In this paper, we present a solution to the multi-objective shape optimization problem for the rigidity design of sheet metal structures. The compliances for multi-loadings are used as indexes of rigidity. The lp norm method is employed to scalarize the vector objective functional of compliances. The volume is set as the constraint. The boundaries to be optimized are assumed to be movable only in-plane direction to maintain the curvatures of the initial shape. The shape gradient function and the optimality conditions are theoretically derived using the Lagrangian approach and the material derivative method.. The traction method is applied to determine the smooth shape variations that minimizes the objective functional, while constraining the shape variations in the normal direction on the sheet metal surfaces. This method is applied to a simple sheet metal structure and a practical automotive chassis component to verify the effectiveness and practical utility for improving the rigidity of sheet metal structures under multi-loading conditions.

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.

In this paper, we present a numerical analysis method for in-plane shape optimization of plate and shell structures subjected to a von Mises strength criterion. The weight minimization problem 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 simple shell examples and practical automotive chassis components to verify the effectiveness and practical utility for weight reduction of plate and shell structures subjected to the strength criterion.