---

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.

---

Reliability and optimization are two key elements for structural design. The reliability-based topology optimization (RBTO) is a powerful and promising methodology for finding the optimum topologies with the uncertainties. In this paper, the particle swarm algorithm (PSO) using performance measure approach (PMA) is proposed in the RBTO procedure. Conventionally, the approximate limit state function along with the most probable point (MPP) search algorithms is used for calculation the reliability index. On the other hand, the choice of penalty function for having a convergent search plays a critical role. In addition one does not need to use approximate limit state function and calculating the derivatives of limit state function with respect to random variables. Furthermore, the convergence problem of the MPP search algorithms for complicated limit state functions does not exist. This paper presents RBTO using bi-directional evolutionary structural optimization (BESO) with an improved filter scheme. The topologies obtained by RBTO are compared with that of obtained by deterministic topology optimization (DTO). Results of the RBTO using PSO show that PSO can be effectively applied to RBTO and its use is quite simple.