可展面を接続した自由曲面シェル構造の形状最適化

Abstract

Recently, a number of designers have focused on free-form surface shell to realize a free architectural form that is different from the analytical curved surface such as cylindrical or spherical surfaces. However, in order to create rational architectural forms, constructability and cost are also essential factors to be considered. Developable surface is a special form of ruled surface generated by continuous movement of the straight line. It can be obtained by adding the condition that the normal vector of the surface does not change along the generating line (generatrix). Because the generatrix is a straight line without torsion, the formwork of continuum shell is easily created. Since the twisting process is not required, it has a high workability characteristics. In this study, several developable surfaces are combined to form a curved roof structure. The (n, 1) Bézier surface is used for modeling the surface. Optimization problem is formulated for minimizing the maximum principal stress under several static loading conditions including vertical and horizontal loads. The coordinates of control points of the Bézier surface are chosen as design variables. The developability condition is numerically assigned so that the tangent vectors at the same parameter value of the two Bézier curves along the boundary exist in the same plane as the directing line. The G⁰ and G¹ continuity conditions are assigned for connecting the Bézier surfaces. Optimal solutions are found using nonlinear programming approach, where the sensitivity coefficients are computed by the finite difference approximation. As the result of optimization, a variety of developable surfaces are obtained by connecting Bézier surfaces. Since the control points of the curves are chosen as design variables, the calculation efficiency is high. The stress distribution also greatly improved by using the maximum stress as the objective function.