Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion.

• Non-intrusive stochastic smoothed finite element model (SS-FEM) is formulated. • The SS-FEM is used to solve the homogeneous and multi-material mechanical structures under uncertainties. • The spatial variability in material parameters is characterized by random field based on KL expansion. A random field of homogeneous and multi-material structures with uncertain scenarios is addressed by constructed the generalized stochastic cell-based smoothed finite element model. Smoothed finite element method (S-FEM) is "Jacobian-free", which is not only overcomes the limitations of "overly-stiff" and low accuracy of the standard FEM, but also demonstrates strong resistance to mesh distortion. This paper proposes an efficient non-intrusive stochastic smoothed finite element method (SS-FEM) based on cell-based smoothing domains (SD) for the stochastic analysis of elastic problems, which describe much more realistically real physical systems under uncertain scenarios. This SS-FEM starts from the Gaussian random field based on representation related to the spatial variability in material parameters based on the Karhunen-Loève (KL) expansion, and then establishes the basic formulation that considers the effects of uncertainties. A generalized solving framework based on numerical integration is further developed. The non-intrusive dimension reduction method is also adopted to obtain the statistical moments and probability density function. The proposed SS-FEM can capture the structural stochastic responses under uncertainty condition by combining gradient smoothing technology and uncertainty quantification. A number of engineering examples are compared with the solution of Monte Carlo simulation to demonstrate both the accuracy and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]