Free-Form Optimization Method for Designing Automotive Shell Structures

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. With this method, the smooth optimal global free-form or the smooth optimal local beads of shell structures in automotive body and chassis parts is created without any shape design parameterization. The validity and practical utility of this method were verified through several design examples. We confirmed that the obtained structures were changed from the initial bending-carrying structures to membrane-carrying ones.