1) unconventional Hamilton-type variational principle
非传统Hamilton型变分原理
1.
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, the unconventional Hamilton-type variational principle in phase space for dynamics of elastic foundation beam with linear damping is established, which can fully characterize the initial-boundary-value problem of this dynamics.
本文根据古典阴阳互补和现代对偶互补的基本思想,首次建立了线性阻尼情形下弹性地基梁动力学的相空间(挠度、动量)非传统Hamilton型变分原理。
2.
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.
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。
3.
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a new,simple and unified way proposed by Luo,the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of membrane structures can be established systematically.
根据古典阴阳互补和现代对偶互补的基本思想,通过罗恩早已提出的一条简单而统一的新途径,系统地建立了弹性膜结构动力学的各类非传统Hamilton型变分原理。
3) unconventional Hamilton-type incremental variational principle
非传统Hamilton型增量变分原理
1.
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.
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。
4) unconventional Hamilton variational principle in phase space
相空间非传统Hamilton变分原理
1.
In a simple and unified new way proposed by Luo, the unconventional Hamilton variational principle in phase space for dynamics of honeycomb sandwich plates is established, and the Hamilton canonical equations, boundary and initial conditions can be derived from this variational principle.
通过作者早已提出的一条简单而统一的新途径,建立了蜂窝夹层板动力学的相空间非传统Hamilton变分原理,并从该原理推导出相应的Ham-ilton正则方程、边界条件与初始条件。
2.
According to a simple and unified way proposed by Luo,the unconventional Hamilton variational principle in phase space for dynamics of elastic thin plates is established,and the Hamilton canonical equations,boundary and initial conditions can be derived from this variational principle.
通过罗恩提出的一条简单而统一的途径,建立了弹性薄板动力学的相空间非传统Hamilton变分原理,并从该原理推导出相应的Hamilton正则方程、边界条件与初始条件。
5) Hamilton-type quasi-variational principle
Hamilton型拟变分原理
1.
One-field Hamilton-type quasi-variational principle in linear damping elastodynamics of the rigid and elastic supported beam is established which can fully characterize the initial-boundary-value problem of this dynamics.
首先建立了能反映动力学初值—边值问题的全部特征的有阻尼刚性与弹性支承梁动力学的一类变量广义Hamilton型拟变分原理,然后提出拉格朗日力学体系下的空间有限元—时间子域法,该法对空间域采用有限元来离散,而时间子域采用5次Hermite插值多项式插值。
6) unconventional Gurtin-type variational principle
非传统Gurtin型变分原理
补充资料：变分原理(复变函数论中的)
变分原理(复变函数论中的)
omplex function theory) variational principles (in
f日In}F(O(只，t)，0)l}乙+:d乙=】nll，—}——，厂:’、一几t)〔.匕，日亡卜OC一“C’日当r，0时下*(:、，t)/:在B*的紧子集上一致地趋于0(k一1，2).该结果已被推广到二连通区域(13」).若加以进一步的限制，就能得到映射函数在B、(t)内关于表征所考虑区域边界形变的参数的展开式余项的估计式(在闭区域内一致)(【4」).份卜注】存在大量的变分原理，见【A3}第10章.亦可见变分参数法(variation一parametrie nlethod);肠”ner方法(幼wner Tnetl〕ed);内变分方法(internalvariations，服t】1‘对of). 还可见边界变分方法(boundary variations，me-tll‘xlof).M.schiffer对单叶函数的变分方法做出了重要的贡献，见〔A3」第10章.变分原理(复变函数论中的)Ivaria石0“目州址妙es(加e网Plex五叮‘6佣山印ry);。即“a双“OHH从e nP一”u“nHI 显示在平面区域的某些形变过程中那些支配映射函数变分的法则的断语. 主要的定性变分原理是ljxlelbf原理(Linde场fpnnciPle)，可描述如下.设B*是z*平面上边界点多于一点的单连通区域，06B*，k=1，2;设二(;，B*)是对于B*的Green函数的阶层曲线，即圆盘王心川C!<1}到B*而使原点保持不变的单叶共形映上映射下圆周C(r)二{乙:{心}二;}的象，o<;<1.进而设函数f(:，)实现B，到B:的共形单射，f(0)‘O，在这些假定下有:l)对于L(:，B，)上任一点:?，存在位于阶层曲线L(:，BZ)上(这仅当f(B，)二BZ才有可能)或其内部的一点与之对应;及2){f’(0)1蕊}夕‘(0)}，其中g(:，)满足g(0)二o是Bl到 BZ的单叶共形映射(等号仅当f(B1)=B:时成立).Lindebf原理系从Rien坦nn映射定理(见Rle-n.lln定理(Rierl飞幻In theorem))与Sdlwarz引理(Schwarz lemrr必)推出.相当精细的构造使之能够求出由被映射区域的给定形变所引起的映射函数的逐点偏差. 定量的基本变分原理系由M.A.几aBpeHTbeB(〔1」)获得(亦可见【2])，可叙述如下，设B:是具有解析边界的单连通区域，0任B!.假定存在给定区域族B，(r)，0‘Bl(r)，0(t蕊T，T>O，B;(0)二B，，具有JOrdan边界rl(t)={:一z，=0(之，t)}，0(又续2兀，0(0，t)二Q(2二，r)，其中Q(又，r)关于t在t二O可微且对又是一致的;设F(::，t)，F(0，t)=0，F:.(0，t)>O，是把B，(t)单叶共形映射为BZ二{22:I:21
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