Special Remarks on The Sizing Algorithm

SemiAnalytical Sensitivity Calculation

In the context of sizing optimization to obtain the sensitivity of design responses, a semianalytical approach is used. It is based on a finite difference of the elemental stiffness and mass matrices. That means that in addition to the original matrices perturbed matrices must be requested from the solver. This is done by a "matrix-step" (see figure below).

This matrix step's only purpose is to perturb all pseudo densities to get the perturbed matrices - the original matrix is obtained in a usual solver step where also the results of the FE-problem are wanted. For situations where matrix step is needed the solver is called twice in each iteration.