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Some studies on mathematical models for general elastic multi-structures

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Abstract

The aim of this paper is to study the static problem about a general elastic multistructure 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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiaotong University, 200240, Shanghai, China

    Huang Jianguo & Xu Yifeng

  2. Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, China

    Huang Jianguo

  3. Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, China

    Shi Zhongci

Authors
  1. Huang Jianguo
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  2. Shi Zhongci
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  3. Xu Yifeng
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Correspondence to Huang Jianguo.

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Jianguo, H., Zhongci, S. & Yifeng, X. Some studies on mathematical models for general elastic multi-structures. Sci. China Ser. A-Math. 48, 986–1007 (2005). https://doi.org/10.1007/BF02879079

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  • DOI: https://doi.org/10.1007/BF02879079

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