摘要
根据古典阴阳互补和现代对偶互补的基本思想,系统地建立了分段线性弹性薄板动力学的各类非传统Hamilton增量变分原理。而这种非传统Hamilton型增量变分原理能反映分段线性弹性薄板动力学初值-边值问题的全部特征。文中给出一个重要的积分关系式,可以认为,在力学上它是分段线性弹性薄板动力学增量广义虚功原理的表式。从该式出发,不仅能得到薄板动力学的增量虚功原理,而且通过所给出的一系列广义Legendre变换,能系统地成对导出分段线性弹性薄板动力学的5类变量、3类变量、2类变量非传统Hamilton型增量变分原理的互补泛函,以及1类变量和相空间非传统Hamilton型增量变分原理的泛函。同时,通过这条新途径还能清楚地阐明这些原理之间的内在联系。
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity,in a simple and unified way proposed by Luo,the unconventional Hamilton-type incremental variational principles for piece- wise linear elstodynamics of thin plates were established systematically.The principles can fully characterize the initial- boundary-value problem with regard to piecewise linear elstodynamics of thin plate.An important integral relation was giv- en,which can be considered as the expression of the corresponding generalized principle of virtual work.Based on the re- lation and the generalized Legendre transformations the complementary functionals for five-fields,three-fields and two- fields unconventional Hamilton-type incremental variational principles,as well as the functional for one-field principles and the principle in phase space were derived systematically.With the proposed approach,the intrinsic relationship a- mong various principles can be explained clearly.
出处
《振动与冲击》
EI
CSCD
北大核心
2008年第11期109-114,共6页
Journal of Vibration and Shock
基金
国家自然科学基金(10172097)
(10772203)
高校博士点科研基金(20030558025)资助项目
关键词
非传统Hamilton型增量变分原理
对偶互补
初值-边值问题
限制变分
相空间
unconventional Hamilton-type incremental variational principle
dual-complementary relation
initialboundary-value problem
restricted variation
phase space
