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

• Published in: Structural and multidisciplinary optimization Vol. 49; no. 1; pp. 39 - 47
• Main Authors: Liu, Yang, Shimoda, Masatoshi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2014; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Design parameters; Engineering; Engineering Design; Research Paper; Shape optimization; Stiffeners; Stiffness; Theoretical and Applied Mechanics; Thin wall structures; Shell; Stiffener optimum design; Shape optimization; Traction method; Node-based; Thin-walled structure; Parameter-free; FEM
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-013-0954-1

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 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.