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The Residual Convergence Criterion

The object of the nonlinear iterative procedure is to restore equilibrium by the elimination of the residual or "out of balance" forces. The residual convergence criterion is a measure of these residual forces and is computed from (Fext - Fint)/Fext, expressed as a percentage. Fext and Fint are the externally applied loads and corresponding internally developed forces respectively. This criterion is output to the nonlinear log file as rdnrm.

Although the current value of the convergence criterion should decrease during the iterative procedure, the decrease is not necessarily monotonic. The following curve is typical of residual norm behaviour, i.e. oscillating but converging:

Convergence_Typical.gif (5030 bytes)

For increments that do not converge, the manner in which rdnrm behaves can provide valuable indicators to the source of the problem. For all convergence problems the convergence checklist should be consulted primarily, but the following list is separated into the most frequent convergence behaviour types and their corresponding potential remedies.

All Convergence Behaviour:
  • Reduce the load increment
  • Check for "pivot" warnings. If present see the pivot checklist
  • For elements that are simulating "stiff" members, reduce their stiffness (round-off problems)
  • Reduce slideline stiffness coefficients ("normal" chatter)
  • Reduce friction coefficient ("tangential" chatter)
  • Improve the aspect ratios of poorly shaped elements
  • Use consistent units throughout the analysis
  • Point loads and supports can promote severe local plasticity. Either distribute the load/support effect over a number of nodes or define elastic properties in the area to eliminate the material failure
  • An element mechanism may have been excited. The remedy is to invoke fine integration
Slow Convergence Behaviour:

Convergence_Slow.gif (4239 bytes)

  • Decrease the threshold for the line search technique to be automatically invoked and increase the maximum number of line searches to 5
  • Ensure that Newton-Raphson iterations are being performed rather than modified Newton-Raphson
  • Increase the number of iterations per increment. Slideline analyses, particularly, can require a significant number of iterations in the first few iterations of an analysis
Oscillating Convergence Behaviour:

Convergence_Oscillating.gif (4483 bytes)

  • Split up any slidelines that traverse sharp angles (e.g. greater than 45-90 degrees)
  • Invoke the slideline extension facility, particularly for irregular slideline surfaces
  • Refine the mesh in the area of slideline definitions. Coarse meshes can produce single point contact and promote instability
  • Has merging/equivalencing been performed fully? There may be a crack in the mesh
  • Check the support conditions will prevent rigid body motion
  • If a geometrically nonlinear analysis is being carried out, try invoking "guide arc-length by current stiffness parameter"
  • Mesh refinement may be helpful for more coarse definitions
Fixed Convergence Behaviour:

Convergence_Fixed.gif (4428 bytes)

  • If the concrete material model is being used, slacken the residual norm
  • Massive plastic strain development with a highly constrained structure can cause locking
  • Large plastic strains with 3-noded triangular elements can cause locking. The remedy is generally to use the corresponding 6/8-noded elements with fine integration
  • Check the material properties if there is more plastic strain developed than expected
  • If the concrete material model is being used, slacken the convergence tolerance to 5
Divergent Convergence Behaviour:

Convergence_Divergent.gif (4287 bytes)

  • Is geometric nonlinearity required? Large deformations/rotations may be causing non-physical stiffening
  • Are the convergence criteria too slack? Tighten the convergence criteria - particularly for geometric nonlinearity


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