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Two-step shape optimization methodology for designing free-form shells

Abstract In this paper, a two-step free-form shape optimization methodology is presented for designing the optimal shapes of shell structures concerning stiffness maximization problem subject to a volume constraint. With this methodology, the optimization design problem of a shell structure is divided into two steps which consist a surface optimization step and a boundary optimization step. The shape sensitivities, called shape gradient function, are theoretically derived for both steps using the Lagrange multiplier method and the formula of the material derivative. The optimal shape is determined by applying the derived each shape gradient function on a design surface or boundaries to the gradient method. By the two-step free-form optimization, a smooth optimal shell with free-form surface and boundaries can be obtained to be a weight reduced form with high stiffness. Several calculated examples are presented to verify the validity and practical utility of the proposed methodology.