A shape optimization method for designing the free boundaries of stiffeners on thin-walled structures

Abstract

This paper presents a shape optimization method for designing the stiffeners on thin-walled or shell structures. The solutions to stiffness maximization problem subject to a volume constraint, and its reciprocal volume minimization problem subject to a compliance constraint are proposed. The boundary shape of the stiffener is determined under the condition where the stiffener is movable in the in-plane direction to the surface. The both optimization problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using the material derivative method and the adjoint variable method. The optimal free-boundary shapes of the stiffeners are determined by applying the derived shape gradient function to the H 1 gradient method for shell, which is a non-parametric shape optimization method proposed by one of the authors. Several optimal stiffener design examples are demonstrated to verify the validity and practical utility of the proposed method for designing stiffeners' shapes on thin-walled or shell structure. ©2013 The Japan Society of Mechanical Engineers.