METBD 450 Lecture Notes

Text: Building Better Products with FEA,
by V. Adams & A. Askenazi, (Read pp. 201-202)

Reference:  ANSYS Advanced Analysis Techniques

• Chapter 4: Submodeling

Submodeling:

• performing a detailed analysis on only a portion of the overall geometry
  • break up a single part
  • sometimes assemblies
  • weldments ? - not common practice
• Don't confuse with SUBSTRUCTURING*

"... determine where the behavior local to the area of interest ceases to be affected by remote features or results"

• look for stress levels approaching zero, or
• look for a constant stress distribution
• NOT in a region of high stress gradient

Boundary conditions at the cutting plane of the submodel through the coarse model are critical to the accuracy of this technique.

*Substructuring

• a procedure that condenses a group of finite elements into one element represented as a matrix.
• This single matrix element is called a superelement. 
• You can use a superelement in an analysis just as you would any other ANSYS element type.
• You first create the superelement by performing a substructure generation analysis.

The reasons for substructuring are

• (a) to reduce computer time and
• (b) to allow solution of very large problems with limited computer resources

Submodeling:

... a finite element technique used to get more accurate results in a region of your model.

Often in finite element analysis, the finite element mesh may be too coarse to produce satisfactory results in a region of interest, such as a stress concentration region.

The results away from this region, however, may be adequate.

Submodeling is also known as

• the cut-boundary displacement method or
• the specified boundary displacement method.
• The cut boundary is the boundary of the submodel which represents a cut through the coarse model. Displacements calculated on the cut boundary of the coarse model are specified as boundary conditions for the submodel.

Submodeling is based on St. Venant's principle

"if an actual distribution of forces is replaced by a statically equivalent system, the distribution of stress and strain is altered only near the regions of load application." This implies that stress concentration effects are localized around the concentration; therefore, if the boundaries of the submodel are far enough away from the stress concentration, reasonably accurate results can be calculated in the submodel.

Aside from the obvious benefit of giving you more accurate results in a region of your model, the submodeling technique has other advantages:

• It reduces, or even eliminates, the need for complicated transition regions in solid finite element models.
• It enables you to experiment with different designs for the region of interest (different fillet radii, for example).
• It helps you in demonstrating the adequacy of mesh refinements.

Some restrictions for the use of submodeling are:

• It is valid only for solid elements and shell elements.
• The principle behind submodeling assumes that the cut boundaries are far enough away from the stress concentration region.

Procedure:

• Create and analyze the coarse model.
  • Save the database and results files
• Create the submodel, using a different jobname
  • "Resume From ..." the coarse model database
  • Clear the mesh, cut the original geometry to your submodel
  • Mesh the submodel
  • Write only the cut boundary nodes to a nodes file:
  • Preproc > Create > Nodes > Write Nodes File
  • SAVE the Submodel database
• Enter the General Postprocessor
  • Resume the coarse model database
  • "Read Results" from the coarse model results file
  • Perform cut boundary interpolation (CBDOF).
  • General Postproc > Submodeling > InterpolateDOF ...
• Enter the Solution Processor
  • Resume the submodel database
  • "Read Input From ..." the cut boundary displacements file
  • Apply any OTHER loads that would act on the remaining portion of the original model (e.g., weight, surface pressure, temperature)
  • Solve the submodel.
• Verify that the distance between the cut boundaries and the stress concentration is adequate by Postprocessing:
  • Overlay a stress contour plot of the submodel on the same stress contour plot of the coarse model.  Use the same contour scaling (/CONT), focal point (/FOCUS), and magnification (/DIST) for both plots
  • Compare a Path Plot around the cut boundary edges on both the coarse and submodels.  Use the exact same path for both models, graphed to the same scales to make the comparison plots.

General Postprocessor, Path Operations

• Define a path by picking a series of nodes (or using the working plane)
• Interpolate any results onto the path (Map Onto Path ...)
• Plot Path Item on a graph or on geometry
• List data along the path
• look at the path on the model geometry
• operate on path data (Linearized stress for Code Evaluations)