非线性耦合热弹性动力学的非传统Hamilton型变分原理

根据古典阴阳互补和现代对偶互补的基本思想, 通过作者早已提出的一条简单而统一的新途径, 系统地建立了几何非线性耦合热弹性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. 文中给出一个重要的积分关系式，可以认为，在力学上它是几何非线性耦合热动力学的广义虚功原理的表式. 从该式出发, 不仅能得到几何非线性耦合热动力学的虚功原理, 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8类变量、6类变量、4类变量和2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.     

Unconventional Hamilton-type variational principle in phase space and symplectic algorithm

By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. Therefore, this new algorithm is a highly efficient one with better computational performance.     

Unconventional Hamilton-type variational principles for nonlinear elastodynamics of orthogonal cable-net structures

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 unconven- tional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically,which can fully charac- terize the initial-boundary-value problem of this kind of dynamics.An important in- tegral relation is made,which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechan- ics.Based on such relationship,it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures,but also to derive systematically the complementary functionais for five-field,four-field,three-field and two-field unconventional Hamilton-type variational principles,and the functional for the unconventional Hamilton-type variational principle in phase space and the poten- tial energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the general- ized Legendre transformation given in this paper.Furthermore,the intrinsic relationship among various principles can be explained clearly with this approach.     

UNCONVENTIONAL HAMILTON-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF REISSNER SANDWICH PLATE

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified way proposed by Luo(1987),some uncon- ventional 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.In this pa- per,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 functionals for five-field,two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender trans- formations.Furthermore,with this approach,the intrinsic relationship among the various principles can be explained clearly.     

弹性正交索网结构动力学的各类非传统Hamilton型变分原理

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,系统地建立了正交索网结构几何非线性弹性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.文中首先给出正交索网结构几何非线性动力学的广义虚功原理的表式,然后从该式出发,不仅能得到正交索网结构几何非线性动力学的虚功原理,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正交索网结构几何非线性弹性动力学的5类变量、4类变量、3类变量和2类变量非传统Hamilton型变分原理的互补泛函、以及相空间非传统Hamilton型变分原理的泛函与1类变量非传统Hamilton型变分原理势能形式的泛函.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.     

Reissner夹层板动力学的非传统Hamilton型变分原理

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一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．     

相空间非传统Hamilton型变分原理与辛算法

通过作者早已提出的新途径, 建立了多自由度系统弹性动力学的相空间非传统Hamilton型变分原理. 这种变分原理不仅能反映这种动力学初值问题的全部特征, 而且具有自然辛结构. 基于该变分原理, 提出一种称之为辛时间子域法的辛算法, 该方法在时间子域上采用Lagrange插值多项式插值, 构造非差分格式. 并且, 证明了这种辛算法是无条件稳定的. 通过两个不同类型算例的计算结果表明, 这种新方法的精度和计算效率都明显高于国际上常用的Wilson-θ 法和Newmark-β 法. 因此, 这种新算法是一种计算性能更好的高效算法.     

Unconventional Hamilton-type variational principles for nonlinear coupled thermoelastodynamics

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 geometrically nonlinear coupled thermoelastodynamics can be established systematically. The new unconventional Hamilton-type variational principle can fully characterize the initial-boundaty-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlinear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of virtual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton-type variational principles by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.