts with respect to each other, you can use bonded contact. It DOES NOT matter how much is the