Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method

This paper presents a mixed perturbation Monte-Carlo method for static and reliability analysis of structural systems with a mixture of random and interval parameters/loadings. Using a combination of the Taylor expansion, matrix perturbation theory and random interval moment method, the expressions for the mean value and standard deviation of random interval structural responses are developed. The Monte-Carlo simulation method is employed to determine the lower and upper bounds of the mean values and standard deviations of structural displacements and stresses. The structural reliability is not a deterministic value but an interval as the structural stress responses are random interval variables. The lower and upper bounds of probability of failure and reliability of structural elements and systems are investigated based on the first-order second-moment reliability method and interval approach. Three numerical examples are used to illustrate the effectiveness of the proposed method.