Abstract
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.
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