Variational method for design sensitivity analysis in nonlinear structural mechanics

Abstract

This paper describes a unified variational theory of design sensitivity analysis of linear and nonlinear structures for shape, nonshape, and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Several analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use. Such analytical examples give insight into the application of the general formula to more complex problems that must be treated numerically. Adjoint state fields are also interpreted as sensitivities for the functional related to the primary structure.