温度场分析的重构核粒子边界无单元法  

Reproducing Kernel Particle Boundary Element-free Method for Temperature Field Problems

作　　者：秦义校[1,2] 程玉民[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]太原科技大学机电工程学院,太原030024

出　　处：《机械工程学报》2008年第6期95-100,共6页Journal of Mechanical Engineering

基　　金：国家自然科学基金(10571118);山西省自然科学基金(20051061)资助项目

摘　　要：将重构核粒子法和Laplace方程的边界积分方程方法结合,提出温度场分析的重构核粒子边界无单元法。推导Laplace方程边值问题的重构核粒子边界无单元法公式,建立相应的重构核粒子边界无单元法离散化方程。重构核粒子法构造的形函数具有不低于核函数的高阶光滑性,能精确重构插值点多项式的真值。数值算例表明,温度场分析的重构核粒子边界无单元法既有无网格方法的优势,又具有较高精度。Combining the reproducing kernel particle method （RKPM） and boundary integral equations of Laplace equation, the reproducing kernel particle boundary element-free （RKP-BEF） method for temperature field is developed. The formulae of the method are derived for temperature field problems governed by 2-D Laplace equation. The discrete boundary integral equation of the reproducing kernel particle boundary element-free method is obtained. The smoothness of the shape function of RKPM is no less than that of the kernel function and the true values of polynomials at interpolating points can be exactly reconstructed. The numerical examples are given, and it is shown that the reproducing kernel particle boundary element-free method for temperature field has the advantages of meshless method and high precision.

关 键 词：温度场 重构核粒子法 边界积分方程 边界无单元法 

分 类 号：TB1[一般工业技术] O29[理学—应用数学]