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利用Neumann展开Monte-Carlo随机有限元法对瞬态随机温度场求解进行了分析,根据计算流程框图编写了求解瞬态随机温度场的Matlab随机有限元计算实施程序.对于每一次随机抽样,文中方法只需形成刚度矩阵,进行前代、回代以及矩阵乘和矩阵加减,便可求得各时刻温度场.因计算中无需矩阵求逆,可大大减少计算量,有限元节点数目越大,计算速度优势越明显.为说明解法的可行性及高效性,算例考虑了导热系数、比热容、换热系数、热流密度、环境温度、介质密度以及内热源等物理参数单独和同时具有随机性的瞬态随机温度场情况.结果表明:Neumann展开Monte-Carlo随机有限元法能有效解决瞬态随机温度场问题,且效率较高;编制的Matlab随机有限元计算程序可直接输出各时刻温度场的统计结果;各随机参数对温度场响应随机性的影响有差异.
Neumann developed Monte-Carlo stochastic finite element method to solve the transient random temperature field is analyzed, according to the calculation flow block diagram to solve transient random temperature field Matlab finite element calculation implementation of the program.For each random sampling, the method Only need to form the stiffness matrix, the predecessors, back to the generation and the matrix multiplication and matrix addition and subtraction, we can get the temperature field at each time.For the calculation without matrix inversion, can greatly reduce the amount of computation, the greater the number of finite element nodes, The more obvious the computational speed advantage is.To illustrate the feasibility and efficiency of the solution, the example considers the thermal conductivity, specific heat capacity, heat transfer coefficient, heat flux density, ambient temperature, dielectric density and physical parameters such as heat source separately and at the same time have random Transient stochastic temperature field.The results show that the Neumann expansion Monte-Carlo stochastic finite element method can effectively solve the transient stochastic temperature field problem and has high efficiency; the prepared Matlab stochastic finite element program can directly output the temperature field at each moment Statistical results; The random parameters have different effects on the randomness of the temperature field response.