LI Wei-hua, LUO En, HUANG Wei-jiang. Unconventional Hamilton-Type Variational Principles for Nonlinear Elastodynamics of Orthogonal Cable-Net Structures[J]. Applied Mathematics and Mechanics, 2007, 28(7): 833-842.
Citation: LI Wei-hua, LUO En, HUANG Wei-jiang. Unconventional Hamilton-Type Variational Principles for Nonlinear Elastodynamics of Orthogonal Cable-Net Structures[J]. Applied Mathematics and Mechanics, 2007, 28(7): 833-842.

Unconventional Hamilton-Type Variational Principles for Nonlinear Elastodynamics of Orthogonal Cable-Net Structures

  • Received Date: 2006-08-09
  • Rev Recd Date: 2007-05-08
  • Publish Date: 2007-07-15
  • According to the basic idea of classical yin-yang complementarity and modern 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 can be established systematically. The unconventional Hamilton-type variational principle can fully characterize the initia-l boundary-value problem of this dynamics. An important integral relation was given, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on this relation, 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. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.
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