Abstract
In this paper, we present a parameter-free free-form optimization method for the reaction force control problem of a shell structure with material and geometrical nonlinearities. The sum of squared error norms to a specified force is minimized subject to a volume constraint. The optimum design problem is formulated as a distributed-parameter shape optimization problem under the assumptions that a shell is varied in the out-of-plane direction to the surface and the thickness is constant. The shape gradient function and the optimality conditions for this problem are theoretically derived by using the material derivative method and the Lagrange multiplier method. The shape gradients derived are applied to the H^1 gradient method for shells with this method. The optimal shape of shell structures can be obtained without the shape parameterization, while maintaining the surface smoothness. The shape gradient function was calculated by a user sub-program which is developed by using the result of non-linear FEM analysis of a commercial solver (e.g. Nastran). Several calculated examples are presented to verify the validity and practical utility of the proposed methodology and the developed system.
