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二维耦合热弹性动力学问题的无网格自然邻接点Petrov-Galerkin法
李庆华, 陈莘莘
华东交通大学 土木建筑学院, 南昌 330013
摘要:
为了更有效地求解二维耦合热弹性动力学问题,对无网格自然邻接点Petrov-Galerkin法在此类问题中的应用进行了研究,并发展了相应的计算方法。该方法建立试函数时可以只依赖于一组离散的节点,有效地避免了复杂的网格划分和网格畸变的影响。相对于常用的移动最小二乘而言,自然邻接点插值不涉及复杂的矩阵求逆运算,更不需要任何人为参数。由于运动方程和瞬态热传导方程相互影响,这些方程必须联立求解。采用Newmark法求解空间离散后得到的二阶常微分方程组,进而可直接获得温度场和位移场的数值结果。
关键词:  无网格法  自然邻接点插值  耦合热弹性动力学  Petrov-Galerkin法
DOI:10.11835/j.issn.2096-6717.2019.101
分类号:TP301.6
基金项目:国家自然科学基金(21466012);江西省教育厅项目(KJLD14041)
Meshless natural neighbour Petrov-Galerkin method for two-dimensional dynamic coupled thermoelasticity problem
Li Qinghua, Chen Shenshen
School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, P. R. China
Abstract:
In order to solve the two-dimensional dynamic coupled thermoelasticity problem more effectively, a novel numerical method based on the meshless natural neighbour Petrov-Galerkin method is proposed in this study. Only a group of scattered nodes are required in this method, to construct approximation function and therefore complex meshing and disadvantage of mesh distortion are effectively eliminated. In comparison with the moving least-squares (MLS) approximation used widely in meshless methods, the natural neighbour interpolation requires no complex matrix inversions and no artificial intermediate parameters. The equations of motion and transient heat conduction equations of the coupled thermoelasticity interaction on each other and therefore these equations must be solved simultaneously. After spatially discretization, a series of second-order ordinary differential algebraic equations is obtained, which is solved by the Newmark method to obtain the numerical temperature and displacement field directly.
Key words:  meshless method  natural neighbour interpolation  dynamic coupled thermoelasticity  Petrov-Galerkin method
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