Multi-objective free-form optimization for shape and thickness of shell structures with composite materials

In this paper, we present a two-phase optimization method for designing the shape and thickness of shell structures consisting of orthotropic materials. We consider a multi-objective in terms of the compliances under multi boundary conditions, and use the weighted sum compliance as the objective functional and minimize it under the volume and the state equation constraints. The 1st phase is shape optimization, in which a shell structure is varied in the out-of-plane direction to the surface to create its optimal shape. In the 2nd phase, thickness optimization is implemented after shape optimization to decrease the compliance further. A free-form shape and thickness optimization problem is formulated in a distributed-parameter system based on the variational method. The shape and thickness sensitivities are theoretically derived and applied to the H1 gradient method for shape and size optimization. The optimal multi-objective free-form of a shell structure with an orthotropic material can be determined using the proposal method, and the influence of the orthotropic angle to the optimal shape and thickness distribution is investigated in detail.