摘要

In this paper, a new triangular discretization method for 2-D random field is proposed, and the computational formula of the covariance for any two triangular random field elements is developed. Its main advantage, compared to the quadrilateral discretization method, is that triangular local average method can perfectly combine with the triangular finite element method. Also, the corresponding relation is clearer and the computer codes are simpler. Based on the new local average method, a numerical analysis for random temperature field of geotechnical structures under heat conduction conditions is presented by the Monte-Carlo method, and the computational formulas of mathematical expectation matrix and standard deviation matrix are provided. A series of computer codes have been compiled by Matrix Laboratory software. A numerical example is presented to demonstrate the random effects of uncertain parameters, and the accurateness of the proposed approach is proven by comparing these results with the results derived from quadrilateral local average method.

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