中文摘要：

通过罗恩已提出的一条简单而统一的新途径,系统地建立了离散索网模型的正交索网结构几何非线性弹性静力学的各类变分原理。文中首先给出正交索网结构几何非线性静力学的广义虚功原理的表式,然后从该式出发,不仅能得到正交索网结构几何非线性静力学的虚功原理,而且通过所给出的广义Legendre变换,还能系统地成对导出正交索网结构几何非线性弹性静力学的3类变量、2类变量变分原理、以及总势能驻值原理和总余能驻值原理的互补泛函。同时,通过这条新途径还能清楚地阐明这些原理的内在联系。

英文摘要：

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.