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In this paper, we present a parameter-free, or a node-based optimization method for finding the smooth optimal free-form of automotive shell structures, including global and local curvature distributions such as beads or embossed ribs. The design problems dealt with in this paper involve a stiffness problem. Stiffness is maximized using the compliance as an objective functional. The optimum design problem is formulated as a distributed-parameter, or non-parametric, shape optimization problem under the assumptions that the shell is varied in the normal direction to the surface and the thickness is constant. The shape gradient function and the optimality conditions are then theoretically derived. The optimum free-form, or optimal curvature distribution, is determined by applying the derived shape gradient function in the normal direction to the shell surface as pseudo external forces to vary the surface and to minimize the objective functional.

This paper describes the shape optimization analysis of solid structures such as chassis components of a car, where the shape optimization problems of linearly elastic structures are treated to improve strength or to reduce weight of solid structures. The optimization method used here is the growth-strain method, and the shape optimization system is developed based on this method. The growth-strain method, which modifies a shape by generating bulk strain, was previously proposed for analysis of the uniform-strength shape. The generation law of the bulk strain is given as a function of a distributed parameter to be uniformed, such as von Mises stress. Two improved generation laws are presented. The first law makes the distributed parameter uniform while controlling the structural volume to a target value. The second law makes the distributed parameter uniform while controlling the maximum value of the distributed parameter to a target value.