边界单元法

The method uses Cartesian grid for the majority of flow field with special treatment to cells cut by the solid boundary, thus not only retains the advantage of Cartesian grid's high solving speed, but also ensures the high precision near the boundary, which avoids the distortion coming from scalariform mesh with traditional difference method.

该方法在流场主要区域采用笛卡尔网格，而对与固体边界相交处的单元采用特殊的处理。这样既保留了笛卡尔网格求解速度快的优点，同时在边界处又保证了精度，避免了传统差分法处理该类问题需采用阶梯形网格逼近而导致的失真问题。

According to axisymmetric unsteady heat conduction equation of orthogonal aniso tropic material and boundary conditions,the equilibrium equation of a system of finite elements is deduced with triangular element of high accuracy,and programs are designed.

根据均匀正交各向异性材料轴对称热传导方程及其边界条件，利用变分法及欧拉理论，选取 6 节点的高精度三角形单元类型，推导了一般轴对称非定常热传导有限元基本方程。并编制了相应的计算程序。

The penalty function is adopted to impose the essential boundary condition, the tensor product weight function with a rectangular influence domain is chosen, and the finite element background cell is considered as the integration unit.

将无网格再生核质点法用于刚塑性可压缩材料轧制过程的模拟，采用罚函数满足本质边界条件，选用矩形影响域的张量积核函数，利用有限元网格作为积分单元，对求解域内和边界上采用不同的高斯积分方案。

Boundary element method is a kind of numerical algorithm on boundary; it is based on the boundary integral equation and employs the element discretization technique.

边界元属于边界型的数值方法，它是以边界积分方程为数学基础，同时采用了有限元法的单元离散技术。

When the formulas of the tetrahedral element are developed, triangular coordinates is used to develop the boundary integral part of outer boundary element.

其中针对四面体单元的第二、第三类边界条件采用面积坐标积分变换法详细推导了边界积分项的计算过程。

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。

The weak formulation permit is satisfied not point by point, finite element method balances only at node neighborhood, in unit balance is not required, in analytical method single check from infinite series does not satisfy the equation, but infinite number of points satisfy the equation, and then the weak formulation of dual system of Hamilton equations was educed.

基于基本方程和边界条件的弱形式，给出相应的广义变分和不同形式的有限元所采用的弱条件，说明弱形式允许不是逐点满足，有限元法只在节点邻域平衡，在单元内不要求平衡，解析法用无穷级数中单取一项也不满足方程，也是无穷多项在积分下满足，进而导出对偶体系弱形式哈密尔顿方程。

An optimum design for the complex body formed together with the volute casing, base ring and cement foundation of a hydraulic turbine is made by the gradient method and a program is developed on the basis of finite element analysis with the plane and shell element, body element, boundary element and pseudo element.

本文对由水轮机蜗壳、座环和水泥基础所构成的复杂组合体，在采用板壳元、块体元、边界元和伪单元等四类单元进行有限元分析的基础上，选用最速下降法研究了优化设计过程，并编制成程序系统。

The gap element method is proposed in the paper for two kinds of problems, which include contact problem and gap joint problem. Elasticity contact problem falls into the category of unknown boundary value problems. It follows that the contact area and contact conditions or states can never be determined without special mathematical analysis, which is a very difficult work. The boundary conditions of the contact surfaces are deduced.

文中给出了间隙元法在空间可动部件接触问题中的应用，推导了其几何边界条件和力学边界条件，利用虚功原理推导了含间隙元弹性接触问题的有限元方程式，给出了其数值解法的迭代步骤，并指出了利用间隙单元进行分析的特点。

That is, the constant element for velocity potential, called 0 type element, and linear element for its nor

即对势函数采用线性元(或称之&1&型单元)，而对势函数法向导数采用常数元(或称之&0&型单元)，以这样的0-1混合型边界元剖分计算域的

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。