Second-order sensitivity analysis of 2D elastic problem by element-free Trefftz method

This paper presents a new scheme for the second-order shape design sensitivity analysis of two-dimensional elastic problem by the element-free Trefftz Method. in the Trefftz method, the physical quantities are approximated by the superposition of the regular T-complete functions satisfying the governing equation. Therefore, the direct differentiation of the approximate expressions with respect to the shape parameter leads to the regular expressions of the sensitivities. The present scheme is applied to the shape design sensitivity analysis of a circular cylinder under internal pressure.