Parameter‐free optimum design method of stiffeners on thin‐walled structures

In this paper, we present a shape optimization method for designing stiffeners on thin‐walled or shell structures. Solutions are proposed to deal with a stiffness maximization problem and a volume minimization problem, which are subject to a volume constraint and a compliance constraint, respectively. The boundary shapes of the stiffeners are determined under a condition where the stiffeners are movable in the in‐plane direction to the surface. Both problems are formulated as distributed‐parameter shape optimization problems, and the shape gradient functions are derived using a material derivative method and an adjoint variable method. The optimal free‐boundary shapes of the stiffeners are obtained by applying the derived shape gradient function to the $H^1$ gradient method for shells, which is a parameter‐free shape optimization method proposed by one of the authors. Several stiffener design examples are presented to validate the proposed method and demonstrate its practical utility.