SIMULTANEOUS OPTIMIZATION WITH RESPECT TO BOTH SHAPE AND THICKNESS AND ITS APPLICATION

Computational morphogenesis of free formed shells (Part 1)

Abstract

The scheme of computational morphogenesis for the shell structures with free curved surface is proposed, where shape and distribution of thickness can be simultaneously optimized. Generally, when nodal coordinates and shell thicknesses of finite element are adopted as design variables in structural optimization problem, computational cost generally becomes very large. In the proposed scheme, distribution of thickness is discretized according to the nodal points, and NURBS (Non Uniform Rational B-Spline) is utilized by which the number of unknowns can be controlled while the high degree of freedom for expression of the shape of the curved surface as well as the distribution of thickness are maintained. Consequently, the problem in question has been mathematically formulated as strain energy minimization problem where coordinates of NURBS control points with respect to both the shape of the curved surface and the distribution of thickness are adopted as design variables and numerical examples are presented where the effectiveness of the proposed scheme is investigated.