Application of element-free Trefftz method to second-order design sensitivity analysis of two-dimensional elastic problem

This paper presents a new scheme for the second-order shape design sensitivity analysis of the two-dimensional elastic problem by the element-free Trefftz method. In the Trefftz formulation, the physical quantities are approximated by the superposition of the regular T-complete functions. Therefore, direct differentiation of the approximate expressions with respect to shape parameters leads to the regular expressions of the sensitivities. The present schemes are applied to simple examples in order to confirm the validity.