A simplified reliability-based design method for multiple design variables considering different limit states.

A generalized reliability model comprising the objective, constraint, and judgment functions is established for the reliability index approach (RIA), taking parameters' properties of engineering practice and negative reliability index into consideration. Based on this, the reliability-based design (RBD) problem with multiple design variables is translated into the solution to the nonlinear equations, and a simplified method consisting of a simple variant of the Newton iteration method and the finite difference method (FDM) is proposed. Numerical examples are presented to verify the efficiency of the proposed reliability approach and to determine the incremental step size for FDM. RBD of a simply supported beam is illustrated and the variabilities of design variables are investigated considering the uncertainties in the manufacturing process and practical operations. Results reveal that the variations of the design variables should not be ignored. Moreover, analysis results show that the design value might not intuitively increase with the increase of its coefficient of variation (CoV), and it might not increase with the increasing reliability requirement for problems involving multiple variables. The reasons for this phenomenon are very complicated, and it is a systematic problem. One should be aware of this phenomenon, and specific analysis is required for specific problems.