Structural reliability analysis using non-probabilistic convex model

By using the convex model approach, the bounds of the uncertain parameters are only required rather than their precise probability distributions, based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information. In this paper, a non-probabilistic reliability model is given for structures with convex model uncertainty, which is defined as a ratio of the multidimensional volume falling into the reliability domain to the one of the whole convex model. A Monte Carlo simulation is then formulated for the reliability model to obtain a reference solution. A first order approximation method (FOAM) is proposed to solve the reliability model based on a linear approximation of the failure surface. A second order approximation method (SOAM) is further formulated to improve the reliability analysis precision for limit-state functions with relatively strong nonlinearity. By introducing the suggested reliability model, a convex-model-based system reliability method is also formulated. Eight numerical examples are provided to demonstrate the effectiveness of the present methods.