Efficient structural optimization for multiple load cases using adjoint sensitivities

Adjoint sensitivity calculation of stress, buckling, and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. In general, it is more difficult to implement the adjoint method than the direct method, but it is shown that the use of the continuum adjoint method, along with homogeneity conditions, can alleviate the problem. Expressions for von Mises stress and local buckling sensitivities for isotropic plate elements are derived. Computational efficiency of the adjoint method is sensitive to the number of constraints, and, therefore, the adjoint method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser functional is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a small high-speed civil transport (HSCT) model, and a large HSCT model. These sensitivity derivatives are then used in optimization.