Abstract
This paper presents a numerical optimization method for optimal configuration design of shell structures. It is assumed that the shell surface is varied in the out-of-plane direction to the surface in order to obtain the optimal free-form shape, and the thickness is not changed with respect to the shape variation. A solution to the maximization problem of vibration eigen value subject to a volume constraint is proposed. With this solution, the optimal shape is obtained without shape design parameterization. The problem is formulated as a non-parametric shape optimization problem. The shape gradient function is theoretically derived using the material derivative formulas, Lagrange multiplier method and the adjoint variable method. The Robin type traction method is applied to determine the free-form shell while minimizing the objective functional. The calculated results show the effectiveness of the proposed method for optimal free-form design of shell structures.
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