Structural Reliability Analysis And Reliability-Based Design Optimization Based On Homotopy Analysis

There are many uncertainties in practical engineering problems. The accurate measurement, analysis and control for parameter uncertainty and whereby conducting corresponding reliability design are effective means of ensuring the normal functions of products or structures under complex working conditions. Currently,the tools of describing uncertainty are mainly probabilistic method,fuzzy method and interval approach.The first order reliability method (FORM) is the classic and most commonly used method in the field of reliability, and it has been widely used in structural analysis and design in various industrial fields. In FORM, the problem of reliability analysis is usually converted into an optimization problem to solve for the reliability index in the standard normal space, based on a probability transformation. The key problem of FORM-based reliability analysis is thus reduced to solving the optimization problem. A series of algorithms aimed at solving this optimization problem have been developed. In this paper, we do some work to solve the structural reliability problems. The main contents of this paper are as follows:(1) In this paper, for the structural reliability problems, we introduce a new performance measure approach based on the homotopy analysis, denoted as the HOMO method. First we establish the Karush-Kuhn-Tucker (KKT) condition of the structural reliability problems, then construct the corresponding homotopy equations, and apply the ?-cone path-tracking algorithm to solve the equations. Finally, several numerical examples and an engineering application are provided to validate the effectiveness of the present method. Several examples are provided to show that the method has robust convergence in solving the limit-state functions of different degree nonlinearity.(2) In this paper, we introduce a new approach based on homotopy analysis to the RBDO problems. First we transform the RBDO based on the performance measure approach, then the optimization is transformed into deterministic optimization.Last we apply homotopy analysis to solve the optimization. Finally, numerical examples are provided to verify the effectiveness of this method. Several examples are provided to show that the approach, established in our paper, has good precision and convergence in solving the RBDO, who has different degree nonlinearity.