查询词典 variational formulation

The thesis consists of three parts:The first part deals with optimal Sobolev inequalities on compact Riemannian manifolds;the second part is concerned with some variational models in image processing,and we propose variational models as well as experimental results for detection,denoising and mosaicking;the last part deals with inverse differential geometry in 3-D non-local image restoration.

本论文由三个部分组成。第一部分是流形上的非线性分析：第二部分是基于能量极小化方法的图像处理；第三部分是三维非局部图像重建及逆向微分几何。在第一部分中，我们研究了紧致流形上的最优Sobolev不等式，证明了某些不等式虽然就整体而言是不成立的，但总是局部成立的。

The variational form of the governing equations is given on the basis of the extended Hu-Washizu three-field variational principle.

基于胡海昌-Washizu三变量广义变分原理结合特征线法给出了控制方程的单元弱形式。

Firstly, the modified H-R variational principle for elastic material was briefly presented, then the quadratic interpolation functions were used to express the out-plane stresses and displacements variables, consequently the formulation of 8-node isoparametric element for Hamilton canonical equation was derived in detail.

首先简要地介绍了弹性材料修正后的H-R变分原理，然后用二次插值函数表示平面外应力和位移变量，并详细地推导了Hamilton正则方程的八节点等参元列式。

The dissertation presents a mathematical modeling approach for the high-speed flexible linkage mechanisms equipped with bonded piezoelectric sensing/actuating elements employing a mixed variational approach with Hamilton's principle in conjunction with the finite element formulation. This model includes both the terms coupling the elastic and rigid-body motions of linkage mechanisms and the terms coupling the elastodynamics and piezoelectricity of the elements, incorporating their effects upon the mass and stiffness matrices which are in general non-symmetric.

本文以国家自然科学基金资助项目《弹性连杆机构有害振动的主、被动控制及混合控制研究》（资助号：59605001）和广东省自然科学基金项目《开链及闭链机构有害振动控制研究》（资助号：970381）为依托，对高速弹性连杆机构振动的主动控制中的建模、求解、控制律的选择、作动/传感元件的优化以及实验研究等几个关键问题进行了比较深入细致的研究，取得了一些具有重要理论意义和重大实际应用价值的成果。

Using the first order shear deformation theory for plate and mechanical-electro coupled variational equation, the two dimensional dynamic finite element formulation containing the effect of pressure in the cavity was derived.

数值分析了在不同的结构和声腔共振频率下主动控制效果，结果表明通过合适地布置压电片，能够很好地控制腔体的声压与位移。

Variational principles play an important role in the formulation of many problems of mathematical physics.

变分原理现在许多数学物理的表述中起着重要作用。

Presents a new formulation of Lagrange s equations by using an augmented Lagrangian function with the first order non linear nonholonomic constraint equations, and offers a unified variational approach to both holonomic and nonholonomic constraints.

采用带有二阶非线性非完整约束方程的扩张性拉氏函数，建立起了拉格朗日方程的又一新公式，该新公式较为规则，它提供了一种完整约束系统和非完整约束系统两者统一的变分方法。

In Chapter 5, we study three dimensional elasto-plastic frictional contact problems with orthotropic friction law. Parametric variational principle and parametric quadratic programming method are applied to analyze this class of complicated mechanics problems. A linear complementarity problem formulation is derived.

在第五章，我们采用正交各向异性摩擦定律模型对三维弹塑性摩擦接触问题进行分析，将正交各向异性的摩擦定律线性化后，将参变量变分原理和参数二次规划法应用到这一复杂的力学问题中来，最终将问题化为线性互补问题模型。

A variational formulation is constructed from the famous Gelfand-Levitan equation to reconstruct the scattering potential.

从著名的Gel＇fandLevitan方程出发，本文构造了一个重建散射位势的变分公式。

Using the variational formulation and its discretization equation, we get its finite element algebra equation and solve it by the method of Newton iteration.

通过对方程做变分、离散得到其有限元代数方程组，并选择了Newton迭代法来求解该方程组。

Salt is good, but if the salt becomes flat and tasteless, with what do you season it?

14：33 盐本是好的，盐若失了味，可用什么叫它再咸呢？

He reiterated that the PLA is an army of the people under the leadership of the Communist Party of China.

他重申，人民解放军是在中国共产党领导下的人民军队。