Stochastic Ultimate Bearing Capacity Analysis Based on Elastic Modulus Reduction Method

To determine the stochastic ultimate bearing capacity of engineering structures, a novel method for stochastic ultimate bearing capacity analysis based on the elastic modulus reduction method (EMRM) was proposed by combining the elastic modulus adjustment procedure (EMAP) and the perturbation stochastic finite element method (PSFEM). The stochastic responses and reliability indices of structural elements were calculated by the PSFEM to define the uniformity of reliability indices and the reference reliability index. Meanwhile, the proportional loading conditions of stochastic limit analysis as well as the proportional relationship between the stochastic responses and the external loads were demonstrated theoretically. Finally, by adjusting the elastic moduli of elements with low reliability index the failure evolution was simulated to form a set of statically admissible stress fields, and further the structural failure mode and the corresponding stochastic ultimate bearing capacity were determined based on the plastic limit analysis theory. Numerical examples demonstrate that the proposed method is converged after 15 iterative steps or so, and compared with the Monte Carlo method for 500 000 samples, it has a relative error of less than 0.5%.