Refined second order semi-analytical design sensitivities

Accurate and e cient calculation of second order design sensitivities in a nite element context is often di cult. The semi-analytical (SA) method is e cient and easy to implement but has accuracy problems even for rst order shape design sensitivities. To overcome accuracy problems a re ned semianalytical (RSA) method has been developed for rst order sensitivities. The present paper investigates the application of the RSA method to second order design sensitivities. It is found that second order RSA sensitivities are signi cantly more accurate than their SA counterparts