Finite Element Analysis For Two-dimensional Thermal Structures With Uncertain Parameters

The research about finite element analysis for two-dimensional thermal structures with uncertain parameters has extensive engineering-background, important theory meaning and academic value. This paper proposed the random factor method which is used in random structure to solve the random thermal field. And the features expressions of structure response random variable are deduced. The degrees of random parameters effect to structure response are analyzed. Based on above argument, this paper obtained the expectation and variance of the response of structures using Monte-Carlo digital simulation. To the problem of uncertain parameters transient temperature field,a method that each parameter of heat conduction is regarded as interval parameters is presented. Global stiffness matrix,thermal matrix and equivalent loads vector of uncertain structure are deduced using Taylor expansion and interval extension of function. At the same time, transient heat transfer problem is converted to static heat transfer problem. Certain quantity and uncertain quantity of temperature field is calculated with matrix perturbation method. Finally a numerical examples show that the methods in this paper are valid and feasible.