分段线性弹性薄板动力学的非传统Hamilton型增量变分原理

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.     

一种基于Hamilton型拟变分原理的时间子域法

本文首先给出有阻尼线弹性动力学的一类变量广义Ｈａｍｉｌｔｏｎ型拟变分原理,它能反映动力学初值一边值问题的全部特征。然后,以这类Ｈａｍｉｌｔｏｎ型拟变分原理为基础,提出一种时间子域以五次Ｂ样条函数插值的时间子域法。算例表明,这种动力响应分析新方法的精度和计算效率都明显高于国际上常用的Ｗｉｌｓｏｎ－法和Ｎｅｗｍａｒｋ－β法。     

带有可伸展平动附件多柔体簇系统动力学拟变分原理及其应用

应用混合坐标法对多柔体簇系统进行运动学描述,得到附件和根体的动能,建立带有可伸展平动附件多柔体簇系统动力学拟变分原理。应用对合变换,得到两类变量的多柔体簇系统动力学拟变分原理。并推导其拟驻值条件对变分原理进行检验。最后,应用多柔体簇系统动力学拟Hamilton原理的拟驻值条件建立空间飞行器附件振动偏微分方程。     

弹性地基梁动力响应分析的新方法

本文首先建立有阻尼弹性地基梁动力学的一类变量广义Ｈａｍｉｌｔｏｎ型拟变分原理，它能反映动力学初值－边值问题的全部特征。     

压电材料修正后的H-R混合变分原理及其层合板的精确法

将三维弹性体的Hellinger-Reissner(H-R)混合变分原理引入到具有机-电耦合效应的压电材料静力学问题中,建立了压电材料修正后的H-R混合变分原理,通过变分运算和分部积分得到了压电材料的状态向量方程。给出了四边简支的压电材料层合板静力学状态向量方程的精确求解方法,数值实例的结果证明了方法是正确性的。这里的理论和求解方法同样适应于纯弹性材料板和压电材料板混合的层合板静力学问题的分析。变分原理将有利于压电材料问题相应的半解析法或有限元法的推导。     

状态空间法分析厚薄壁圆筒的统一问题

根据平面极坐系系统的弹性力学控制方程和二类变量广义变分原理导出状态方程，对轴对称厚薄壁圆筒的统一问题，给出了状态变量的解答，由于一次获得位移与应力场变量值，故其精度均较高。     

基于变分原理的整体道床结构动力有限元分析

根据国内外铁路隧道整体道床的建设经验,针对弹性支承块式整体道床结构,建立轨道-道床底板-底部垫层相互作用的粘弹性地基梁模型。依据弹性梁动力分析的第一类变量广义HAMILTON拟变分原理,推导出了粘弹性地基上弹性地基梁的动力分析方程,建立了相应的有限元解析方法对整体道床结构的动力响应特征与影响因素进行分析。研究成果对优化整体道床结构的设计参数,分析其动力稳定性具有重要意义。     

变形体动力学的变分原理及其应用

在变形体动力学的变分原理及其应用方面的研究工作从１９８５年开始，至今已进行了十多年，本文主要从三个方面对此进行综述。１．原理的研究，提出一条新途径，其基本思想是古典阴阳互补和现代对偶互补，它的特点是完全不用拉格朗日乘子法，但能简单而系统地从一般到特殊建立各种变分原理，通过这条新途径，作者建立了某些变形动力学的一系列基本原理，其中很多是新的结果。２．原理的应用研究，提出了分别基于简化Ｇｕｒｔｉｎ型分     

弹性动力学显含初始条件的广义变分原理

本文给出了显含初始条件并含有两个任意参数的弹性动力学广义变分原理,参数的不同取值以及附加不同的约束条件,可以得到多种显含初始条件的变分原理.     

压电材料变分原理逆问题的研究

研究了压电材料变分原理的逆问题, 采用文献[ 8 ]提出的变积方法, 系统地建立了压电材料的变分原理及其广义变分原理, 除得到文献中已有的结果外, 还得到了一些新的变分原理, 为建立压电材料的有限元分析模型提供了依据。     

Variational principles for generalized plane strain problems and their applications

This paper is concerned with the variational principles for the generalized plane strain problem of elasticity, which do not seem to have been documented well in the literature, hitherto. Both the total potential energy and the total complementary potential energy principles have been formulated and presented. Their counterparts in the context of generalized variational principles have also been presented. As a result, of the introduction of a discrete degree of freedom, i.e. the uniform direct strain out of the plane, which characterizes the generalized plane strain problem, a fair bit of complications arises. The minimum nature of the stationary values of the energy functionals may not be taken for granted as expected in their counterparts in conventional plane stress or strain elasticity. The expression of the total complementary potential energy obtained here has not been found before in the literature to the best of the authors' knowledge. This might be responsible for the fact that the generalized plane strain problem has been avoided in published work employing the variational principle based on the total complementary potential energy. The presently formulated total complementary potential energy functional has been applied to some classic problems in composites materials, viz. the analysis of transversely cracked laminates and the micromechanics of unidirectionally fibre-reinforced composites. Some interesting and/or new results have been obtained.     

物理模拟虚功和余虚功原理及它们在金属成形工艺中的应用

在文[1]的基础上,本文建立了金属成形工艺非耦联系统和相似非耦联系统的物理模拟虚功原理及余虚功原理,并从该两原理出发导出了文[1]所建立的物理模拟变分原理。上述诸原理共同组成物理模拟能量原理。而物理模拟虚功原理及余虚功原理是物理模拟能量原理的统一理论。同时,给出了模拟虚功原理的应用。     

A variational approach to a circular hyperelastic membrane problem

Summary The variational principles of nonlinear elasticity are applied to a problem of axially symmetric deformation of a uniform circular hyperelastic membrane. The supported edge of the membrane is in a horizontal plane and its radius is equal to that of the undeformed plane reference configuration, so that an initially plane unstretched membrane is subjected to a dead load due to its weight.It is shown how the stationary complementary energy principle can be used to obtain an accurate approximate solution for the deformation and stress distribution. It is also shown how the potential energy principle can be applied to the problem and how close bounds for an energy functional can be obtained from the two theorems. Numerical results are presented for realistic properties for a rubberlike material and for two strain energy functions, the semi-linear and the neo-Hookean.     

多体非连续变形系统的计算力学模型及其应用

针对由不同特性物体所组成的多体系统,探讨了能够涵盖各种变形状态和运动形式的广义有限单元模式及其插值函数形式。对于多体接触问题,发展了能够合理描述界面特性的接触力元模型,即采用某种应力插值函数将界面上的相互作用力由接触对上的接触应力来表达,并将接触对上的接触应力当作需满足界面上屈服准则与流动法则等状态控制条件的参变量,将其作为约束条件加入系统控制方程。根据非连续变形系统的分区参变量最小势能变分原理,联立变分驻值条件与参变量的状态控制条件建立了多体系统非连续变形计算力学分析的基本控制方程,将问题最终归结为一个含有自由变量和等式约束条件的线性互补问题,对此发展了数值解法,并进行了多个算例的数值分析。计算结果表明该模型不仅能够对多体系统进行静、动力耦合分析,而且还能够模拟多体系统的变形与应力及接触界面上的接触应力和相对运动等复杂的非线性过程。     

On the principle of stationary complementary energy in finite elastostatics

In this work, we explore conditions sufficient to guarantee the existence of a principle of stationary complementary energy in finite elastostatics. We are then able to derive a principle of complementary energy. The results also apply to a large class of incompressible and almost incompressible materials.     

一种建立分区变分原理的新方法

提出了一种建立弹性理论分区变分原理的新方法。放松了分区交界面上位移、应力连续的条件，证明了弹性理论分区求解体系的微分形式与积分形式的等价关系。本文以微分形式为前提，利用这种等价关系,在统一的构架下,导出了分区广义虚功方程和弹性理论分区变分原理。变分原理是积分形式的一种表现形式。讨论了积分形式的物理含义，提出了广义虚函数的概念。广义虚函数具有任意性、虚拟性。     

On Mitchell conditions for plane problems in elastostatics

Summary The main objective of the present work is the investigation of the conditions of single-valuedness for plane problems of elastostatics. It has been shown that in addition to the usual conditions further conditions, referred to as supplementary conditions of single-valuedness or generalized Mitchell's, conditions in the case of isotropic materials, are to be, satisfied by the strains in order that the corresponding displacements and rigid body rotations should be single-valued along those bounding curves on which displacements and tractions are alternatively prescribed.It has also been proved that both the supplementary conditions of single-valuedness and the so called kinematic boundary conditions are natural boundary conditions of the principle of minimum complementary energy as a variational principle.     

金属成形工艺相似非耦联系统的模拟变分原理和广义模拟变分原理

本文引入了相似非耦联系统和方程的概念。应用加权余量法于相似非耦联方程，建立了金属成形工艺相似非耦联系统的模拟势能原理和模拟余能原理。应用拉氏乘子法，据模拟势能原理和模拟余能原理，导出了广义模拟势能原理和广义模拟余能原理。给出了模拟势能原理的应用。这些模拟变分原理为在几何相似，但边界条件不同和本构关系也不相同的模型体和原型体之间实现力学场量的准确转换奠定了理论基础。     

Fluid-fluid and -solid interaction problems: Variational principles revisited

We systematically review some unified variational principles for a strong interaction problem in both a stratified fluid region and a fluid-solid region. The problem is described by a general Lagrangian formulation for an anisotropic elastic solid region, either surrounded by an incompressible non-Newtonian fluid region or surrounding the fluid region. In the first part, we express the fundamental equations of the regular fluid and solid regions in differential form. Then, we deduce the variational principles respectively from the principle of virtual power and the principle of virtual work for the fluid and solid regions. The physics principles are modified through an involutory transformation together with a dislocation potential. In the second part, we similarly establish some multi-field variational principles for a stratified fluid of two or more distinct fluid layers of different thicknesses and mass densities. In the third part, we derive the variational principles for the interior and exterior interaction problems in a fluid region with a surface piercing solid, within either a rigid or an elastic structure. The variational principles, which operate on all the field variables lead to the fundamental equations of the regions, including the interface conditions, as their Euler-Lagrange equations. Some special cases of the variational principles are given.