An improved response function based stochastic meshless method for problems in elasto-statics

• Published in: Computer methods in applied mechanics and engineering 2020-12, Vol.372, p.113419, Article 113419
• Main Authors: Aswathy, M, Arun, C O
• Format: Article
• Language: English
• Subjects: Ad-hoc response function; Coefficient of variation; Fields (mathematics); Finite element method; Galerkin method; Improved response function; Matrix algebra; Matrix methods; Meshless methods; Modulus of elasticity; Monte Carlo simulation; Perturbation; Random field; Random variables; Response functions; Second order perturbation; Series expansion; Shape functions; Simulation; Stiffness matrix; Stochastic element free Galerkin method; Stochastic processes; Taylor series
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113419

The current study proposes an improved response function (IRF) based stochastic element free Galerkin method (SEFGM) for the analysis of problems in elasto-statics, wherein Young’s modulus is modelled as a homogeneous random field with symmetric distribution characteristics. The proposed SEFGM approximates displacement as the sum of a deterministic part and a stochastic part. The stochastic part is modelled with the help of an IRF, which is a function of discretized set of random variables. Moving least square shape functions are employed to discretize the random field. Utilizing Taylor series expansions of stiffness matrix and force vector and IRF approximation of displacement, explicit expressions for system responses in terms of random variables are derived. Stochastic informations of system responses are evaluated by employing Monte Carlo Simulation (MCS) on the response function, which eliminates the need of construction and simulation of system matrices at each set of sample generation. 1D and 2D numerical examples in elasto-statics are solved using proposed method. Results are validated with those obtained by direct simulation of system of equations using MCS and also compared with other methods like second order perturbation and ad-hoc response function based SEFGM. Normalized computational times required for all the methods are also compared. It is found that the proposed method is computationally efficient and can produce accurate results even for higher coefficient of variation of input random fields. •A novel method is suggested for stochastic meshless analysis of problems in elasto-statics.•The method is based on an improved response function based stochastic element free Galerkin method.•Proposed method takes care of cross-dependency of random variables on response.•All probabilistic characteristics of structural responses can be captured.•The method is efficient and produces accurate results for higher coefficient of variation of input random fields.