平面框架结构折线型弹塑性动力学非传统Hamilton型增量变分原理  

THE UNCONVENTIONAL HAMILTON-TYPE INCREMENTAL VARIATIONAL PRINCIPLES FOR PIECEWISE LINEAR ELASTODYNAMICS OF FRAME STRUCTURE

作　　者：姜凤华[1] 罗恩[2] 

机构地区：[1]台州学院建筑工程学院,台州318000 [2]中山大学应用力学与工程系,广州510275

出　　处：《动力学与控制学报》2015年第4期256-265,共10页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10772203);浙江省科技厅公益技术应用研究资助项目(2011C31032)~~

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,系统地建立了平面框架结构折线型弹塑性动力学的各类非传统Hamilton型变分原理.文中首先给出平面框架结构折线型弹塑性动力学的广义虚功原理的表式,然后从该式出发,不仅能得到平面框架结构折线型弹塑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平面框架结构折线型弹塑性动力学的5类变量分原理的互补泛函,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.According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type incremental variational prin- ciples for broken line elasto-plastic dynamics of frame structure can be established systematically. The unconven- tional Hamilton-type incremental variational principle can fully characterize the initial-boundary-value problem of broken line elasto-plastic dynamics of frame structure. In this paper, an important integral relation was given, which can be considered as the expression of the generalized principle of virtual work for broken line elasto-plastic dynamics of frame structure. Based on this relation, it is possible to derive systematically the complementary functionals for five-field, and the functional for one-field unconventional Hamilton-type incremental variational principles and the unconventional Hamihon-type incremental variational principle in phase space by the general- ized Legendre transformations were also given. Furthermore, with this new approach, the intrinsic relationship a- mong various principles can be explained clearly.

关 键 词：框架结构 弹塑性动力学 相空间 非传统HAMILTON型变分原理 初值-边值问题 

分 类 号：O344.3[理学—固体力学] O302[理学—力学]