Convergence and Accuracy

1
Convergence and Accuracy

• GE393
• Computer-Aided Design, Analysis and Prototyping

2
Rationale Definition

• Discrete FEA model more rigid than actual
  geometric continuum. With successive mesh
  refinement, FEA model stiffness begins to
  approach actual stiffness.
• Convergence refers to the process of successively
  refining a mesh in order to produce optimal FEA
  results.
• Least ambiguous indicator of accuracy is a
  comparison between results after one or more
  convergence runs.

3
Understanding Convergence

• Area under curve analogy
• As number of nodes increases, so does flexibility
  of structure
• Increased flexibility means larger deformations,
  strains, and even stresses
• Stress rises as mesh density increases, up to a
  practical limit

4
Convergence Assessment

• Convergence best described as percent change in
  result of interest (e.g., Von Mises Stress)
  between convergence runs

5
Error Estimation

• FEA error estimation refers to the relative
  differences between results across an element
  edge or at a node

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Convergence Dependencies

• Convergence results, as well as the success of 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) are
  nonlinear 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 boundary conditions (e.g., point/edge
  loads and constraints)
• Geometric discontinuities
• Singularities cause convergence 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 from the applied load can be represented by a
  statically equivalent loading scenario
• Leave fillets and other model discontinuity
  smoothers unsuppressed
• Converge on geometry result some distance away
  from 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 to
  geometry to which an environment object (e.g.,
  load or 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 a
  given convergence control

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Scoping Example
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Convergence and Accuracy

• GE393
• Computer-Aided Design, Analysis and Prototyping