Sensitivity analysis of shape memory alloy shells

This paper presents procedures for efficient design sensitivity analysis for shape memory alloy (SMA) structures modeled with shell elements. Availability of sensitivity information at low computational cost can dramatically improve the efficiency of the optimization process, as it enables use of efficient gradient-based optimization algorithms. The formulation and computation of design sensitivities of SMA shell structures using the direct differentiation method is considered, in a steady state electro-thermo-mechanical finite element context. Finite difference, semi-analytical and refined semi-analytical sensitivity analysis approaches are considered and compared in terms of efficiency, accuracy and implementation effort, based on a representative finite element model of a miniature SMA gripper. Keywords: Shape memory alloys; Semi-analytical design sensitivities; Finite differences; Fast reanalysis