加权最小二乘无网格法的随机稳态温度场分析

Meshless weighted least square method for thermal analysis of stochastic steady-state temperature field

对加权最小二乘无网格法在随机稳态温度场中的应用进行了研究.在移动最小二乘近似的基础上,采用罚函数法满足边界条件,通过变分原理详细推导了求解稳态温度场问题的加权最小二乘无网格公式,与无网格伽辽金法相比,该方法无须进行高斯积分,具有计算量小、处理方便等优点.同时考虑结构物理参数和边界条件随机性的影响,利用Neumann展开蒙特卡罗法对含有随机参数温度场的加权最小二乘无网格方程进行求解,得到了温度场响应量的统计特征值并考察了各随机参数对节点温度的影响.通过数值算例分析结果与有限元方法所得结果进行比较,验证了本方法的正确性和有效性.

A meshless weighted least square （MWLS） method was investigated for the analysis of sto‐chastic steady‐state temperature field .Based on the moving least‐squares （MLS） approximation ,the penalty function method was used to satisfy the boundary conditions ,and the MWLS equation was de‐rived in detail by variation principle for solving the steady‐state temperature field problems .Compared with Galerkin based meshless method ,the proposed method has a small amount of calculation without integration ,which is easy for process and some other advantages .By considering the randomness of physical parameters and boundary condition ,the MWLS of stochastic temperature field with random variables w as derived ,and the statistics feature of response of stochastic steady‐state temperature field was obtained by Neumann expansion Monte Carlo method .Numerical examples comparison between the results of the proposed method and the finite element method simulation was presented to illus‐trate the effectiveness and validity of proposed method .