lecture slides chapter 6

Practical Stress Analysis with Finite Elements (2nd Edition)

Dr. Bryan J Mac Donald

BryanMacDonald/GlasnevinPublishing20072011

Bryan Mac Donald/Glasnevin Publishing 2007-2011

Chapter 6: Modelling & Meshing Pages 191 to 192 of book

ModellingOverview

Q1:Haveyoucheckedyourmodeldimensions?(section6.2.2)

Q2: Isatrussorbeamassumptionvalidforyourmodel?(section6.2.3)

Q3:Isaplanarassumptionvalidforyourmodel?(section6.2.4)

Q4:Isathinshellassumptionvalidforyourmodel?(section6.2.5)

Q5:Isacombinedbeam/shellassumptionvalidforyourmodel?(section6.2.6)

Q5: Doesyourmodelexhibitanysymmetry?Canitbeusedtosimplifythemodel?(section6.2.7)

Q6: Doesyourmodelrequireanydefeaturingtosimplifythemodel?(section6.2.8)

Q7:Doesyourmodelrequirecleaningupbeforeanalysiscantakeplace?(section6.2.9)

Q8:Wouldusingacylindricalorsphericalcoordinatesystemsimplifythemodelormakemodelingeasier?(section6.2.10)

Q9:Wouldtheanalysisbemadeeasierbysplittingitupintoseveralmoresimpleanalyses,orbyusingsubstructuringorsubmodeling?(section6.2.11)



TrussandBeamAssumptions



TrussandBeamAssumptions

3DSolid? PlaneStress/Plane

Strain? Axisymmetric? Beam? Truss?

Mostbeginnersstarthereandworkdown!

Youshouldstarthereandworkup!!!!



PlanarAssumptions



ThinShellAssumptions



CombinedBeam&ShellAssumptions

Neutralaxisoffsetiskey!!!



SimplificationthroughSymmetry



ReflectiveSymmetry2D



ReflectiveSymmetry3D

When the shaded portion isreflected across all three planeswe get the full structure.

Thus, in this case only 1/8 of thefull model is required. (providedthe loading is also symmetric)



AxiSymmetry



CyclicSymmetry



RepetitiveSymmetry



Defeaturing



ModelCleanup



CoordinateSystems



SubModelling&SubStructuring



MeshingOverview

Q1: Are linear or quadratic elements more suitable for your model? (Section 6.3.2)

Q2: Are you aware of areas in your mesh that will require a finer mesh due to stressconcentrations? (Section 6.3.3)

Q3: Are you aware of special considerations for meshing the particular element type you areusing? (for beams, shells and solids see section 6.3.3)

Q4: Have you ensured that there are smooth transitions between element sizes or types?(Section 6.3.4)

Q5: Have you checked your mesh to ensure that there are no excessively distorted elements?(Section 6.3.5)

Q6: Do you know the difference between a good and a bad quality mesh? (Section 6.3.6)

Q7: Have you performed a convergence test on your mesh? (Section 6.3.7)



Linear&QuadraticElements



StressConcentrators



MeshingBeamElements

Essentially you are meshing a line

Splitting the line up into smaller lines (i.e. line elements)

Smaller elements will be required where bending is more prevalent (e.g. the built in endof a cantilever).

Beam elements require convergence!

Cross sectional properties must be assigned: section properties, orientation, neutral axisoffset, etc.

Taper is available in some cases and is usually defined as a cross sectional property

See case study B and case study C.



MeshingShellElements

You must generate a midplane surface if youare using a solid model

Mapped meshing with quads is preferable tofree meshes and/or triangular elements.

Make sure you check the direction of shellnormals particularly if you are usingpressure loads!



MeshingSolidElements Mapped mesh bricks are preferable to tetrahedrons. Where this is not possible it can be overcome by splitting the volume up into a number of

smaller (more regularly shaped) volumes known as volume segmentation:



ChangesinElementSize

We always want a gradual change from large to small

Sudden changes will result in artificial stress concentrations



ChangesinElementType

Watch out for inconsistencies at the interface between different element types!

Loads may not be transferred between different types and artificial mechanisms (such ashinges) or rigid body motion may occur.

Example: 3DShell joins 3DSolid shells can rotate/bend, solids cannot result is a hinge atthe ShellSolid interface!



ElementShape&Distortion



WhatMakesaGoodQualityMesh?



Mappedvs FreeMeshing

Requirements for Mapped Meshing

Areas:Can have 3 or 4 sides no more.You can force this in some cases.

Volumes:6 sides brick shaped5 sides wedge or prism shaped4 sides pyramid shaped

RememberYou can split an area or volume upinto a number of smaller shapes inorder to allow for mapped meshing(volume segmentation)



MeshConvergence

UncertaintyintheFEmodel:Utotal =Ugeom +Umaterial +Uloads/bcs + Umesh



Summary of Chapter 6:

After completing chapter 6, you should:

be able to simplify your model by using a beam assumption, planarassumption, thin shell assumption, or any combination of these, whereappropriate.

be able to recognise and simplify your model using the inherentsymmetry in the problem.

understand the concepts of model defeaturing and cleanup and be ableto appropriately apply these concepts.

understand different coordinate systems and how models can be builtand/or analysed in these systems.

understand the concepts of submodelling and substructuring and beable to appropriately apply them to your FE model.

understand the various factors that contribute to the accuracy of a finiteelement mesh and understand the concept of mesh convergence and beable to carry out a mesh convergence test on your FE model.

lecture slides chapter 6

Documents

modelling meshing pages

finite elements

practical stress analysis

providedthe loading

shaded portion

thefull model