Controller-based bead optimization

The optimality criteria used in the controller-based bead optimization method is described in this chapter.

The controller-based bead optimization (BEAD_CONTROLLER) is based upon a special bending hypothesis developed at IPEK at Karlsruhe University. It determines the orientation of the maximum bending stress or Differential Stress Tensor (DST) for each point in the design domain. The Differential Stress Tensor (DST) is the difference tensor between the stress tensors at the top and at the bottom shell layer. The emerging bead flanks are oriented parallel to the DST eigenvectors. Special filters are used to generate these beads along the bending trajectories.

This method has the following advantages:

  • Solver-independent and sensitivity-independent
  • mesh-independent
  • clear results
  • restrictions on the bead form can be included

Important: Bead optimization does NOT always give better mechanical behavior. The design problem must be suited for bead optimization, that is:

  • Design area should be mainly in bending or a bending mode. The bead algorithm will then increase the moment of inertia which leads to a greater stiffness or eigenfrequency.
  • Design area should NOT be in a membrane stress state (see also Penalty conditions (BEAD_MIN_STRESS and BEAD_MAX_MEMBRANE)). A bead may in this case make the structure softer.