Topology optimization method for stiffener layout design of curved thin-walled structures under random excitations

Traditional topology optimization methods for curved thin-walled stiffened structures predominantly focus on static load conditions, neglecting the critical influence of random excitations. This paper presents a topology optimization method for stiffener layout design of curved thin-walled structures under random excitations. This method takes the root-mean-square value of von Mises stress as the optimization objective, and ensures the structural safety margin under the random excitation by optimizing the stiffener layout. For the random dynamic response, the pseudo excitation method is utilized to calculate the response values. For the topological design, the coordinates of the endpoints of stiffeners are considered as the positional design variables to find the optimal layout, and the relative thicknesses of stiffeners are considered as the topological design variables to realize the material increase or decrease. In order to solve the local modal problem caused by variations in stiffener thickness, a penalty mechanism based on the Heaviside function is constructed to penalize the stiffener relative thickness and material density. In addition, an adaptive mesh discretization strategy is proposed to seamlessly couple the base panel and stiffener elements. Numerical examples demonstrate that the topology configurations obtained by the proposed method exhibit a lower random dynamic response compared with the equivalent static topology designs.