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Applied Mathematics and Mechanics

, Volume 28, Issue 7, pp 931–942 | Cite as

Unconventional Hamilton-type variational principles for nonlinear elastodynamics of orthogonal cable-net structures

  • Li Wei-hua  (李纬华)
  • Luo En  (罗恩)Email author
  • Huang Wei-jiang  (黄伟江)
Article

Abstract

According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An important integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper. Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.

Key words

unconventional Hamilton-type variational principle geometric nonlinearity elastodynamics orthogonal cable-net structures dual-complementary relation initialboundary-value problem phase space 

Chinese Library Classification

O316 O342 

2000 Mathematics Subject Classification

74K05 74K10 49S05 

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References

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Li Wei-hua  (李纬华)
    • 1
  • Luo En  (罗恩)
    • 1
    Email author
  • Huang Wei-jiang  (黄伟江)
    • 1
  1. 1.Department of Applied Mechanics and EngineeringSun Yat-sen UniversityGuangzhouP. R. China

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