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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