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

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 si-multaneously considered in the problem formulation. The surface shape is modeled using Bézier 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 Bézier surface, and the surface shape with an irregular plan is modeled using a triangular patch Bézier 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 impos-ing appropriate algebraic invariants constraints. The effectiveness of the present approach is confirmed through several numerical examples and the characteristics of the results are dis-cussed