Design Sensitivity Derivatives for Isoparametric Elements as an Integrated Part of Finite Element Analysis

This work presents an approach for incorporating design sensitivity calculations into the finite element analysis. The formulation depends on the implicit differentiation approach and requires few additional calculations to obtain the design sensitivity derivatives. The implicit differentiation approach is developed and implemented to calculate the design sensitivities for continuum and structural isoparametric elements. To demonstrate the developed approach test cases using different structural and continuum element types are presented.