【摘要】 根据古典阴阳互补和现代对偶互补的基本思想,通过罗恩提出的一条简单而统一的新途径,系统地建立了空间框架结构弹性动力学的各类非传统Hamilton型变分原理.文中首先给出空间框架结构弹性动力学的广义虚功原理的表式,然后从该式出发,不仅能得到空间框架结构弹性动力学的虚功原理,而且通过所给出的广义Legendre变换,还能系统地成对导出空间框架结构弹性动力学的5类变量、3类变量、2类变量变分原理的互补泛函,以及1类变量和相空间非传统Hamilton型变分原理的泛函.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.更多还原

【Abstract】 According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified new way proposed by Luo,the unconventional Hamilton-type variational principles for elasto-dynamics of space frame structures were established systematically. The unconventional Hamilton-type variational principle can fully characterize the initial-boundary-value problem of space frame structures’ elasto-dynamics. In this paper,an important integral relation was given,which can be considered as the expression of the generalized principle of virtual work for elasto-dynamics of space frame structures. Based on this relation,it is possible not only to obtain the principle of virtual work for elasto-dynamics of space frame structures,but also to derive systematically the complementary functionals for five-field,three-field and two-field unconventional Hamilton-type variational principles,and the functional for one-field and the unconventional Hamilton-type variational principle in phase space by the generalized Legendre transformations given in this paper. Furthermore,with this new approach,the intrinsic relationship among various principles can be explained clearly.更多还原