Abstract
In this paper, we present a numerical analysis method for shape ontimization in the rigidity design of plate and shell structures. It is assumed that the design damain is varied in the in-plane direction to maintain the curvatures of the initial shape. An external work, or a compliance is used as an index of the rigidity. The weight minimization problem subjected to the rigidity constraint is formulated as a non-parametric shape optimization problem using the Lagrangian approach and the material derivative method. The shape gradient function and the optimality conditions are theoretically derived for this problem. The traction method is applied to determine the smooth in-plane domain variation that minimizes the objective functional. This method is applied to a simple shell example and a practical automotive chassis component to verify the effectiveness and practical utility for weight reduction of plate and shell structures subjected to the rigidity constraint.
