Shape Optimization of Free-form Shells Considering Strain Energy and Algebraic Invariants of Parametric Surface

Abstract

A new approach is proposed for shape optimization of shell surfaces, where requirements on the aesthetic aspect and the constructability as well as the structural rationality are simultaneously considered in the problem formulation. The surface shape is modeled using B'ezier surface to reduce the number of variables, while the ability to generate moderately complex shape is maintained. To apply the new approach to shell structures that have various plan shapes, the surface shape which has a rectangle plan is modeled using a tensor product B'ezier surface, and the surface shape with an irregular plan is modeled using a triangular patch B'ezier surface. The strain energy is used to represent the mechanical performance, and the aesthetic aspects and smoothness of the surface are quantified by algebraic invariants of the surface. The developable surface that has high constructability is created by imposing appropriate algebraic invariants constraints. The e ectiveness of the present approach is confirmed through several numerical examples and the characteristics of the results are discussed.