Perturbation-Based Spectral Stochastic Meshless Local Petrov-Galerkin Method in Predicting Probabilistic Settlements

ABSTRACT

In an attempt of solving stochastic boundary-value problems sufficiently accurately without creating a finite element discretization, a previous study (Comput. Geotech. 2011, vol. 38, No. 4, pp. 407-415) developed the spectral stochastic meshless local Petrov-Galerkin (SSMLPG) method. Some different approaches of deriving an SSMLPG formulation have been developed using various random field discretization methods. This study presents the SSMLPG formulation composed of perturbation expansions of random fields and a 2D meshfreee weak-strong (MWS) form in elasticity. A performance evaluation of this SSMLPG formulation is implemented through a stochastic elastostatic problem in which probabilistic settlements are predicted with the uncertainty in the spatial variability of Young's modulus. The evaluation results demonstrate that SSMLPG-based predicted probabilistic settlements approach more close to the Monte Carlo simulation (MCS) results than spectral stochastic finite element-based predicted probabilistic settlements do. In addition, generating the SSMLPG results is time-saving than completing the MCS does. In conclusion, the SSMLPG method can be an efficient alternative tool to solve stochastic boundary-value problems.