Hybrid uncertain analysis for random convex response of structures with a mixture of random and convex properties

This paper presents a new numerical algorithm named hybrid Neumann Lagrange method for static analysis of structural systems with a mixture of random and convex variables. The random variables are used to treat the uncertain parameters with sufficient statistical information, whereas the convex variables are used to describe the uncertain parameters with limited information. The expressions for expectation and variance of random convex structural displacements are developed based on the Neumann series theory. Then the first-order Taylor series and the Lagrange multiplier method are employed to determine the upper and lower bounds of these probabilistic characters of the structural responses. By comparing with the results of Monte Carlo simulation, numerical examples are given to verify the effectiveness of the proposed method.