Abstract: To solve the stochastic parameter variation problem in engineering structures， the cell-based stochastic smoothed finite element method was proposed based on the orthogonal expansion theory. In the method， the Karhunen-Loève series orthogonally decompose the random field into independent random variables and the chaotic polynomial expands the random displacement response， and then the expended random field and displacement response are introduced into the cell-based stochastic smoothed finite element. The equilibrium equation of the proposed method is derived， and the computational formulas of the covariance matrix and the mean structural displacement are given. The numerical calculation indicates that the method has low meshing requirements and high precision. The random response of the square plate with a hole which has random material characteristics was further analyzed. The numerical results show that the proposed method is correct and feasible.

Key words: cell-based stochastic smoothed finite element, Karhunen-Loève expansion, chaotic polynomial, gradient smoothing technology, random field