Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Course inFEM – ANSYS Classic

Introduction

Introduction 2Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Introduction

• Presentation– Anders Schmidt Kristensen– M.Sc. in Mechanical Eng. from Aalborg

University in 1993– Ph.D. in Mechanical Eng. from Aalborg

University in 1997– Consultant for PTC Denmark 1997-1998 –

implementation of Pro/ENGINEER– 1998 to pt. Associate Prof. at Aalborg

University Esbjerg

Introduction 3Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Introduction

• The course is conducted the following way:– 20-40 minutes lecture followed by 40-60

minutes exercise (including a break)– Questions are allowed at any time

Introduction 4Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

References• [ANSYS] ANSYS 10.0 Documentation (installed with ANSYS):

– Basic Analysis Procedures– Advanced Analysis Techniques– Modeling and Meshing Guide– Structural Analysis Guide– Thermal Analysis Guide– APDL Programmer’s Guide– ANSYS Tutorials

• [Cook] Cook, R. D.; Concepts and applications of finite element analysis, John Wiley & Sons

• [Burnett] Burnett, D. S.; Finite element analysis: From concepts to application, Addison-Wesley

• [Kildegaard] Kildegaard, A.; Elasticitetsteori, Aalborg Universitet

Introduction 5Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

FEM - ANSYS Classic• Lecture 1 - Introduction:

– Introduction to FEM– ANSYS Basics– Analysis phases– Geometric modeling– The first model: Beam model

• Lecture 2 - Preprocessor:– Geometric modeling– Specification of Element type, Real Constants, Material, Mesh– Frame systems– Truss systems– Element tables

• Lecture 3 - Loads:– Boundary conditions/constraints/supports– Loads– Mesh attributes, meshing– Sections

• Lecture 4 – 2D plane models :– 2D Plane Solid systems– Geometric modeling– Postprocessing

• Lecture 5 – Analysis types:– Analysis types– Modal analysis– Buckling analysis

Introduction 6Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

FEM - ANSYS Workbench/CAD• Lecture 6 – 3D Solids:

– 3D solid models– Booleans– Meshing issues

• Lecture 7 – 3D Modeling:– Operate– Import CAD– Advanced topics

• Lecture 8 – Analysis types:– Analysis types– Postprocessing– TimeHistProc

• Lecture 9 – Workbench basics:– Workbench basics– Geometric modeling

• Lecture 10 – Workbench analysis:– Workbench analysis types

Introduction 7Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Overview• CAD - Computer Aided Design

– AutoCAD, Bentley MicroStation, CadKey• CAD - Solid Modeling

– Pro/ENGINEER, Inventor, IDEAS, CATIA, UGS, Solid Works• FEM/FEA - Finite Element Method/Analysis

– ANSYS, ABAQUS, Algor, Altair, MscNastran, Cosmos• CAE - Computer Aided Engineering

– Workbench, Design Space, Pro/Mechanica, CosmosWorks, Inventor/ANSYS

• BEM - Boundary Element Method• Mesh-less systems• CFD - Computational Fluid Dynamics

– ANSYS/Fluent, ANSYS/Flotran, ANSYS/CFX, CF-Design, Altair• Multi-scale systems• Optimization – sizing, shape and topology

Introduction 8Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Introduction to Finite Element Analysis

• What is Finite Element Analysis?• Advantages• Disadvantages• How to avoid pitfalls• History• FEM - Resources• Examples

Introduction 9Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

•• The FEM is a computerThe FEM is a computer--aided aided mathematical technique for obtaining mathematical technique for obtaining approximate numerical solutions to the approximate numerical solutions to the abstract equations of calculus that predict abstract equations of calculus that predict the response of physical systems the response of physical systems subjected to external influencessubjected to external influences – [Burnett]

Introduction 10Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

Real modelContinuum

Analysis modelDiscrete

Each point have aninfinite number ofdeformation statevariables, i.e. degre-es of freedom (dof)

Each point have afinitefinite number ofdeformation statevariables (u,v), i.e. degrees of freedom

Transformation

Introduction 11Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

• Divide a continuum with infinitely degrees of freedom in to finite elements with a given number of degrees of freedom

• An element is geometrical defined by a number of nodes in which the elements are connected. The directions a node can move in is termed degrees of freedom (dof)

Introduction 12Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

• Following conditions must alwaysalways be satisfied– Equilibrium conditions– Compatibility conditions– Constitutive conditions– Boundary conditions

Introduction 13Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

• Most FEA systems are displacement based, i.e. an approximate displacement field is established

• Using a deformation based method yield one unique kinematic determined system to be determined

u(x,y) = a1 + a2 x + a3 y

Introduction 14Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

• The deformation method yield the FEM characteristic system of equations:

• This system of equations is solved for {D} by, e.g. Gaussian elimination

• Note on matrix algebra is found here

[K]{D} = {R}

Stiffness matrixStiffness matrix

Unknown displacement vector

Load vector

Introduction 15Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

• Formulation techniques to determine the stiffness matrix [K]– Direct method– Variational methods, i.e. principle of stationary

potential energy– Weighted Residual methods, e.g. the Galerkin

formulation

Introduction 16Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

• The unknown displacements (can be any field variable, e.g. temperature) {D} = {u1, v1, u2, v2 …}T in the element nodes (nodal values) are determined from

[K]{D} = {R}u3

u2u1

v1v2

v3

x

yIn 2D: (u,v)In 3D: (u,v,w)

Stiffness matrixStiffness matrix

Unknown displacement vector

Load vector

Displacement field variables:

ndof = 6

Introduction 17Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?

• It is assumed that displacements within an element can be interpolated from known nodal values

u1

xix1 x2

u2ui=?

u1

xix1 x2

u2uiu ≈ N1 u1 + N2 u2

N1 = (1 – x/L)N2 = x/L Linear case

Introduction 18Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is Finite Element Analysis?The element stiffness matrix for a beam element with 2 nodes and2 dof at each node [Cook], see also note:

[K]{D} = {R} → {D} = [K] -1{R}

Known stiffness matrixndof x ndof

Unknown displacement vectorndof x 1

Known load vectorndof x 1

Found by the Direct Method

ndof = 4

Introduction 19Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Advantages

• Irregular Boundaries• General Loads• Different Materials• Boundary Conditions• Variable Element Size• Easy Modification• Dynamics• Nonlinear Problems (Geometric and/or Material)

Introduction 20Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Disadvantages

• An approximate solution• An element dependent solution

– Shape quality of elements affect the solution, e.g. poorly shaped elements (irregular shapes) reduce accuracy of the FE solution

– Element density affect the solution, i.e. the element size should be adjusted to capture gradients

• Example: plate with a circular hole

• Errors in input data

NB: Always document assumptions!NB: Always document assumptions!

Introduction 21Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Disadvantages

[Cook]

Introduction 22Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Disadvantages

[Cook]

Introduction 23Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

How to avoid pitfalls

• Carry out:– Hand calculations (Navier, Airy,

Timoshenko…)– Norm based calculations (Euro-Code, EN,

API…)– Experiments (strain-gauge, accelerometer…)– Evaluate the kinematic behaviour

(deformations)

Introduction 24Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

History• A. Hrennikoff [1941] - Lattice of 1D bars• McHenry [1943] - Model 3D solids• R. Courant [1943] - Variational form• Levy [1947, 1953] - Flexibility & Stiffness • M. J. Turner [1953] - FEM computations on a wing• Boeing [1950's] Engineer's at Boeing apply FEM to delta

wings• Argryis and Kelsey [1954] - Energy Prin. for Matrix

Methods• Turner, Clough, Martin and Topp [1956] - 2D elements• R. W. Clough [1960] – Coins the term “Finite Elements”

Introduction 25Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

History

• 1963 - Mathematical validity of method established - applied to non-structural problems

• 1960's - First general purpose FEA code developed

• 1970's - Non-linear solvers developed• 1980's - Graphical pre-/postprocessors are

developed• 1990's - FEM tools integrated in CAD software

Introduction 26Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

FEM - Resources• ALGOR• ANSYS• COSMOS/M• STARDYNE/FEMAP• MSC/NASTRAN• SAP90/2000• ADINA• NISA• GT Strudl• ABAQUS• Plaxis

• Matlab based:– CalFem– FemLab

• CAE products:– Pro/ENGINEER

• Pro/FEA• Pro/MECHANICA

– Cosmos/Works– Inventor/ANSYS– IDEAS

• Resources

Introduction 27Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Introduction to ANSYS

• What is ANSYS• Facilities in ANSYS• Interfacing with ANSYS• Common terms

Introduction 28Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

What is ANSYS• ANSYS finite element analysis software enables

engineers to perform the following tasks: – Build computer models or transfer CAD models of

structures, products, components, or systems.– Apply operating loads or other design performance

conditions.– Study physical responses, such as stress levels,

temperature distributions, or electromagnetic fields.– Optimize a design early in the development process to

reduce production costs.– Do prototype testing in environments where it otherwise

would be undesirable or impossible (for example, biomedical applications).

Introduction 29Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Facilities in ANSYS• Structural Linear• Structural Nonlinear• Structural Contact/Common Boundaries• Structural Dynamic• Structural Buckling• Thermal Analysis• CFD Analysis• Electromagnetic - Low Frequency• Electromagnetics - High Frequency• Field and Coupled-Field Analysis

Introduction 30Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Facilities in ANSYS

• Solvers– Iterative– Sparse– Frontal– Explicit

• Preprocessing• Postprocessing• General Features

Introduction 31Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Facilities in ANSYS

..ANSYS Commands referenceANSYS Element reference..Basic Analysis ProceduresAdvanced Analysis Techniques..Structural Analysis Guide..ANSYS Tutorials

Introduction 32Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Facilities in ANSYS

• You can access the following file operations from the session editor dialog:

– OK: Enters the series of operations displayed in the window below. You will use this option to input the command string after you have modified it.

– Save: Saves the command string displayed in the window below to a separate file. ANSYS names the file Jobnam000.cmds, with each subsequent save operation incrementing the filename by one digit. You can use the /INPUT command to reenter the saved file.

– Cancel: Dismisses this window and returns to your analysis.

– Help: Displays the command reference for the UNDO command.

During an analysis, you may want to modify or deletecommands entered since your last SAVE or RESUME.

The Session Editor is available in interactive (GUI) mode only.

Introduction 33Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Facilities in ANSYS

Introduction 34Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Interfacing with ANSYS

• Matlab, Excel• CAD – Pro/ENGINEER• IGES• Log-file editing• Application Programming Interface (API)

Introduction 35Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Interfacing with ANSYS

Introduction 36Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Common termsProcessor Function GUI Path Command

PREP7 Build the model (geometry, materials, etc.) Main Menu> Preprocessor /PREP7

SOLUTION Apply loads and obtain the finite element solution Main Menu> Solution /SOLU

POST1 Review results over the entire model at specific time points Main Menu> General Postproc /POST1

POST26 Review results at specific points in the model as a function of time Main Menu> TimeHist Postpro /POST26

OPT Improve an initial design Main Menu> Design Opt /OPT

PDS Quantify the effect of scatter and uncertainties associated with input variables of a finite element analysis on the results of the analysis

Main Menu> Prob Design /PDS

Utility Menu> File> List> Binary Files

AUX2 Dump binary files in readable form

Utility Menu> List> Files> Binary Files

/AUX2

AUX12 Calculate radiation view factors and generate a radiation matrix for a thermal analysis

Main Menu> Radiation Matrix /AUX12

AUX15 Translate files from a CAD or FEA program Utility Menu> File> Import /AUX15

RUNSTAT Predict CPU time, wavefront requirements, etc. for an analysis Main Menu> Run-Time Stats /RUNST

Introduction 37Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Basics• Launching of ANSYS• Graphical User Interface (GUI)• Menus, dialogs and toolbars• Working area• Preferences• Files used by ANSYS• ANSYS Menus• ANSYS File menu• ANSYS PlotCtrls menu• Units• Undo• Hints

Introduction 38Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Analysis phases

• Build the model.• Apply loads and

obtain the solution.• Review the results.

PREPROCESSOR

SOLUTION

POSTPROCESSOR

Introduction 39Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Analysis phasesElement Type – select appropiate element type to modelthe structural response/behaviour most accurately.

Material Props – material properties, e.g. modulus ofelasticity E and Poisson’s ratio n

Real Constants – properties depending on the elementtype, e.g. cross-sectional properties, area, area momentof inertia

Sections – cross-section definition

Modeling – define the geometry of the structure - “it is essential to make some modeling considerations inthis phase”

Meshing – divide the geometry of the structure intoelements – “take care of element distribution/density”

Introduction 40Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Analysis phasesAnalysis Type – specify the character of the problem

Define Loads – apply loads to the element model

Solve – run the solution process, e.g. for linear staticsystems solve (Gaussian elimination) for the unknowndisplacements:

[K]{D} = {R} → {D} = [K] -1{R}

Known globalstiffness matrix

ndof x ndof

Known load vectorndof x 1

Unknown displacement vectorndof x 1

The global stiffness matrix [K]:ndof = total number of nodes x number degrees of freedom per node

Introduction 41Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Geometric modelingCreate – geometrical entities

Operate – perform Boolean operations

Move / Modify – move or modify geometrical entities

Copy – copy geometrical entities

Delete – geometrical entities

Update Geom – update the geometry in relationto for example buckling analysis

Introduction 42Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Modeling - Create

• The hierarchy of modeling entities is as listed below:– Elements (and Element Loads)– Nodes (and Nodal Loads)– Volumes (and Solid-Model Body Loads)– Areas (and Solid-Model Surface Loads)– Lines (and Solid-Model Line Loads)– Keypoints (and Solid-Model Point Loads)

Introduction 43Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

Examples - content

• Example0100’s: Link and/or beam models• Example0200’s: Plane 2D models• Example0300’s: Solid 3D models• Example0400’s: Vibration/dynamic models• Example0600’s: Thermal models

Introduction 44Computational Mechanics, AAU, EsbjergFEM – ANSYS Classic

The first model