| 正交各向异性轴对称位势问题的Trefftz有限元分析 |
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| 引用本文： | 王克用,黄争鸣,李培超,刘博.正交各向异性轴对称位势问题的Trefftz有限元分析[J].应用数学和力学,2013,34(5):462-469. |
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| 作者姓名： | 王克用 黄争鸣 李培超 刘博 |
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| 作者单位： | 1上海工程技术大学 机械工程学院,上海 201620;2同济大学 航空航天与力学学院,上海 200092 |
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| 基金项目： | 上海高校青年骨干教师国内访问学者计划基金，上海高校青年骨干教师国内访问学者计划基金和校启基金(2012-gp04)资助;特此感谢 |
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| 摘 要： | Trefftz有限元法（Trefftz finite element method, TFEM）因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题，提出了一种4节点四边形环状单元．在该单元模型中，首先假设两套独立的位势插值模式:即单元域内场和网线场，然后代入修正变分泛函并利用Gauss散度定理消除区域积分，最后根据驻值原理导得只含边界积分的单元刚度方程．数值算例表明了该单元的准确性、稳定性以及对网格畸变的不敏感性.
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| 关 键 词： | Trefftz有限元法 修正变分泛函 位势问题 轴对称 正交各向异性介质 |
| 收稿时间： | 2013-03-04 |
Trefftz Finite Element Analysis of Axisymmetric Potential Problems in Orthotropic Media |
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| Institution: | 1School of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, P.R.China;2School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P.R.China |
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| Abstract: | Trefftz finite element method (TFEM) has received considerable attention due to its excellent feasures. A four-node quadrilateral annular element was proposed for analyzing axisymmetric potential problems in orthotropic media. In the element model, two independent potential interpolation modes, namely intra element field and frame field, were firstly assumed. Then, they were both substituted into the modified variational functional and the domain integral involved was eliminated using the Gaussian divergence theorem. Finally, the element stiffness equation including boundary integrals only was derived based on the stationary principle. Numerical examples demonstrate that the developed element is accurate, stable and insensitive to mesh distortion. |
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