Efficient stochastic finite element method for the reliability analysis of nonlinear frame structures.

An efficient stochastic finite element-based procedure is proposed for the reliability analysis of frame and truss structures with geometrical and material nonlinearities under static loading condition. The material properties, geometry and external loads of the structure are considered as random variables. The failure criteria of the structure are expressed in terms of limit-state functions. The method is based on the advanced first order second moment reliability analysis procedure. The assumed stress field approach is used in the finite element formulation to compute nonlinear structural responses and the corresponding response gradients. The proposed method is suitable for the reliability analysis of geometrically nonlinear frame structures with flexible connections. The mechanical properties of the nonlinear flexible connections can be deterministic or random. A random index parameter is introduced as a basic random variable to consider the uncertainties in the modeling of the connections. Structures with different types of connections can be handled by this method. An efficient method is also proposed for the reliability analysis of highly redundant elastic-perfectly-plastic frame structures with large deformations under proportional loading. The proposed method avoids dealing with the complicated failure mechanisms and stable configurations in the structure system reliability analysis, and has several advantages over the other available methods.