In a simple and unified new way proposed by Luo

some variational principles for geometrically nonlinear elastostatics of orthogonal cable-net structures based on discrete model are established systematically.An important integral relation is given

which can be considered as the generalized principle of virtual work for geometrically nonlinear statics 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 statics of orthogonal cable-net 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 geometrically nonlinear elastostatics of orthogonal cable-net structures by the generalized Legendre transformations given in this paper.Furthermore

with this approach

the intrinsic relationship among the various principles is explained clearly.