随机温度场Monte-Carlo法的一类近似处理  

Approximate Method of Monte-Carlo Method in Stochastic Temperature Field

作　　者：王小兵[1] 陈建军[1] 梁震涛[1] 李金平[1] 

机构地区：[1]西安电子科技大学机电工程学院,西安710071

出　　处：《系统仿真学报》2007年第10期2156-2160,2164,共6页Journal of System Simulation

基　　金：陕西省自然科学基金(2005A009);国防预研基金资助(51421060505DZ0155)

摘　　要：以非线性热辐射边界条件下多种材料构成的层叠板为研究对象,利用伽辽金法得到了瞬态非线性热传导微分方程组。考虑结构所有物理、几何和环境参数均具有随机性时,通过引入随机因子并提出一类关于热传导矩阵和热容矩阵的近似处理方法,实现了对随机温度场Monte-Carlo数值模拟时间的节省;并通过灵敏度和一阶泰勒展开线性化的方法去近似求解由于前面近似处理所造成的温度场数字特征的误差;算例表明了所给方法能节省大量的Monte-Carlo数值模拟时间,且给出的误差估计具有一定的精度。For laminated plates with materials different in each layer, under the radiation boundary condition, its transient nonlinear differential equations were derived by means of Galerkin method. When all parameters were stochastic, in order to decrease the operating time of Monte-Carlo method, by introducing random factor, an approximate treatment of heat conduction matrix and heat capacity matrix was proposed. The errors of temperature＇s numerical characteristics caused by that approximate treatment method were computed approximately by computing sensitivity and the linearization technique of first order Taylor series expansion. A 3-layer plates is taken as an example, which shows that the time can be saved largely, and the estimated error has precision in a certain extent.

关 键 词：有限元法 MONTE-CARLO法 数字仿真 随机温度场 运算时间 

分 类 号：TB131[理学—物理] O211.5[理学—应用物理]