| 轴对称弹性动力学问题的重构核插值法 |
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| 引用本文： | 陈莘莘,曾佳伟.轴对称弹性动力学问题的重构核插值法[J].应用数学和力学,2019,40(8):938-944. |
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| 作者姓名： | 陈莘莘 曾佳伟 |
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| 作者单位： | 华东交通大学 土木建筑学院, 南昌 330013 |
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| 基金项目： | 国家自然科学基金（11462006;11772129） |
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| 摘 要： | 重构核插值法是近年来提出的一种新型无网格方法.该方法的形函数具有点插值性和高阶光滑性，不仅能够直接施加本质边界条件，而且能保证较高的计算精度.为了更有效地求解三维轴对称弹性动力学问题，对重构核插值法(reproducing kernel interpolation method, RKIM)应用于此类问题进行了研究，并发展了相应的数值模拟方法.由于几何形状和边界条件的轴对称性，计算时只需要横截面上离散节点的信息，因而前处理变得简单.采用Newmark-β法进行了时域积分.数值算例表明，轴对称弹性动力学分析的重构核插值法既有无网格方法的优势，又有较高的计算精度.
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| 关 键 词： | 弹性动力学 轴对称 无网格法 重构核插值法 |
| 收稿时间： | 2018-09-13 |
A Reproducing Kernel Interpolation Method for Axisymmetric Elastodynamic Problems |
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| Affiliation: | School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, P.R.China |
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| Abstract: | The reproducing kernel interpolation method (RKIM) is a novel type of meshless method emerging in recent years. Because the shape functions of the RKIM have point interpolation property and high-order smoothness, the essential boundary conditions can be imposed directly and high computational accuracy is ensured as well. In order to solve the elastodynamic problems for 3D axisymmetric solids more effectively, a novel numerical method based on the RKIM was presented and discussed. Due to axial symmetry of geometry and boundary conditions, only a set of discrete nodes on a cross section are required in the computation and therefore the preprocessing of this method is very simple. The Newmark-β algorithm was employed for time integration. Numerical examples show that, the proposed method for solving axisymmetric elastodynamic problems possesses the advantages of meshless methods and high accuracy. |
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