A Deterministic Approach for Reliability Based Topology Optimization

Abstract

This paper presents an efficient approach for the reliability based topology optimization (RBTO), where the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented in this paper is built upon the Bidirectional Evolutionary Structural Optimization (BESO) used for solving the DTO problem. The proposed method deals with the solution of specific type of problems involving independent and normally distributed loads with deflection and reliability constraints, where the response of the structure is assumed to be evaluated from a linear elastic analysis. Linear relationship between the deflection and stiffness matrices along with the principle of superposition is exploited to handle reliability constraints and various load case scenarios as well as multiple random variables. Few example problems with various random variables and single or multiple loads applied on the structure are presented to demonstrate the applicability and efficiency of the proposed approach for solving RBTO problems. The most significant contribution of this paper comes from the improved efficiency of the proposed algorithm, when measured in the number of finite element analysis runs required to compute the optimum solution. For example, in the case of a single random variable RBTO, where the random variable is in the form of an applied load, the number of finite element analysis runs required to compute the optimum solution for the RBTO problem is the same as the number of runs required for the DTO problem.