Shape Design Sensitivity Analysis of Elastic Structures

ABSTRACT ABSTRACT Design problems in which the shape of two- or three-dimensional elastic bodies plays the role of design are studied. Five prototype problems are formulated in a unified variational form, with performance measures involving natural frequency, displacement, and stress in the structure. The material derivative of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to develop an explicit formula for variation of performance measures in terms of normal movement of the boundary of the physical domain. Examples are presented for beams, membranes, shafts, and three-dimensional elastic solids.