Interpreting Adjoint Equations in Structural Optimization

The adjoint method has been used in structural optimization to compute sensitivity coefficients of cost and constraint functions with respect to design parameters. The adjoint method involves the calculation of an adjoint vector from certain adjoint equations. So far, the adjoint equations have been considered only as a numerical tool for computing sensitivity coefficients. In this paper, the adjoint equations are given a physical interpretation, and it is shown that the components of the adjoint vector are the influence coefficients associated with the given function. Importantly, the interpretation of adjoint equations in this paper provides a new method for obtaining influence coefficients.