fea presentation

Optical Sciences CenterThe University of Arizona

110/19/10 FEA Presentation

FEA PresentationIntroduction to Finite Element Analysis

includingCommon Pitfalls/Problems, Tips and Examples

Robert StoneResearch Professor

College of Optical Sciences


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FEA Pitfalls Tony Rizzo (Bell Labs) quotes:

– “Some engineers and managers look upon commercially available FEA programs as automated tools for design. In fact, nothing could be further from reality than that simplistic view of today's powerful programs. The engineer who plunges ahead, thinking that a few clicks of the left mouse button will solve all his problems, is certain to encounter some very nasty surprises.”

– “With the exception of a very few trivial cases, all finite element solutions are wrong, and they are likely to be more wrong than you think. One experienced analysis estimates that 80% of all finite element solutions are gravely wrong, because the engineers doing the analyses make serious modeling mistakes.”

– “Finite element analysis is a very powerful tool with which to design products of superior quality. Like all tools, it can be used properly, or it can be misused. The keys to using this tool successfully are to understand the nature of the calculations that the computer is doing and to pay attention to the physics.”


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• Finite element method – numerical procedure for solving a continuum mechanics problem with acceptable accuracy.

• Subdivide a large problem into small elements connected by nodes.

Flexure Solid Model

FEA Theory

Flexure FEA Model• 123399 DOF• 25795 TRETA4 Elements• 41303 Nodes


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Nodes – Properties and Characteristics• Infinitesimally small• Defined with reference to a global coordinate system• Typically nodes are defined on the surface and in the interior

of the component you are modeling• Form a grid work within component as a result of the mesh• Typically defined the corners of elements• Where we define loads and boundary conditions• Location of our results (deformation, stress, etc.)• Nodes are the byproduct of defining elements

Nodes“What are they”

A node is simply a coordinate location in space where a DOF (degree of freedom) is defined.


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Elements – Properties and Characteristics• Point, 2D and 3D elements• Define a line (1D), area (2D) or volume (3D) on or within our

model• Dimensions define an “Aspect Ratio”• A set of elements is know as the “mesh”• Mesh shape and density is critical to the analysis• Typically have many options that may be preset for the user• Elements are typically what we define

Elements“What are they”

An element is a mathematical relation that defines how a DOF of a node relates to the next.


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FEA Method• Subdivide the structure into simple elements

– More elements = more nodes = more DOF = improved accuracy– As DOF increases the solution typically converges to a solution.– Most element formulations are overly stiff – flexibility increases as

the DOF increases• As you increase the mesh density the deformations increase

– Deformations converge rapidly (typically a course model will yield good deformation results)

– Stresses converge slowly - in most cases, a fine mesh model is required to capture accurate stresses


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FEA Method• Linear Static (small displacement, linear

materials)• Nonlinear (large displacement, nonlinear

material properties)• Linear or nonlinear dynamics

– Frequency analysis– Random vibration analysis

• Buckling• Thermal and heat transfer• Fluid mechanics• Electromagnetics• Optimization


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FEA Method• In general odd geometries are easily

handled• An accurate FEA models may have

little or no resemblance to the CAD model

• Simple models have many advantages

– Easy to develop and easy to change– Fast solution time– Easy to optimize or perform “What If”

studies• Complex models are time

consuming to develop– Require precise modeling and care– Difficult to change– May require long run times

• Engineer / Analyst determines the complexity


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FEA Limitations• Accurately modeling of

load and boundary conditions is very difficult

• Complex joints are difficult

• Any form of member pre-tensioning requires a work around

• Symmetric problem with a mesh that lacks symmetry will produce asymmetric results


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Modeling Steps

Model Geometry• Define points, curves,

surfaces, volumes and coordinate systems

Model geometry requires thought and planning•Create and define coordinate systems . Optical system post processing requires the “Z” axis to be the optical axis•Decide which aspects of the geometry are important to the analysis•Good FEA models may lack the detail of CAD models•FEA programs apply load and BCs at nodes (fixtures and external loads in Solidworks simulation)•Single node loads / constraints rarely represent reality•Start with a sketch and refer to it often

SolidWorks Simulation Problems, Pitfalls and Tips


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Modeling Steps

Solid Mesh• TETRA4 and TETRA10 (4 &10

node tetrahedron solid elements)

Shell Mesh• SHELL3 and SHELL6 (3 & 6 node

thin shell elements)

Requires planning and element / DOF knowledge•The element defines the number of active DOFs.

TETRA4 & TETRA10 Elements•3 translational DOF per node•1 DOF per node for thermal•TETRA4 (linear) TETRA10 (parabolic)•Supports adaptive “P” method

SHELL3 & SHELL6 Elements•6 DOF per node (3 translational + 3 rotational )•1 DOF per node for thermal•Membrane and bending capabilities•Uniform thickness element•SHELL3 (linear) SHELL6 (parabolic)•Supports adaptive “P” method



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Modeling Steps

Beam Mesh• BEAM3D (2 node uniaxial

element)

Truss Mesh• TRUSS3D (2 node uniaxial

element)

Requires planning and element / DOF knowledge•The element defines the number of active DOFs.

BEAM3D Element•6 DOF per node (3 translational + 3 rotational )•1 DOF per node for thermal•Displayed as hollow tube regardless of cross section

TRUSS3D Element•3 translational DOF per node •1 DOF per node for thermal•Single element per truss member•Axial loads only (no moments)•Displayed as hollow tube regardless of cross section



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Modeling Steps

Define Real Constants• BEAM3D has 27 real

constants to be defined

Requires thought and planning. Real constants define:oCross sectional areas, perimeteroMoment of inertia, torsional constant, shear factor, width, depthoGeometry constants, NA offsetsoEnd release codes for beamsoTemperature differences along axis

•Make a list and refer to your sketch•Real constants must be defined and active prior to meshing



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Modeling Steps

Define Model Materials• Pick material from library• Define material properties

Requires thought and planning. Common material properties are:oElastic modulus, Poisson’s Ratio, Shear ModulusoDensity (i.e. mass density)oThermal conductivity, coefficient of thermal expansion, specific heat

•Units, Units, Units (understand the units)•Make a materials list and refer to it•Pick a material from the library and check the units for understanding•Materials must be defined and active prior to meshing•May define dummy materials



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Modeling Steps

Meshing Parameters and Options• Mesh Parameters• Mesh Options• Mesh Properties Manager• Mesh Control Parameters• Mesh Quality ChecksIn General• Activate element group, real

constants and material properties• Define number of elements along

curves or define mesh density• Merge and compress nodes

Mesh density must be suitable for the analysis type and required accuracy •Before meshing, activate appropriate material properties and real constants•Define average element size or element density•Stress gradients require a very fine mesh•Displacement contours should be smooth•Verify accuracy by performing a convergence study

Rules of Thumb•4 elements minimum through the thickness (plane of interest)•Keep element aspect ratio less than 4 –preferably 2-3•Considering that the sides of a linear element remain straight – are there enough elements to accurately display the deformed shape•Mirrors, windows, lens, etc. require a symmetric mesh.



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Modeling Steps

Define “Connections” & “Fixtures”(Boundary Conditions)

• Define constraints on nodes, curves, surfaces or regions

• Define coupling and DOF sets

SolidWorks Simulation Problems, Pitfalls and TipsPlan ahead and use care when applying constraints•Is the model fully constrained – avoid over constraining the model•Single node constraints rarely represent reality but may be acceptable•Think carefully about the physics of the real constraints. Does it resist displacement and rotation•When in doubt – release constraints are rerun the model – apply soft springs if necessary•Always request reaction forces•Loads or constraints – can you use loads instead of constraints to better simulate the physics of the problem.


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Modeling Steps

Define Loads • Loads / pressure on nodes, curves

or surfaces• Define gravity loads• Temperature / heat on nodes,

curves or surfaces

COSMOSM Problems, Pitfalls and TipsPlan ahead and use care when applying loads•Applying loads at a single node rarely represent reality – but may be acceptable•Always request reaction forces – do the reaction forces match the applied load•Is the gravity direction correct•Use multiple load cases to better understand the performance and accuracy


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Modeling Steps• Define Analysis Options

– Renumber, data check, reaction, static options, output options, etc.

• Run Analysis• Check, Check and Recheck

– Deformation – does it look correct– Did symmetric loads and BCs

produce symmetric results– Reaction forces – do they match

the applied loads– Is there separation / gaps in

elements– Always assume your analysis is

wrong until proven otherwise– Always perform a “back of the

envelope sanity check”– Be prepared to justify your model

accuracy to other engineers


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Modeling Tips

• Tip #1 Understand the physics of the problem and always start with a sketch. Before you model have a plan and know:– What you are going to model and what results do you need?– How you are going to develop your model?– How you are going to support the model and apply loads?

• Tip #2 Start simple and increase complexity as required.– When modeling systems – start with a single optical element.

• Tip #3 Build simple test models for understanding.– Check for load and boundary condition accuracy

• Above depends on the type of analysis you are running– Check for mesh accuracy – do convergence studies

• Tip #4 Always request reaction forces in the output.– For models with both structural and gravity loads, turn off gravity

and check your reaction forces. Do they match the applied load?– Turn on gravity. Is the increase in reaction force consistent with

the gravity load? Is the direction correct?


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Modeling Tips

• Tip #5 Understand your constraints and use care not to over constrain the model.

– Are all six (6) rigid body translations and rotations accounted for?– A model with too few constraints causes a singular stiffness matrix.– An over constrained model creates alternate load paths.– When in doubt, release constraints and add soft springs.

• Tip #6 Study the deformed shape. Does it look correct?– Properly modeled, symmetric loads and constraints will produce symmetric

results.– Always generate a symmetric mesh for optical surfaces. Automatic mesh

generators rarely produce a symmetric mesh.• Tip #7 As a starting point, there must be enough elements to

accurately predict the deformed shape.– Use a minimum of 4 elements through the height or thickness or sections

subjected to bending.– Do simple convergence studies to determine an acceptable mesh density.

• Tip #8 An accurate stress analysis requires more elements than an accurate displacement analysis.

– Increase the mesh density for accurate stress analysis.– Check nodal stress in surrounding elements sharing a common node.


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Modeling Tips

• Tip #9 Check, check and recheck your model and results.– Do hand calculations and back of the envelope calculations to verify results.– Assume the results are wrong until proven correct.

• Tip #10 When in trouble – get help.– Consult a senior analyst for help and tips


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FEA Model


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FEA Model• COSMOS FEA Model Details• High fidelity model• Element Types

– 8 node solids, 3 node beams– 4 node shells , 2 node springs

• Elements = 20427• Nodes = 26105• DOF = 81035• Materials – ULE, Invar, steel• Gravity simulates +/- 8.5° from 35°

zenith• “Z” axis is the optical axis with origin

at the vertex of M2


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FEA Model

COSMOS FEA Model Details• Constraint equations simulate whiffle

tree rocker motion• Springs simulate flexures• Flexure Stiffness = 165000 lbs/in• Equivalent thickness for pretensioned

spider arms• Stiff massless beams and springs

simulate torsional stiffness of pretensioned spider for frequency analysis

• Massless beams support vertex node for each mirror

• FEA Weight = 1234 lbs


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FEA ModelSpider Torsional FrequencySpider Vane Stiffness

Vertex NodeRocker Arm Coordinate SystemConstraint Equations


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Frequency ResponseFundamental Frequency

32.5 Hz2nd Frequency

33.3 Hz


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Frequency Response3rd Frequency

43.8 Hz4th Frequency

44.0 Hz


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Frequency Response5th Frequency

44.3 Hz


2911/06/09 FEA Presentation

FEA Thermal Model• COSMOS FEA Model Details• Element Types

– 3D truss elements replace the 2 node spring elements

• Eliminated massless beams and springs from M4 spider

• Materials – ULE, Invar, steel, stainless steel

• Varied CTE of steel knuckles, then calculated an equivalent length of steel in M4 truss tubes

• Thermal simulates ΔT = 20°C (36°F)


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M4/M5 Athermalization

• Compensates for negative CTE of Invar truss

• Model simulates 6.5” of steel from midplane of strongback

Invar Truss Tubes

Steel Knuckle


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FEA Thermal Distortions• Uniform distortion in “Z”

direction• Zero rotation about “X” axis and

“Y” axis

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