Simultaneous optimization of shape, thickness and topology of shell structures using sigmoid function

Abstract

Advancement of computer technologies as well as the developments of structural materials and construction methods have enabled us to design a so-called free-form shell, which has complex shape and topology that cannot be categorized to traditional shapes. However, the mechanical behavior of such a shell is very complicated, and it is very diffcult for a designer to decide feasible shape of a real-world structure based on his/her experience. Based on such background, in recent years, some shape optimization methods for continuum shell structures, which have a strong relationship between shape and structural rationality, have been proposed actively. On the other hand, thickness distribution is also an important aspect of shell structures. There exist not so many studies on the optimization methods which treat shell shape and plate thickness simultaneously. From the view point of structural feasibility, constructability and topological clarity, it is not acceptable that the plate thickness takes an extremely small value. Therefore, the part with a thin plate thickness should be an opening, which requires to use a topology optimization approach. In this paper, a simultaneous optimization method of shape, thickness, and topology of shell structures is proposed. Efficiency of the proposed approach is investigated through several numerical examples, and the characteristics of the computational results are discussed.

Keywords

• shape optimization
• thickness optimization
• topology optimization
• nonlinear programming
• sigmoid function