Configuration design sensitivity analysis of built‐up structures part I: Theory

Abstract

AbstractA continuum based configuration design sensitivity analysis method is developed for built‐up structures that include truss, beam, plane elastic solid and plate design components. The configuration design variation of a structural component can be characterized by changes in the domain shape and in the orientation of the component. A variational approach is then used to incorporate both shape and orientation effects in the same energy equation. A continuum shape design sensitivity analysis method that utilizes the material derivative idea of continuum mechanics is employed to account for effects of shape variation. An approach that is similar to the continuum shape design sensitivity analysis method is developed in this paper to account for the effect of orientation variation. Variations of energy bilinear and load linear forms, with respect to both shape and orientation design variables, are derived for each structural component. Using the adjoint variable or direct differentiation method, configuration design sensitivity results for built‐up structures are obtained in terms of the design velocity fields. Configuration design sensitivity analyses of both static and eigenvalue responses are considered.