According to the basic idea of classical yinyang complementarity and modern dualcomplementarity, in a new, simple and unified way proposed by Luo, the unconventional Hamiltontype variational principles for geometrically nonlinear elastodynamics of membrane structures can be established systematically. The unconventional Hamiltontype variational principle can fully characterize the initialboundaryvalue problem of geometrically nonlinear elastodynamics. An important integral relation is given, which can be considered as the generalized principle of virtual work for dynamics of membrane structures in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work for dynamics of membrane structures, but also to derive systematically the complementary functionals for fivefield (pα,pβ,pγ,vα,vβ,vγ,Nα,Nβ,Sαβ,εα,εβ,εαβ,u,v,w),fourfield (pα,pβ,pγ,Nα,Nβ,Sαβ,εα,εβ,εαβ,u,v,w),threefield (Nα,Nβ,Sαβ,εα,εβ,εαβ,u,v,w) and twofield (Nα,Nβ,Sαβ,u,v,w) unconventional Hamiltontype variational principles. And the functional for the unconventional Hamiltontype variational principle in phase space(pα,pβ,pγ,u,v,w) and the potential energy functional for onefield (u,v,w)unconventional Hamiltontype variational principle for geometrically nonlinear elastodynamics of membrane structures are obtained by the generalized Legendre transformation. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.