stages of fea in cad environment
TRANSCRIPT
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Ken Youssefi Mechanical Engineering Dept 1
History of Finite Element Analysis Finite Element Analysis (FEA) was first developed in 1943 by R. Courant, who utilized the Ritz method of numerical analysis and minimization of variational calculus.
A paper published in 1956 by M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp established a broader definition of numerical analysis. The paper centered on the "stiffness and deflection of complex structures".
By the early 70's, FEA was limited to expensive mainframe computers generally owned by the aeronautics, automotive, defense, and nuclear industries. Since the rapid decline in the cost of computers and the phenomenal increase in computing power, FEA has been developed to an incredible precision.
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Ken Youssefi Mechanical Engineering Dept 2
Basics of Finite Element Analysis Why FEM ?• Modern mechanical design involves
complicated shapes, sometimes made of different materials.
• Engineers need to use FEM to evaluate their designs.
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Ken Youssefi Mechanical Engineering Dept 3
Basics of Finite Element Analysis
FEA Applications • Evaluate the stress or temperature
distribution in a mechanical component.• Perform deflection analysis.• Analyze the kinematics or dynamic response.• Perform vibration analysis.
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Ken Youssefi Mechanical Engineering Dept 4
Finite element analysis starts with an approximation of the region of interest into a number of meshes (triangular elements). Each mesh is connected to associated nodes (black dots) and thus becomes a finite element.
Basics of Finite Element Analysis
Consider a cantilever beam shown.
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Basics of Finite Element Analysis• After approximating the object by finite elements, each
node is associated with the unknowns to be solved.• For the cantilever beam the displacements in x and y
would be the unknowns.• This implies that every node has two degrees of freedom
and the solution process has to solve 2n degrees of freedom.
• Once the displacements have been computed, the strains are derived by partial derivatives of the displacement function and then the stresses are computed from the strains.
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Formulation of the Finite Element Method • The classical finite element analysis code (h version)
The system equations for solid and structural mechanics problems are derived using the principle of virtual displacement and work (Bathe, 1982).
• The method of weighted residuals (Galerkin Method)weighted residuals are used as one method of finite
element formulation starting from the governing differential equation.
• Potential Energy and Equilibrium; The Rayleigh-Ritz Method.
Involves the construction of assumed displacement field. Uses the total potential energy for an elastic body
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Finite Element Analysis
• Pre-Processing• Solving Matrix (solver)• Post-Processing
FEA requires three steps
FEA is a mathematical representation of a physical system and the solution of that mathematical representation
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FEA Pre-ProcessingMesh
Mesh is your way of communicating geometry to the solver, the accuracy of the solution is primarily dependent on the quality of the mesh.
The better the mesh looks, the more accurate the solution is.
A good-looking mesh should have well-shaped elements, and the transition between densities should be smooth and gradual without skinny, distorted elements.
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FEA Pre-Processing - meshingThe mesh transition from .05 to .5 element size without control of transition (a) creates irregular mesh around the hole which will yield disappointing results.
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FEA Pre-ProcessingFinite elements supported by most finite-element codes:
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FEA Pre-Processing – ElementsBeam Elements
Beam elements typically fall into two categories; able to transmit moments or not able to transmit moments.
Rod (bar or truss) elements cannot carry moments.
Entire length of a modeled component can be captured with a single element. This member can transmit axial loads only and can be defined simply by a material and cross sectional area.
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FEA Pre-Processing – ElementsThe most general line element is a beam.
(a) and (b) are higher order line elements.
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FEA Pre-Processing – ElementsPlate and Shell Modeling
Plate and shell are used interchangeably and refer to surface-like elements used to represent thin-walled structures.
A quadrilateral mesh is usually more accurate than a mesh of similar density based on triangles. Triangles are acceptable in regions of gradual transitions.
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FEA Pre-Processing – ElementsSolid Element Modeling
Tetrahedral (tet) mesh is the only generally accepted means to fill a volume, used as auto-mesh by many FEA codes. 10-node Quadratic
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CAD Modeling for FEA
• CAD models prepared by the design group for eventual FEA.
• CAD models prepared without consideration of FEA needs.
• CAD models unsuitable for use in analysis due to the amount of rework required.
• Analytical geometry developed by or for analyst for sole purpose of FEA.
CAD and FEA activities should be coordinated at the early stages of the design process to minimize the duplication of effort.
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CAD Modeling for FEA
• Solid chunky parts (thick-walled, low aspect ratio)parts mesh cleanly directly off CAD models.
• Clean geometrygeometrical features must not prevent the mesh
from being created. The model should not include buriedfeatures.
• Parent-child relationshipsparametric modeling allows defining features off
other CAD features.
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CAD Modeling for FEAShort edges and Sliver surfacesShort edges and sliver surfaces usually accompany each other and on large faces can cause highly distorted elements or a failed mesh.
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CAD Modeling for FEA – Sliver Surfaces
The rounded rib on the inside of the piston has a thickness of .30 and a radius of .145, as a result a flat surface of .01 by 2.5 is created. A mesh size of .05 is required to avoid distorted elements. This results in a 290,000 nodes. If the radius is increased to .15, a mesh size of .12 is sufficient which results in 33,500 nodes.
Flat surface
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CAD Modeling for FEA
Fillet across shallow angle
Sliver surface caused by a slightly undersized fillet
Sliver surface caused by misaligned features.
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Guidelines for Geometry Planning
• Delay inclusion of fillets and chamfers as long as possible.
• Try to use permanent datums as references where possible to minimize dependencies.
• Avoid using fillet or draft edges as references for other features (parent-child relationship)
• Never bury a feature in your model. Delete or redefine unwanted or incorrect features.
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Guidelines for Part Simplification
• Outside corner breaks or rounds.• Small inside fillets far from areas of interest.• Screw threads or spline features unless they are
specifically being studied.• Small holes outside the load path.• Decorative or identification features.• Large sections of geometry that are essentially
decoupled from the behavior of interested section.
In general, features listed below could be considered for suppression. But, consider the impact before suppression.
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Guidelines for Part SimplificationFillet added to the rib
Holes removed
Fillet removed
Ribs needed for casting removed
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CAD Modeling for FEAModel Conversion
• Try to use the same CAD system for all components in design.
• When the above is not possible, translate geometry through kernel based tools such as ACIS or Parasolids. Using standards based (IGES, DXF, or VDA) translations may lead to problem.
• Visually inspect the quality of imported geometry.
• Avoid modification of the imported geometry in a second CAD system.
• Use the original geometry for analysis. If not possible, use a translation directly from the original model.
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Example of a solid model corrupted by IGES transfer
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FEA Pre-ProcessingMaterial Properties
The only material properties that are generally required by an isotropic, linear static FEA are: Young’s modulus (E), Poisson’s ratio (v), and shear modulus (G).
G = E / 2(1+v)
Provide only two of the three properties.
Thermal expansion and simulation analysis require coefficient of thermal expansion, conductivity and specific heat values.
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FEA Pre-ProcessingNonlinear Material Properties
A multi-linear model requires the input of stress-strain data pairs to essentially communicate the stress-strain curve from testing to the FE model
Highly deformable, low stiffness, incompressible materials, such as rubber and other synthetic elastomers require distortional and volumetric constants or a more complete set of tensile, compressive, and shear force versus stretch curve.
A creep analysis requires time and temperature dependent creep properties. Plastic parts are extremely sensitive to this phenomenon
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FEA Pre-Processing
• Their properties hold constant throughout the assigned entity.
• Average values are used (variation could be up to 15%).
• Localized changes due to heat or other processing effects are not accounted for.
• Any impurities present in the parent material are neglected.
Comments
If possible, obtain material property values specific to the application under analysis.
If you are selecting the property set from the code’s library, be aware of the assumptions made with this selection.
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FEA Pre-ProcessingBoundary Conditions
In FEA, the name of the game is “boundary condition”, that is calculating the load and figuring out constraints that each component experiences in its working environment.
“Garbage in, garbage out”
The results of FEA should include a complete discussion of the boundary conditions.
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Boundary Conditions
LoadsLoads are used to represent inputs to the system. They can be in the forms of forces, moments, pressures, temperature, or accelerations.
ConstraintsConstraints are used as reactions to the applied loads. Constraints can resist translational or rotational deformation induced by applied loads.
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Boundary Conditions
Linear Static AnalysisBoundary conditions are assumed constant from application to final deformation of system and all loads are applied gradually to their full magnitude.
Dynamic AnalysisThe boundary conditions vary with time.
Non-linear AnalysisThe orientation and distribution of the boundary conditions vary as displacement of the structure is calculated.
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Boundary ConditionsDegrees of Freedom
Spatial DOFs refer to the three translational and three rotational modes of displacement that are possible for any part in 3D space. A constraint scheme must remove all six DOFs for the analysis to run.
Elemental DOFs refer to the ability of each element to transmit or react to a load. The boundary condition cannot load or constrain a DOF that is not supported by the element to which it is applied.
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Boundary ConditionsConstraints and their geometric equivalent in classic beam calculation.
Fixed support
Pin support
Roller support
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Boundary Conditions
A solid face should always have at least three points in contact with the rest of the structure. A solid element should never be constrained by less than three points and only translational DOFs must be fixed.
Accuracy
The choice of boundary conditions has a direct impact on the overall accuracy of the model.
Over-constrained model – an overly stiff model due to poorly applied constraints.
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Boundary Conditions -ExampleExcessive Constraints
Model of the chair seat with patches representing the tops of the legs.
Patch 3
Patch 1
Patch 2
Patch 4
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Patch 3
Patch 1
Patch 2
Patch 4
Boundary Conditions -ExampleIt may appear to be acceptable to constrain each circular patch in vertical translation while leaving the rotational DOFs unconstraint. This causes the seat to behave as if the leg-to-seat interfaces were completely fixed. A more realistic constraint scheme would be to pin the center point of each circular patch (translational), allowing the patch to rotate. Each point should be fixed vertically, and horizontal constraints should be selectively applied so that in-plane spatial rotation and rigid body translation is removed without causing excessive constraints.
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Boundary Conditions -Example• Constraining the center point of patch 1 in all 3
translational DOFs.
• Constraining x and y translations of the center point of patch 2.
• Constraining z and y translation of the center point of patch 3.
• Constraining just the y translation of the center point of patch 4.
This scheme allows in-plane translation induced by bending of the seat without rigid body translation or rotation.
Patch 3
Patch 1
Patch 2
Patch 4
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Summary of Pre-Processing
• Build the geometry• Make the finite-element mesh• Add boundary conditions; loads and
constraints• Provide properties of material• Specify analysis type (static or dynamic,
linear or non-linear, plane stress, etc.)
These activities are called finite element modeling.
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Solving the Model - SolverOnce the mesh is complete, and the properties and boundary conditions have been applied, it is time to solve the model. In most cases, this will be the point where you can take a deep breath, push a button and relax while the computer does the work for a change.
Multiple Load and Constraint Cases
In most cases submitting a run with multiple load cases will be faster than running sequential, complete solutions for each load case.
Final Model Check
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Unexpectedly high or low displacements (by order of magnitude) could be caused by an improper definition of load and/or elemental properties.
Post-Processing, Displacement Magnitude
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Post-Processing, Displacement AnimationAnimation of the model displacements serves as the best means of visualizing the response of the model to its boundary conditions.
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Post-Processing, FEA of a connecting rod
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Second Mode (Twisting)
The magnitude of the stresses should not be entirely unexpected.
First Mode (Bending)
Post-Processing, Stress Results
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Deformation of a duct under thermal load
Post-Processing, thermal analysis
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Post-ProcessingView AnimatedDisplacements
Does the shape of deformations make sense?
View DisplacementFringe Plot
Yes
Review BoundaryConditions
No
Are magnitudes in line with your expectations?
View Stress Fringe Plot
Yes
Is the quality and mag. Of stresses acceptable?
Review Load Magnitudesand Units
No
Review Mesh Density and Quality of Elements
No
View Results SpecificTo the Analysis
Yes
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FEA - Flow Chart