Shape design optimization of joining mechanism using doubly curved shell

Methods for shape and topology design sensitivity analysis (DSA) and optimization of joining mechanisms, such as spot welding and adhesive bonding, using a doubly curved (Hughes–Liu) shell are presented in this article. The material derivative concept of continuum mechanics and the adjoint variable method are used to derive the shape and topology design sensitivity expressions in the domain integral form. The shape optimization is performed to find the optimum locations of spot welds to maximize the stiffness of the structure. This optimum design is used as the initial design to perform topology optimization based on a density approach to study the effects of material distribution on structural performances. A numerical example, by postprocessing NIKE3D finite element analysis (FEA) code, of shape and topology optimization is given to demonstrate the validity of the methodologies presented in this study.