Computational Morphogenesis of Free Form Shells

The scheme 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 simultaneously obtained. For the topology optimization, the optimization process for the shell thickness is utilized, where the topology of the curved surface with a multi-connecting surface is dealt with as a limit of the case in which the shell thickness vanishes. For numerical expression for the configuration of the shells, NURBS(Non Uniform Rational B-Spline) is utilized, 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 maintained. Additionally, the contour line method which has been originally developed by the authors as the extension scheme for the topology optimization of elastic continuums is also introduced for the expression of the shell thickness distribution as well as the shell topology. In this paper, the fundamental formulation of the proposed scheme for the optimization problem for both the shape and the topology of the free form shell is shown, followed by the numerical examples which clearly show the effectiveness of the proposed method.