| 正交各向异性薄板弯曲问题分裂模量有限元法 |
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| 引用本文： | 党发宁,荣廷玉,孙训方.正交各向异性薄板弯曲问题分裂模量有限元法[J].应用数学和力学,2001,22(9):943-951. |
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| 作者姓名： | 党发宁 荣廷玉 孙训方 |
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| 作者单位： | 1. 西安理工大学岩土工程研究所西安 710048
2. 西南交通大学应用力学与工程系成都 610031 |
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| 基金项目： | 国家博士后科学基金资助项目 |
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| 摘 要： | 讨论了建立分裂模量有限元法的必要性，推导出了正交各向异性薄板变曲问题分裂模量变分原理的函数，以此为基础建立了该问题的分裂模量有限元法。该模型的特点是其中含有一个被称为分裂因子的参数，通过算例说明：适当调整分裂因子的值，可以达到调整有限元模型的刚度，降低有限元刚度矩阵的谱条件数，克服常规有限元病态问题的目的，最后分析了克服病态问题的机理。
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| 关 键 词： | 分裂模量 变分原理 有限元法 各向异性 病态问题 正交各向异性 薄板弯曲问题 |
| 文章编号： | 10000887(2001)07094309 |
| 修稿时间： | 2000年2月28日 |
Splitting Modulus Finite Element Method for Orthogonal Anisotropic Plate Bending |
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| DANG Fa_ning,RONG Ting_yu ,SUN Xun_fang.Splitting Modulus Finite Element Method for Orthogonal Anisotropic Plate Bending[J].Applied Mathematics and Mechanics,2001,22(9):943-951. |
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| Authors: | DANG Fa_ning RONG Ting_yu SUN Xun_fang |
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| Institution: | DANG Fa_ning1,RONG Ting_yu 2,SUN Xun_fang 2 |
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| Abstract: | Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill_conditioned problems in usual finite elements. The cause why the new method could transform the ill_conditioned problems into well_conditioned problem, is analyzed finally. |
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| Keywords: | splitting modulus variational principle method of splitting modulus finite elements anisotropic ill-conditioned problems |
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