摩擦约束广义变分不等原理的临界变分现象及分析

对于具有摩擦约束的弹塑性接触问题,由于边界接触面上的摩擦力由不等式表示,导致得到包含摩擦约束的广义变分原理为广义变分不等原理.广义变分不等原理通过将摩擦力纳入问题的能量泛涵,可避免考虑摩擦力变化的具体过程,便于数值方法如有限元等在弹性接触问题上的应用.但是,通过对广义变分不等原理的研究,发现在弹性力学广义变分不等原理中,势能型和余能型广义变分不等原理,均存在临界变分现象,即变分时拉格朗日乘子为零,变分失败;或者得到的能量泛函变分后得不到问题的欧拉方程.在对弹性力学广义变分不等原理临界变分现象进行分析后,提出了避免发生临界变分现象的方法.实际应用证明了方法的有效性.通过避免临界变分现象的发生,可以保证拉格朗日乘子方法的有效使用.     

广义变分不等原理在圆柱体非均匀镦粗中的应用

基于摩擦约束广义变分不等原理，对圆柱体非均匀镦粗成形工艺进行详细的塑性加工工步分析，实践证明了广义变分不等原理理论的正确性和实际操作的可行性以及优越性。     

摩擦约束塑性力学变分不等原理的半反推法

带摩擦约束的弹塑性接触问题,由于摩擦约束条件是一种判别性的条件,它的变分问题的逆问题的研究比较困难。本文对弹塑性接触力学中的变分不等问题的逆问题进行了研究,改进了半反推法并将其应用到弹塑性变分不等原理的研究中,导出了摩擦约束弹塑性增量广义变分不等原理中的能量泛函,消除了用拉氏乘子法可能产生的临界变分现象,在证明中,巧妙地处理了增量表示的接触摩擦边界条件,避免了使用非线性泛函分析和凸分析,简化了证明。     

建议一种非线性弹性论的约束变分原理及其与广义变分原理的协调性

本文建议一种新的约束变分原理,通过拉氏乘子法构成广义变分原理,其拉氏乘子不为零值.     

弹性理论中广义变分原理的研究及其在有限元计算中的应用

本文的目的在于说明怎样系统地建立各种广义变分原理,怎样合理地使用各种广义变分原理来改进有限元计算的成效。为了易于说明问题,本文只局限于弹性理论的各种广义变分原理,但其推广并不困难。本文指出,广义变分原理的泛函,可以系统地采用拉格朗日乘子法,把一般有条件的变分原理化为无条件的变分原理来唯一地决定的。拉格朗日乘子所代表的物理量,可以通过变分求极值或驻值的过程求得,从而消除了在建立广义变分原理的泛函时,人们经常陷入的象猜谜一样的困境。本文也指出:我们同样可以用拉格朗日乘子法把一般有多个条件的变分原理,化为条件个数较少的变分原理。我们称变分条件减少了的变分原理为各级不完全的广义变分原理。凡是把全部变分条件都消除了的变分原理,称为完全的广义变分原理,或简称广义变分原理;实际上是完全无条件的变分原理。本文建立了弹性小位移变形理论中的各级不完全的广义位能原理,和各级不完全的广义余能原理,包括从最小位能原理和最小余能原理分别导出的最完全的广义变分原理;并且证明了这两个弹性力学广义变分原理的泛函是等同的。在这些广义变分原理中,包括了Hellinger-Reissner(1950),胡海昌-鹫津久一郎(1955)的广义变分原理。本文也建立了弹性大位移变形理论中的位能原理和余能原理,并建立了有关位能余能的各级不完全的广义变分原理,包括以大位移变形的最小位能和最小余能原理分别导出的弹性力学广义变分原理,并且也证明了在大位移变形情况下,这两个弹性力学的广义变分原理也是等同的。本文除了列举广义变分原理在有限元法上的众所周知的应用外,还补充了三个比较重要的应用范围。     

弹性理论中广义变分原理的研究及其在有限元计算中的应用(续)

四大位移非线性弹性体的广义变分原理--完全的和不完全的我们也可以通过拉格朗日乘子法,导出大位移非线性弹性体的有关广义变分原理,设λ_(ij)和μ_i为待定的拉格朗日乘子,于是根据(49)式导出的无条件的广义变分泛函为 ...     

弹性理论中的临界变分及消除方法

临界变分现象是拉氏乘子法的固有特性，钱伟长应用高阶拉氏乘子消除了临界变分现象。本文将提出一种新的方法－凑合反推法，这种方法摒充了拉氏乘子法，把拉氏乘子所在的项目一个待定函数Ｆ代替。这样构成的泛函，作者称之为试泛函。而待定函数Ｆ的识别类似于拉氏乘子的识别。通过该法可以方便地构造出各种多变量广义变分原理，并且可以消除临界变分现象。     

金属刚粘塑性变形的能量泛函与动力显式算法有限元分析

设计出刚粘塑性动态变形场的能量泛函，采用罚函数法和Ｌａｇｒａｎｇｉａｎ乘子法取消对运动容许速度场满足体积不可压缩的约束条件，运用虚功原理和广义变分原理，推导出刚粘塑性变形的动力分析显式算法有限元方程，以及速率形式的中心差分求解的时间积分显式，给出了两个金属变形的算例。     

平面曲杆的广义变分原理

1. 引言本文应用Lagfange乘子法,建立了两端边界均为完全约束的地下拱形结构动力分析的广义泛函(15);对于地面拱形结构的广义泛函,只要去掉广义泛函(15)中的抗力项即可;此外,还可以很简便地推广到各种不完全约束边界的情况中。对于非保守体系的各种情况,我们考虑了非保守力,给出了非保守体系的广义变分原理。同时在弹塑性分析中也是适用的。另外还给出了地下拱形结构静力分析的广义变分泛函(22)。     

粘性流动动力学有限元变分原理

本文把建立有限元变分原理的一种新方法“Ｎ〉２直接方法”从固体力学推广到流体力学，并用该方法把粘性流体动力学的广义功率消耗原理＾［２］和广义变分原理＾［２］发展成为有限元变分原理。还在论证中发现，相邻有限元交界面上的应力协调条件会自然地满足而无需引进任何拉氏乘子。本文还建立了混合杂交非协调元的变分原理和广义变分原理，它解除了全部协调性约束条件和其它的边界性约束条件，但是并不增加待定的拉氏乘子，因此使     

On Chien's question to the Hu-Washizu three-field functional and variational principle

There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the comb...     

A variational principle for fully developed laminar heat transfer in uniform channels I

Summary A variational principle for forced convection in laminar flow in uniform channels is formulated. The concepts of thermal potential, dissipation function and thermal force have been introduced and a Lagrangian formulation of the thermal flow field using generalized coordinates is given. Special consideration is given to heat transfer in plug flow when the thermal field is a linear function of the generalized coordinates. The concept of normal and ignorable coordinates is introduced. An example showing the use of Lagrangian equations is worked out.     

率型的广义变分原理

本文提出一个适合于率型本构方程的边值-初值问题的广义变分原理,此原理是在现时构形上以卷积形式给出,可用于建立大变形分析中适时的Lagrange描述的增量分析公式。     

Variational principles in hydrodynamics of a non-Newtonian fluid

I.IntroductionTileresearchworkonvariationalprincipleinhydrodynamicsstartedasearlyas1940's.Referencesl:~6]aretheoneswhichmakemoreimportantcolltributions.l-lowevcr,mostoftheseworksstudied11on-viscousflow,putemphasisontheproblemsofexternalllcld,andworkedontilebasisofBernoulli'sequation.Prot'essorChienWeizang11I.slesttlblishcdvariationalprincipleforhydrodynalllicpl-oblemofviscousfluid,thatistheprillciplcofmaxilnLllllpowerlosses,alldgeneralizedvariational(stationary)pl.inciplesoiltilebiLsisofNav…     

GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN FC-SPACES

A class of generalized vector variational-type inequality problems (GVVTIP) are studied in FC-spaces, which includes the most of vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems and generalized vector variational inequality problem as special cases. By using F-KKM theorem, some new existence results for GVVTIP are established in noncompact FC-space. As consequences, some recent known results in literature are obtained under much weaker assumption.     

时间尺度上Herglotz变分原理及其Noether定理

Herglotz变分原理的作用量是由微分方程定义的,不仅可以描述所有经典变分原理能够描述的动力学过程,还可以对经典变分原理不能适用的非保守系统或耗散系统进行变分描述．时间尺度上微积分理论提供了一种可同时研究离散系统和连续系统的有效方法．本文结合Herglotz变分原理和时间尺度微积分理论来研究时间尺度上的Herglotz变分原理及其Noether定理．首先,给出时间尺度上Lagrange系统的Herglotz变分原理．其次,根据Herglotz变分原理和Dubois-Reymond引理,推导出时间尺度上Lagrange系统的Herglotz变分问题的运动微分方程．再次,基于时间尺度上Hamilton-Herglotz作用量在群的无限小变换下的不变性,给出Noether对称性的定义并导出其Noether等式．最后,建立了时间尺度上Lagrange系统的Herglotz变分问题的Noether定理,给出了连续和离散两种情况下基于Herglotz变分问题的Noether守恒量．文末举例说明结果的应用．     

Variational principles and generalized variational principles in hydrodynamics of viscous fluids

In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.     

Existence and algorithm of solutions for general multivalued mixed implicit quasi-variational inequalities

A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the e     

Variational irreversible thermodynamics of physical-chemical solids with finite deformation

A new thermodynamics of open thermochemical systems and a variational principle of virtual dissipation are applied to the finite deformation of a solid coupled to thermomolecular diffusion and chemical reactions. A variational derivation is obtained of the field differential equations as well as Lagrangian equations with generalized coordinates. New formulas for the affinity and a new definition of the chemical potential are presented. An outline is given of an unusually large field of applications, such as active transport in biological systems, finite element methods, plastic properties as analogous to chemical reactions, phase changes and recrystalization, porous solids, heredity and initially stressed solids. A new and unified insight is thus provided in highly diversified problems.