轴对称Poisson方程的Trefftz有限元解法

刘博; 王克用; 王明红

doi:10.3879/j.issn.1000-0887.2015.02.003

轴对称Poisson方程的Trefftz有限元解法

doi: 10.3879/j.issn.1000-0887.2015.02.003

¹上海工程技术大学机械工程学院,上海 201620;²美国加州大学机械工程系,美国加利福尼亚河滨 92507

基金项目: 上海高校青年骨干教师国外访问学者计划

详细信息

作者简介:
刘博（1990—），男，河南南阳人，硕士生（E-mail: 708989488@qq.com）；王克用（1975—），男，河北唐山人，讲师，博士（通讯作者. E-mail: keyong.wang@hotmail.com）.

中图分类号: O242.21;O242.82
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出版历程
- 收稿日期: 2014-09-09
- 修回日期: 2014-11-13
- 刊出日期: 2015-02-15

A Trefftz Finite Element Method for Solving Axisymmetric Poisson’s Equations

¹School of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, P.R.China;²Department of Mechanical Engineering, University of California, Riverside, CA 92507, USA

摘要

摘要: 将径向基函数应用到一类轴对称Poisson方程的数值求解中，提出了一种Trefftz有限元计算格式.非0右端项将问题的特解引入Trefftz单元域内场，致使单元刚度方程涉及区域积分.利用径向基函数对特解近似处理，可消除区域积分，从而保持Trefftz有限元法只含边界积分的优势.为获得特解，选取求解域内所有单元的节点和形心作为基本插值点，而在求解域之外构造一个虚拟边界，在其上布置一定数目的虚拟点作为额外插值点.数值算例验证了该方法的有效性和可行性.
- 轴对称Poisson方程 /
- Trefftz有限元法 /
- 径向基函数 /
- 完全椭圆积分
Abstract: A Trefftz finite element formulation was proposed for solving a kind of axisymmetric Poisson’s equations by means of the radial basis functions (RBFs). The non-zero right-hand side term brought the particular solution into the Trefftz intra-element field, which gave rise to domain integration related to the resultant element stiffness equation. The involved domain integration was eliminated through approximation of the particular solution with the RBFs. Furthermore, the‘boundary integration only’advantages were preserved for the Trefftz finite element method (TFEM). To obtain the particular solution, all elemental nodes and centroids in the whole solution domain were chosen as the fundamental interpolation points. In the meantime, a virtual boundary was constructed outside the solution domain, and a number of virtual points were selected as the additional interpolation points on the virtual boundary. Numerical examples demonstrate that the proposed method is valid and applicable.
- BEM in time domain /
- saturated porous medium /
- dynamic response /
- Green’s function

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参考文献(12)

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