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ruc uraEngineering Software

Application

By

Dr. Muhammad Fahad Assistant Professor

Earthquake Engineering Center

University of Engineering & Technology Peshawar

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Lecture 1:

Overview and marks distribution CE-401L_Fall_2009_CourseOutline.xls .

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Introduction to FEMFinite Element Analysis is a mathematicalmethod based on Energy stored or releasedduring any straining action.FEM is extensively used to modelcomplicated elements which cannot besolved by conventional methods of Mechanics. Distribution of Temperature in Piston Engine. Distribution of displ/stresses in paving slabs Flow of blood in veins & pumping of blood Extensively used in aerospace, earthquake,

Biomedical, Automobile, Simulation of Magnetic

flux in Alternators and counting

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Introduction to FEM

Finite Elements can be visualized assmall pieces of structuresDifference between finite andinfinitesimal used in calculus.In one FE a field quantity is allowed tohave a simple spatial VARIATION , maybe described by a polnomial terms in X 2 ,

xy or Y2.

Actual variation is different thanassumed so FEM is an approximationCould be a good approximation or bad!!!

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Introduction to FEM

Finite elements are connected at pointscalled nodes. Total assembly is calledF.E Structure or body or region.Particular arrangement of elements iscalled MeshNumerically, FE mesh is represented bya system of algebraic equations to besolved for unknowns at nodes.

Solution at node points when combinedwith the assumed field in any givenelement completely determines thespatial variation of the field in that

element

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Introduction to FEMFEA has advantages over other numericalmethod techniques, including versatility andphysical appeal.

Applicable to any field problem, heat transfer, stressanalysis, magnetic fields

No geometric restrictions, body/region can take anyshape. Boundary conditions and loading are not restricted,

e.g. in stress analysis any portion can be supported. Material properties are not restricted to isotropy and

may change from one element to another Components having different behaviors and differentmathematical descriptions can be combined

FE structures resemble actual bodies Approximation is easily improved by grading the

mesh

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Solving a problem using FEM

Learning about the problemPreparing a mathematical modelDiscretizing itHaving a computer for calculations

And the most important Checking theresults.

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Learning about the problem

Analyst/ Engineer must understandthe nature of the problem.Software does not understand thedimensions of the problem (to includelinear or non-linear analysis, buckling.

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Learning about the problem

Mathematical model Deciding what features are important to

model ( just because computer speed is great doesnt mean one should model it ).

May ignore geometric irregularities, consider some loads as point loads, assume somesupports as fixed, material may be idealizedas linear or non-linear.

Depending on these idealizations, the

structure behaves as beam element, shellelement or by equation of plain plasticity.. Usually first model always need refinements.

(in meshing, loading or boundary ocnditions)

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Learning about the problem

Preliminary Analysis One Preliminary analysis should be

obtained to using simple analyticalcalculations, some of this effort mightimprove the model.

Subsequently it will be used to checkcomputer (FE) results.

Doing so, before FEA rather than after can reduce a natural tendency to findanswers that support whatever FEAresults have already been obtained,especially if the efforts involved are large.

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Learning about the problem

Finite Element Analysis Pre processing

Define geometry, material properties, loads andboundary conditions. Mesh of desired density iscreated, and type of formulation is considered.

Numerical AnalysisSoftware generates matrix that describes thebehavior of each element. Solves to determineunknowns Reactions, forces SFD and BMD etc

Post processingThe FEA solutions and quantities derived are listedor graphically displayed. This step is automatedexcept that the designer must tell the software whatlists or displays to prepare. Contours of stress,SFDs or BMDs

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Learning about the problem

Check The RESULTS First Examine the results qualitatively and

ask if they look alright. check for obvious

errors B.C almost always misrepresented: does

the deform shape makes sense? If the FEshows some kind of deformations shouldthere be any ? Or is it a modeling mistake.

And soo many more things to consider!!!

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Questions