VARIATIONAL PRINCIPLES FOR NONLINEAR ELASTOSTATICS OF MEMBRANE STRUCTURES

By a simple and unified new way proposed by Luo, some variational principles for nonlinear elastostatics of membrane structures can be established systematically. An important integral relation is given, which can be considered as the generalized principle of virtual work for statics of membrane structures in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work for statics of membrane structures, but also to derive systematically the complementary functionals for three-field, two-field variational principles and principles of stationary total potential energy and stationary total complementary energy for nonlinear elastostatics of membrane structures by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly.