Continuum approach for second-order shape design sensitivity of three-dimensional elastic solids
A second-order shape design sensitivity analysis method for three-dimensional linear elastic solids is derived, using a continuum approach with the material derivative. To compute the second-order shape design sensitivity, a shape design acceleration field is defined, which is similar to the shape design velocity field for the first-order shape design sensitivity. Both direct differentiation and hybrid methods are presented in this paper. The shape changes are assumed on the traction-free boundary only. A numerical method, which can be implemented using established finite element analysis codes, is developed to demonstrate feasibility and accuracy of the proposed second-order shape design sensitivity analysis method