General Information

Shape optimization is mostly used at the end of the design process when the general layout of a component is more or less fixed and only minor changes and improvements are allowed.

Related Topics
About Design variables (DV_SHAPE)

In the following figure an example of non-parametric shape optimization is demonstrated. (Pictures by courtesy of Audi AG).

Typically, the objective function is to minimize stress concentrations. Based on the results of a stress analysis modifications of the surface geometry of a component are performed until the required stress level is reached. This process is usually carried out manually by trial-and-error.

SIMULIA Tosca Structure.shape allows an automatization of this improvement process. The surface geometry of a given FE model is modified iteratively based on the FE results, such that the required optimization target is reached. The start model is taken from an existing design, which should be improved, or from a previous topology optimization.

SIMULIA Tosca Structure.shape enables you to perform the following tasks

  • Minimization of the equivalent stress
  • Maximization of selected natural frequencies

Under the possible restrictions:

  • Specification of a volume constraint
  • Surface-based manufacturing constraints for casting, forging, stamping, extrusion and drilling
  • Minimum and maximum member size
  • Symmetry constraints
  • Specification of design domain restrictions by FE meshes
  • Mesh adjustment and mesh smoothing in each optimization cycle

Additional functionalities like optimization using durability results are available with SIMULIA Tosca Structure.durability. Functionalities like optimization using nonlinear results or optimization of contact areas are available with SIMULIA Tosca Structure.nonlinear.

Sensitivity-based shape optimization

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.