Shape optimization of a double-layer space truss described by a parametric surface

A method is presented for finding the optimal configuration of a double-layer space truss described by a parametric surface. The number of design variables is drastically reduced, without sacrificing the smoothness of the upper layer surface, by using the control net parameters as design variables. The coordinates of the lower nodes are defined by using a vertical or normal offset vectors from the upper surface. Curvatures of the curve associated with the lower polygon are calculated for evaluating feasibility and regularity of the a double-layer lattice space truss. In the examples, a feasible optimum design, which minimizes compliance under constraints on structural volume, are successfully found by using the proposed method. It is shown that the optimal solutions strongly depend on the specified ratios of the cross-sectional areas of the members.