Parameter-free method for the shape optimization of stiffeners on thin-walled structures to minimize stress concentration

This paper presents a parameter-free shape optimization method for the strength design of stiffeners on thin-walled structures. The maximum von Mises stress is minimized and subjected to the volume constraint. The optimum design problem is formulated as a distributed-parameter shape optimization problem under the assumptions that a stiffener is varied in the in-plane direction and that the thickness is constant. The issue of nondifferentiability, which is inherent in this min-max problem, is avoided by transforming the local measure to a smooth differentiable integral functional by using the Kreisselmeier-Steinhauser function. The shape gradient functions are derived by using the material derivative method and adjoint variable method and are applied to the H1 gradient method for shells to determine the optimal free-boundary shapes. By using this method, the smooth optimal stiffener shape can be obtained without any shape design parameterization while minimizing the maximum stress. The validity of this method is verified through two practical design examples.