fea presentation
TRANSCRIPT
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
Optical Sciences CenterThe University of Arizona
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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.”
Optical Sciences CenterThe University of Arizona
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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
Optical Sciences CenterThe University of Arizona
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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
Optical Sciences CenterThe University of Arizona
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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
Optical Sciences CenterThe University of Arizona
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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
SolidWorks Simulation Problems, Pitfalls and Tips
Optical Sciences CenterThe University of Arizona
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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
SolidWorks Simulation Problems, Pitfalls and Tips
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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
SolidWorks Simulation Problems, Pitfalls and Tips
Optical Sciences CenterThe University of Arizona
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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
SolidWorks Simulation Problems, Pitfalls and Tips
Optical Sciences CenterThe University of Arizona
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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.
SolidWorks Simulation Problems, Pitfalls and Tips
Optical Sciences CenterThe University of Arizona
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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
Optical Sciences CenterThe University of Arizona
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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?
Optical Sciences CenterThe University of Arizona
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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.
Optical Sciences CenterThe University of Arizona
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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
Optical Sciences CenterThe University of Arizona
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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
Optical Sciences CenterThe University of Arizona
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