变分法

The distributed parameter model is changed into variable coefficient nonlinear stiff ordinary differential equations by central difference method.

运用中心差分法将分布参数形式的系统模型转换为一变系数非线性的刚性常微分方程组。

The time-dependent Dirichlet boundary condition was used to describe the variation of water head during water level fluctuation.

模型的求解采用效率较高的积分有限差分法进行空间离散，并编制了全隐式联立求解的计算程序，通过变换主要变量，实现了饱和与非饱和的相互转变，采用随时间变化的Dirichlet边界条件精确模拟水位波动时的变水头边界条件。

At present, although finite element methods is a kind of effective measures in analyzing metal plastically forming problems with friction, dynamic friction in the process of metal forming is substituted with static friction and constant frictional force as one of independent constraint conditions is transposed to equivalent node-load or FEM unit is divided into contact unit and inner unit in numerous studys and applications, so that it result in relative bad accuracy and awkward operation. These defects mostly attribute to the fact that FEM bases on the variational equality principles, however frictional constraint will actually result in variational inequality energy functional.

目前，应用于分析金属塑性成形的有限元法是一种有效的处理摩擦效应的定量计算方法，但是许多应用和研究是用常摩擦来代替金属塑性成形过程中的动态摩擦；把常摩擦力作为单独的约束条件移置到等效结点载荷上或把有限元单元划分成接触单元和内单元，这些将导致解的精度相对不高及实际操作不方便等一系列问题，产生这些不足的重要原因之一在于它的理论基础是变分等式原理。

Based on the continuity equation of groundwater and the normal velocity formula of free surface, taking element e as a subdomain R in the seepage flow domain R, according to variation principle, the finite element equation of seepage field can be obtained.

由地下水的连续方程和自由面的法向流速公式，把单元e作为渗流求解区域R上的一个子域ΔR，根据变分原理，得到岩土体渗流场有限元方程。

Nodal and edge elements. Galerkin's method and variational formulations. The Method of Moments.

一维、二维和三维的有限元法，节点和边界单元，Galerkin方法和变分原理。

Rubber ; Yeoh model ; incompressibility ; generalized ; variational principle ; FEM

橡胶； Yeoh模型；不可压缩性；广义变分原理；有限元法

Due to its versatility and flexibility, the FEM is capable of modeling complicated structures as well as inhomogeneous materials.

有限元法求解的基本思想是把边值问题的求解转化为条件变分问题的求解。

Firstly, the article expatiates the concept of fuzzy reliability and the relation between random and fuzzy. It presents a list of random-finite element formula that is suitable for the reliability analysis for mechanical rigid frame system. Secondly, it presents two arrangements' reliability analysis methods that fit for component and fabric system. Finally, according to the characteristic of engineering mechanical, the article first brings forward half random-half fuzzy"stress-intensity intermeddle model"for mechanical intensity analysis, and according to Gerber equation for weariness intensity calculation, the article presents fuzzy number's calculating principle and the fuzzy reliability analysis method for engineering structure weariness intensity.

首先阐述了模糊可靠性概念、随机性与模糊性的关系；在导出摄动随机有限元法随机变量的变分原理、随机有限元控制方程和递归方程组基础上，给出了适合于工程机械刚架系统可靠性分析的随机有限元列式；给出了构件和结构体系两个层次的可靠性分析方法；根据工程机械的特点，首次提出机械强度分析的半随机半模糊"应力-强度干涉模型"，并依据疲劳强度计算的Gerber方程，给出了模糊强度的模糊数运算法则及工程结构疲劳强度模糊可靠性分析计算方法，该方法具有简便实用的特点和普遍意义。

Based on the Maxwell\'s equations, the boundary value problem, variation problem, interpolation function and stiffness matrix in two-dimensional magnetotelluric are derived.

从麦克斯韦方程组出发，推导出二维大地电磁测深的边值问题、变分问题、有限单元法的插值函数以及单元刚度矩阵。

Combining the modified variational principle functional with the Moving Least Squares approximation, the HBNM involves three types of independent variables, i.

杂交边界点法将修正变分原理与移动最小二乘法结合起来，涉及三类独立的场变量。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。