Convergence and Accuracy
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Transcript of Convergence and Accuracy
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Rationale & Definition
Discrete FEA model more rigid than actualgeometric continuum. With successive meshrefinement, FEA model stiffness begins toapproach actual stiffness.
Convergencerefers to the process ofsuccessively refining a mesh in order toproduce optimal FEA results.
Least ambiguous indicator of accuracy is acomparison between results after one ormore convergence runs.
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Understanding Convergence
Area under curve analogy
As number of nodes increases, so doesflexibility of structure
Increased flexibility means largerdeformations, strains, and even stresses
Stress rises as mesh density increases, up to
a practical limit
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Convergence Assessment
Convergence bestdescribed aspercent change in
result of interest(e.g., Von MisesStress) betweenconvergence runs
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Error Estimation
FEA error estimation refers to the relativedifferences between results across anelement edge or at a node
Node
Element
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Convergence Dependencies
Convergence results, as well as the successof a convergence run, depend upon: Result converged on
Fundamental quantities (e.g., displacement,temperature) are well-behaved, easy to converge on
Derived quantities (e.g., stress, heat flux) arenonlinear responders, may not converge smoothly
Element quality
Loading Extreme case: no load any mesh will do
Scoping
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Singularities
Singularities arise from:
Unrealistic boundaryconditions (e.g., point/edge
loads and constraints) Geometric discontinuities
Singularities causeconvergence problems
Stress = Force/Area As element area get smaller,
fictitious (divide by zero)stresses arise
Divergence
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Overcoming Singularities
Only use results some distance from singularity
St. Venants Principle stress and deflection far fromthe applied load can be represented by a staticallyequivalent loading scenario
Leave fillets and other model discontinuity smoothersunsuppressed
Converge on geometry result some distance awayfrom singularity - Scoping
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St. Venants Principle
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Suppress Features
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Scoping
In general, scope in Design Simulation refers togeometry to which an environment object (e.g., loador support) is applied
Design Simulation also allows a result object (e.g.,Von Mises stress) to be scoped to a specific region(part, surface, edge, vertex)
Result scoping impacts convergence. Mesh
refinement does not occur outside the scope for agiven convergence control
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Convergence and
Accuracy
GE393
Computer-Aided Design, Analysis andPrototyping