Reliability based topology optimization for maximizing stiffness and frequency simultaneously

Reliability based Topology optimization (RBTO) is a process of determining of optimal design satisfying uncertainties of design variables. Sometimes frequency optimization might produce a design with low stiffness or stiffness optimization might lead to a design with low frequency. In this paper, the multi-objective optimization for both stiffness and frequencies isare presented. This article presents (RBTO) using bi-directional evolutionary structural optimization (BESO) with an improved filter scheme. A multi-objective topology optimization technique is implemented to simultaneously considering the stiffness and natural frequency. In order to compute reliability index the first order reliability method (FORM) and standard response surface method (SRSM) for generating limit state function is employed. To increase the efficiency of the solution process the reliability estimates areis coupled with the topology optimization process. Topology optimization is formulated as volume minimization problem with probabilistic displacement and frequency constraints. Young’s module, density, and external load are considered as uncertain variables. The topologies are obtained by (RBTO) are compared with that obtained by deterministic topology optimization (DTO). Results show that (RBTO) using (BESO) method is capable of the multi-objective optimization problem for stiffness and frequency effectively.