Semi-Analytical Sensitivity CalculationThe sensitivity-based algorithm uses semi-analytical sensitivities based on a finite difference of the stiffness and mass element matrices:
Where K is the stiffness matrix, is the original matrix and is the perturbed matrix when one of the nodes is moved. The first term in the above equation is necessary to calculate the sensitivity for most of the design responses that are available in Tosca Structure.bead. To get this term, we utilize a "matrix-step" (see figure below).
This matrix step's only purpose is to perturb all design nodes to get these perturbed matrices - the original matrix is obtained in the last perturbation (PERTURBATION = 0) where also the results of the FE-problem are wanted. To avoid too long optimization run times, it is important to understand this workflow. It has two potential pitfalls that might slow the optimization tremendously:
It would demand a lengthy discussion to explain in detail exactly when and why which loads are added but some guidelines are given here:
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