Sensitivity-based shape optimization

The shape optimization method that is based on gradient information is described in this chapter.

Related Topics
About Design variables (DV_SHAPE)

Sensitivity-based shape optimization (SHAPE_SENSITIVITY) makes it possible to define very complex optimization tasks. It has been shown in industrial size examples that the method is very powerful and attractive for problems with many CONSTRAINTs.

The typical problems which can be solved by this algorithm are:

  • Minimize volume with stiffness or displacement constraint
  • Minimize volume with stress constraint
  • Maximize stiffness (linear static) with a volume constraint
  • Minimize displacement for critical nodes (linear static) with a volume constraint
  • Maximize first eigenvalue (modal) with a volume constraint
  • Maximize a certain eigenvalue (using mode tracking)
  • Move eigenvalues away from certain frequency (band gap optimization with modal analysis)
Important:

  1. Current algorithm only supports linear analysis, with the exception of use of contacts. Optimization will not stop when using non-linear analysis (eg. plasticity, large strains, etc.) but only warn the user that sensitivities will be calculated on a wrong basis.
  2. Design nodes must be connected to elements which are supported by SIMULIA Tosca Structure.

    Supported elements by shape sensitivity, see Supported elements attached to shape sensitivity design nodes.

Analysis types

Analysis type Supported
Linear Analysis Yes
Linear modal (no pre-tension) Yes
Frequency response Yes
Non-linear contact only, linear material, linear strains (NLGEOM=NO) Yes
Non-linear material (e.g. *PLASTICITY) No
Non-linear strains (NLGEOM=YES) No

Other boundary conditions

  • Prescribed displacements are also supported.
  • Temperature pre-loading is NOT allowed.
  • Forces, surface forces, gravity forces and contact forces on design nodes are NOT supported as well.