A novel hyperspace division method for probabilistic analysis of nonlinear truss structures with multiple modes of failure

In the probabilistic analysis of redundant structural systems, a series of new parameters should be taken into account to accurately assess their probability of failure. The present paper introduces a new technique that allows estimating the reliability of redundant structural systems by the identification of the sequence of multiple modes of failure, which are classified as ultimate or serviceability limit-states. This technique is based on the (HDM) Hyperspace Division Method procedure with a multidimensional radial sampling technique. Besides, in this work, inelastic analysis of steel truss including both geometric and physical nonlinearities are considered using an incremental-iterative technique based on the generalized displacement control method, in addition to constitutive laws to predict the inelastic behavior in tension and compression. Numerical applications show the accuracy and efficiency of the methodology in the evaluation of the failure probability in simple to difficult problems with high nonlinear limit-state functions with multiple discontinuous failure regions. The method confirms results from the literature, allied to a better performance in terms of less number of limit-state function evaluations.