Two Approaches to Sensitivity Analysis for Shape Variation of Structures

The equations that govern sensitivity of structural response to shape variation are obtained by using the principle of virtual work and the material derivative approach. Both the direct and adjoint methods are presented. For both cases, sensitivity calculations require the solution of structural response to additional loads that are characterized by initial strains, initial stresses, or body forces. This characterization in terms of physically meaningful loads permits implementation by any structural-response solution method. Two example problems of a moving interface are presented. One of the examples, which is implemented in a general-purpose finite element code, shows good results for the direct method, but reveals numerical difficulties with the adjoint method associated with the use of surface integrals, as observed previously in the literature.