An IRF method for stochastic meshless analysis of 2D beams with lognormally varying random Young's modulus

The current paper proposes to use an improved response function (IRF) method for stochastic meshless analysis of a 2D beam wherein Young’s modulus is assumed to vary as a lognormal random field. The meshless tool used in the present study is the element-free Galerkin method. In IRF method, the total displacement response is evaluated in each simulation by adding a deterministic part and an IRF. This displacement decomposition combined with the stiffness modelling using the second order expansion of Taylor series is substituted in the stochastic system of equations to find the expressions for the deterministic solution and the IRF. The deterministic solution evaluation is possible outside the loop for simulation and the expression for IRF involves only simple algebraic operations to be carried out inside the simulation loop. A 2D beam with cantilever boundary conditions loaded at the free end with a parabolic traction is analysed and the response moments are determined using the IRF method proposed. The first two moments of response obtained are observed to be matching well with the MCS moments even at higher values of coefficient of variation. The IRF method proposed also produces the distributions of response comparable with the distributions evaluated using MCS. The difference in response moments evaluated using IRF method and the second order perturbation method is in the acceptable limit. The computational efficiency of the IRF method is evidently better compared to MCS.