Efficient design sensitivity derivatives for multi-load case structures as an integrated part of finite element analysis

In most structural optimization problems the accurate calculation of design sensitivity derivatives is required many times during the optimization process. For large structures with multi-load cases the computational costs are sometimes prohibitive. In this paper an approach for incorporating design sensitivity calculations into the finite element analysis of multi-load case structures is presented. A formulation designed to minimize the computational time for the assembled stiffness matrix derivatives is discussed for different element types. The formulation depends on the implicit differentiation method and requires few additional calculations to obtain the design sensitivity derivatives. The approach is developed and implemented to calculate the design sensitivities for continuum and structural isoparametric elements. To demonstrate the accuracy and efficiency of the developed approach some test cases using different structural and continuum element types are presented.