摘要
根据古典阴阳互补和现代对偶互补的基本思想,通过早已提出的一条简单而统一的新途径,系统地建立了Reissner夹层板动力学的各类非传统Hamilton型变分原理.这种新的非传统Hamilton型变分原理能反映这种动力学初值_边值问题的全部特征.文中首先给出一个Reissner夹层板广义虚功原理的表式.然后从该式出发,不仅能得到Reissner夹层板动力学的虚功原理,而且通过所给出的一系列广义Legendre变换,还能系统地成对导出五类变量、二类变量和一类变量非传统Hamilton型变分原理的互补泛函.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.
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified way proposed by Luo（1987）, some unconventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically. The unconventional Hamilton-type variation principle can fully characterize the initial-boundary-value problem of this dynamics.An important integral relation is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work,in dynamics of Reissner sandwich plate,but also to derive systematically the complementary functionais for five-field, two-field and one-field unconventional Hamilton-type variational principles by the generalized Legendre transformations. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly.
出处
《应用数学和力学》
CSCD
北大核心
2006年第1期67-74,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10172097)
高校博士点基金资助项目(20030558025)
