Reliability-based topology optimization of vibrating structures with frequency constraints

There are many inevitable uncertain parameters in engineering systems, and the ignorance of these random factors results in a remarkable reduction in the dynamical system’s performance for the eigenvalue topology optimization problem. To address the problem, a reliability-based topology optimization (RBTO) model for lightweight design with frequency constraints is established, which aims to account the probabilistic behavior incurred by material properties and geometric dimensions. Then, the single loop approach is used to tackle the RBTO problem. The sensitivities of eigenvalues with respect to the design and random variables are also deduced, in which the simple and multiple eigenfrequencies are simultaneously considered. Moreover, the threshold projection approach is used to eliminate the checkerboard phenomena and grey elements for the eigenvalue topology optimization problem. Three examples are discussed to exhibit the validity of the proposed RBTO methodology.