Computational Morphogenesis of Free Form Shells

Abstract

A new method of computational morphogenesis for the shell structures with free curved surface is proposed, where not only the shape of shell surface but also the topology of the curved surface can be obtained at the same time. For the topology optimization, the optimization process for the shell thickness is used, where the topology of the curved surface with a multi-connecting surface is dealt with as a limit in which the shell thickness vanishes. For mathematical expression for the shape of the shells, NURBS (Non Uniform Rational B-Spline) is used, by which the number of unknowns can be effectively controlled while the high degree of freedom for the expression of the shape of shell surface as well as the shell thickness are kept. This paper shows the fundamental formulation of the proposed method for the optimization problem for both the shape and the topology of the free-form shell, followed by numerical examples in which the effectiveness of the proposed scheme is investigated through the application to several existing shell structures.