Unconventional Hamilton-type variational principles for nonlinear elastodynamics of orthogonal cable-net structures |
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Authors: | Li Wei-hua Luo En Huang Wei-jiang |
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Institution: | Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China |
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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 unconven- tional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically,which can fully charac- terize the initial-boundary-value problem of this kind of dynamics.An important in- tegral relation is made,which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechan- ics.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 functionais 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 poten- tial energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the general- ized Legendre transformation given in this paper.Furthermore,the intrinsic relationship among various principles can be explained clearly with this approach. |
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Keywords: | unconventional Hamilton-type variational principle geometric nonlinearity elastodynamics orthogonal cable-net structures dual-complementary relation initialboundary-value problem phase space |
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