Probabilistic Interval Response and Reliability Analysis of Structures with A Mixture of Random and Interval Properties

Static response and reliability of structures with a mixture of random and interval parameters under uncertain loads are investigated in this paper. Structural stiffness matrix is a random interval matrix when some structural parameters are modeled as random variables and others are considered as intervals. The structural displacement and stress responses are also random interval variables. From the static finite element governing equations, the random interval structural responses are obtained using the random interval perturbation method based on the first- and second-order perturbations. The expressions for mean value and standard deviation of random interval structural displacement and stress responses are developed by the random interval moment method. The structural reliability is not a deterministic value but an interval as the structural responses are random interval variables. The lower and upper bounds of reliability index, probability of failure and reliability of structural elements and systems are investigated using the combination of the first-order reliability method and interval approach. Four examples are used to demonstrate the validity and feasibility of the presented methods.