Shape Optimization of Free-Form Shells Using Invariants of Parametric Surface

Abstract

A new approach is proposed for shape optimization of shells, where the requirements on geometrical properties, constructability, and mechanical performance are simultaneously considered in the problem formulation. The surface shape is modeled using a triangular Bézier patch to reduce the number of design variables, while the ability of generating moderately complex shape is maintained. The strain energy under specified loading condition is used to represent the mechanical performance, and the geometrical properties are quantitatively defined using algebraic invariants of the parametric surface. The developable surface that has high constructability is generated by assigning an appropriate constraint on an algebraic invariant. The effectiveness of the proposed approach is demonstrated through several numerical examples, and the characteristics of the optimal shapes under various constraints are discussed.