Shape–thickness–topology coupled optimization of free-form shells

Shell structures are widely used in architectural design and civil engineering. However, it remains challenging to simultaneously optimize their shape, thickness, and topology under various design constraints and construction requirements. This work presents a method for the shape–thickness–topology coupled optimization of shell structures. In this method, the shape of shells is described by the non-uniform rational B-splines surface. Both shell elements and brick elements are used to discretize the design domain, so that the effect of shell thickness can be accounted for during the form-finding process. The structural self-weight is taken into consideration due to its practical importance. The minimum thickness is constrained to improve the constructability of the obtained designs. Several numerical examples are used to demonstrate the effectiveness of the proposed method. The results show that this method is capable of designing structurally efficient and aesthetically pleasing shells. This work holds potential applications in architectural design.