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| Some studies on mathematical models for general elastic multi-structures | |
| 作者姓名： | HUANG Jianguo SHI Zhongci & XU Yifeng |
| 作者单位： | HUANG Jianguo，SHI Zhongci & XU Yifeng Department of Mathematics，Shanghai Jiaotong University，Shanghai 200240，China，Division of Computational Science，E-lnstitute of Shanghai Universities，Shanghai Normal University，China，Institute of Computational Mathematics，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China |
| 基金项目： | 国家重点基础研究发展计划(973计划)，上海市高等学校社会学E-研究院资助项目，上海市自然科学基金 |
| 摘 要： | The aim of this paper is to study the static problem about a general elastic multi-structure composed of an arbitrary number of elastic bodies, plates and rods. The mathematical model is derived by the variational principle and the principle of virtual work in a vector way. The unique solvability of the resulting problem is proved by the Lax-Milgram lemma after the presentation of a generalized Korn's inequality on general elastic multi-structures. The equilibrium equations are obtained rigorously by only assuming some reasonable regularity of the solution. An important identity is also given which is essential in the finite element analysis for the problem. |
| 收稿时间： | 6 September 2004 |
Some studies on mathematical models for general elastic multi-structures |
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| HUANG Jianguo,SHI Zhongci & XU Yifeng.Some studies on mathematical models for general elastic multi-structures[J].Science in China(Mathematics),2005,48(7):986-1007. | |
| Authors: | HUANG Jianguo SHI ZHONGCI XU Yifeng |
| Institution: | 1. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China;Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University,China 2. Institute of Computational Mathematics, Academy of Mathematics .and System Sciences, Chinese Academy of Sciences, Beijing 100080, China 3. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
| Abstract: | The aim of this paper is to study the static problem about a general elastic multi-structure composed of an arbitrary number of elastic bodies, plates and rods. The mathematical model is derived by the variational principle and the principle of virtual work in a vector way. The unique solvability of the resulting problem is proved by the Lax-Milgram lemma after the presentation of a generalized Korn's inequality on general elastic multi-structures. The equilibrium equations are obtained rigorously by only assuming some reasonable regularity of the solution. An important identity is also given which is essential in the finite element analysis for the problem. |
| Keywords: | elastic multi-structures mathematical models unique solvability generalized Korn's inequality equilibrium equations |
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