Reliability based structural design optimization for practical applications

This paper presents a new method for reliabilitybased optimization which requires only a modest increase in computational cost over that of deterministic design optimization. The method has been implemented for comparison with existing methods, and appears to be robust in terms of convergence from arbitrarily selected initial design points to the solutions determined by existing methods. Implementation in commercial software for application to structures with large numbers of design variables and constraints has been examined and is considered to be feasible. Numerical examples are included to illustrate the method. Introduction Existing methods for reliability-based structural design optimization are believed to be impractical for general application to problems involving large numbers of design variables and constraints. Compared with deterministic design optimization, these methods can increase the computational effort by orders of magnitude. The method presented in this paper is conservatively estimated to require less than twice the computation of effort of deterministic methods, because it does not require nested optimization loops or an increase in the number of design variables. The paper presents numerical examples based on a standard benchmark test case (the Complexity Wing), and a simple box-beam structure. Three methods are compared: the probabilistic safety margin (PSM) or constraint padding method described by Hasselman, et.al.,' the reliability-based optimization (RBO) method described by Luo and Grandhi, and the new RBO method also described in Reference 1. The PSM method was originally devised as an approximate method for computationally efficient probabilistic design optimization. It was implemented in ASTROS and compared with published results by Luo and Grandhi 2 for the Intermediate Complexity Wing (ICW) illustrated in Figure 1. The comparison shown in Figure 2 indicates that the PSM method may be a good approximation for modest degrees of uncertainty and modest levels of design reliability, but is inaccurate for large uncertainty and a high degree of reliability. Careful evaluation of the RBO method of Luo and Grandhi, along with other published RBO methods, revealed that existing RBO methods were too costly for practical application. This realization led to the new method described herein General Problem Statement A general statement of the deterministic design optimization problem is given as follows: Minimize : f(x) Subject to: gj (x) < 0; j = 1, m and: X < x < x' (la)