查询词典 variational formulation

To avoid the trouble to construct the basis functions, we introduce a Lagrange multiplier into the variational formulation to replace the constraint condition for the basis.

本文采用同样的思路用Galerkin 边界元方法求解带有约束条件的与第一类Fredholm 间接边界积分方程等价的变分方程，为避免构造基函数时约束条件的限制，我们采用Lagrange 乘子法，把约束条件放入变分方程中去，形成扩展的变分方程，用线形单元离散后求解。

A variational formulation level set model based on the image global information is obtained, which can detect contours both with and without gradient based on global information and eliminate the re-initialization procedure. The stopping term does not depend on the boundary gradient of the image, which overcomes greatly the "over segmentation".

针对这种情况，该文提出了一种基于图像全局信息并且不需要重新初始化的变分水平集红外图像分割方法，不考虑图像边缘梯度的影响，将图像全局信息作为外部能量项，在很大程度上克服了边缘模糊时过分割的情况。

In the thesis a novel formulation of variable-domain variational principle for fluidmechanics has been successfully deduced,and the Kelvin's theorem has beenextended to steady compressible ones.

本文还排导得到了一个新型的变域变分公式，并把Kelvin原理推广到定常可压无旋流体。

The method uses expansion in terms of scaling functions to approximate the axial field component and transforms the field equation into a matrix equation by applying a variational formulation.

在该方法中，用尺度函数把场分量近似为级数，通过变分公式把波导问题化为矩阵方程。

For the first patern, elastic dynamics is adopted to study the steady state rolling contact, elastic dynamics incorporating with rigid dynamics is adopted to study the non-steady state. For the steady state, the analytical solution is obtained, and for the non-steady state, the variational formulation to solve the problem numerically is derived For the later patern, the function type friction coefficient is introduced. On the basis of the quasi-stastic theories of constant friction coefficients, both the exact theory and the simplified theory of the function type friction coefficient are established, the computer programms for both the theories are also made out. Using the function type friction coefficient, Shen-Hedrick-Elkins theory's application range is extended to large creepage .

对于速度对接触体力学特性的影响，本文采用弹性动力学方法和弹性动力学与刚体动力学相结合的方法分别对稳态和非稳态两种情况进行了研究，得到了稳态情况的解析解，给出了对非稳态情况进行数值求解的变分公式；对于速度对相关物理量的影响，本文主要讨论了速度对摩擦系数的影响，在滚动接触准静态理论的基础上引进了函数型摩擦系数，建立了函数型摩擦系数的滚动接触准静态精确理论和简化理论，并分别编制了相关的计算程序，还用函数型摩擦系数将简便的Shen-Hedrick-Elkins理论的适用范围扩展到大蠕滑区。

The long-term seepage control effects of the surrounding rocks of the underground powerhouse are performed by a stationary seepage analysis method combining the variational inequality formulation of Signorini's type with an adaptive penalty Heaviside function to guarantee the numerical stability and convergence. Meanwhile, the difficulty in finite element mesh generation is reduced and the calculation time and modeling accuracy are balanced with a global model of equivalent modeling and a submodel of accurate modeling for drainage hole array.

为确保数值计算的稳定性和收敛性，采用Signorini型变分不等式和自适应罚函数相结合的稳定渗流分析方法，对厂房围岩的长期渗控效应进行计算分析；同时，采用基于等效模拟的整体模型分析和基于精细模拟的子模型分析相结合的方法，以减小有限元建模难度并协调计算量和计算精度之间的矛盾。

Weak formulation of mixed state equations including boundary conditions are presented in a cylindrical coordinate system by introducing Hellinger_Reissner variational principle.

从Hellinger_Reissner变分原理出发，在柱坐标系中，导出圆柱壳的弱形式混合状态方程和边界条件，联用状态空间法给出叠层柱壳的解析解，此法使得求解该类问题的形式得以扩大和统一。

Basing on a modified Reissner-type incremental variational principle in conjunction with mechanical subelement model and updated Langrangian description, a finite-deformation hybrid/ mixed finite element formulation is presented.

根据修正的Reissner变分原理，采用Updated Lagrange描述，建立了基于力学子单元模型的增量型大变形杂交/混合有限元列式方法。

To maintain the consistency of ODEs, FEMOL formulation based on moving boundary variational principle was established, including

二、建立了基于动边界变分的有限元线法分析的基本理论。

The boundary contour formulations of evaluatingstresses from the Somigliana stress identity are derived for 2-D problemswith quadratic boundary elements.The boundary contour method basedon the traction boundary integral equation is further discussed.Elasticproblems are first solved using the traction boundary contour method.Amixed collocation of the displacement boundary contour formulation andtraction boundary contour formulation is given.(4)The dual boundarycontour method is developed for the analysis of crack problems.

3建出了Somigliana应力积分式的二维和三维问题的边界轮廓法理论；给立了二维问题由Somigliana应力积分式计算应力的二次形函数的边界轮廓法方程，进而给出了基于面力边界积分方程的边界轮廓法；提出了一种以位移边界轮廓法方程与面力边界轮廓法方程混合配置的方案，首次实现了用两种积分方程相结合来求解弹性力学问题。

Finally it offers the analysis of the fault-tolerance system as well as its test verification.

这样，运行于空间环境中的系统的设计目标就是在保证系统实时性

However, it is still difficult to find out the real reason of the increase of the keratinized gingiva during the orthodontic extrusion whether it is due to the proliferation of the gingival tissue or to its elastic nature, that is because the proliferation of the fibroblasts as well as the connective tissue changes in volume and the intra-fibers spaces were all immeasurable in most of the studies.

然而，仍然难以找到真正的原因增加的角化牙龈在正畸挤压它是否是由于扩散的牙龈组织或其弹性性质，这是因为增殖的成纤维细胞以及作为结缔组织的变化量和内部纤维空格都是不可估量的，大多数的研究。