## THERMAL SCIENCE

International Scientific Journal

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### Leijian Yin

online first only

### A local average method for stochastic thermal analysis under heat conduction conditions

ABSTRACT
In this paper, a new triangular discretization method for two-dimensional random field is proposed, and thecomputational formula of the covariance for any two triangular random field elements is developed. Its main advantage, compared to thequadrilateral discretization method, is that triangular local average method can perfectly combine with thetriangular 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 beencompiled by Matrix Laboratory (MATLAB) 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.
KEYWORDS
PAPER SUBMITTED: 2017-01-13
PAPER REVISED: 2017-08-16
PAPER ACCEPTED: 2017-09-09
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI170113181W
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