Shape Optimization for Weight Reduction of Automotive Shell Structures Subject to a Strength Constraint

In this paper, we present a numerical solution to shape optimization problems in automotive shell structural designs subject to a strength constraint. Using the proposed method, the optimal shape can be obtained without any parameterization of design variables. With the aim of reducing the weight, a volume minimization problem subject to a von Mises stress constraint is formulated as a distributed-parameter shape optimization problem, or a non-parametric shape optimization problem. It is assumed that the design domain is varied in the tangential direction to the surface to maintain the curvatures of the initial shape. The shape gradient function and the optimality conditions are theoretically derived for this problem using the material derivative method, Lagrange multiplier method and the adjoint variable method. The traction method we have proposed earlier is applied to determine the smooth domain variation that minimizes the objective functional. The solution is applied to fundamental design examples and actual automotive components to verify its effectiveness and practical utility.