本质边界条件

采用与有限元法耦合的连续掺混法（ContinuousBlendingMethod）施加本质边界条件，使得边界条件不仅在边界节点上而且在整条边界上都得到严格满足。

The continuous blending method is adopted to enforce the essential boundary condition in a correct manner . This method makes the essential boundary condition satisfied not only at the boundary nodes but also at the whole essential boundary .

利用变换法施加本质边界条件；

The transformation method is used to impose the essential boundary condition .

由于插值函数具有Delta函数特点，因此可以很方便地施加本质边界条件。

The interpolation function has the Delta function property , so the essential boundary conditions can be simply imposed .

由于该方法中的形函数满足Delta函数性质，因此本质边界条件可以像传统的有限元方法一样很容易施加。

The formulated shape functions have the property of delta function and the essential boundary conditions can be applied as easy as in conventional finite element method ( FEM ) .

Laplace插值比Sibson插值在计算上要简单的多，并且不论对凸的或非凸的区域都能精确施加本质边界条件。

Laplace interpolation is easier than Sibson interpolation in computation .

采用边界奇异核方法对EFG形函数进行修正，直接施加本质边界条件。

Boundary singular kernel method is adopted to modify EFG shape function to impose essential boundary conditions directly .

基于自然邻接点插值构造的试函数，具有Kroneckerdelta函数性质，能够方便地施加本质边界条件和处理不连续面问题。

The trial functions which are constructed based on the natural neighbor interpolations have the Kronecker Delta function property , which facilitate imposition of essential boundary conditions and dealing with discontinuity problems .

而点插值方法的插值函数具有Delta函数性质，可以很方便的施加本质边界条件，不利之处是在计算插值函数时矩阵易于奇异。

On the other hand , interpolation functions in the point interpolation method ( PIM ) have delta function property , and it is convenient to apply the essential boundary conditions . The limitation of the PIM is that the matrix may be singular sometimes .

无网格伽辽金法（EFG）由于其近似函数的特殊性很难处理本质边界条件以及不连续介质边界条件。

Element free Galerkin method ( EFG ) is hard to handle nature boundary condition and the discontinuous medium boundary condition because of its special approximate function .

本质边界条件实现；

Difficulties in the implementation of essential boundary conditions ;

无网格方法中本质边界条件的处理

Treatment of Essential Boundary Conditions for Element-free Galerkin method

本质边界条件的并行处理。

Parallel enforcement of essential boundary condition .

在处理本质边界条件及数值计算三线性泛函方面作了有成效的尝试。

Successful attempts have been made to treat essential boundary condition and to compute trilinear form .

无网格伽辽金法中形函数一般不具有插值函数的特征，本质边界条件需特殊处理。

Thus , it is a notorious problem to treat essential boundary conditions for element-free Galerkin method .

采用完全变换法施加本质边界条件，给出求解椭圆型边值问题的无网格伽辽金方法。

The full transformation method is used in element-free Galerkin method for solving the elliptic boundary value problems .

采用单位分解积分是一个很好的选择。5.本质边界条件的并行处理。

Partition of unity quadrature is a good choice for numerical quadrature in MNS . 5 . parallel enforcement of essential boundary condition .

无网格法中的近似函数大都不是插值函数，在处理本质边界条件时较为困难。

It is difficult to settle essential boundary conditions in meshless method because the meshless approximation functions are not built by interpolation schemes .

采用完全变换法处理本质边界条件，实现了本质边界条件在节点处的精确施加；

The full transformation method is used to impose the essential boundary conditions , which realizes explicit implementation of the essential boundary conditions in EFGM .

由于移动最小二乘法的近似函数不一定精确地通过计算点，从而使本质边界条件的施加和集中载荷的处理变得复杂。

This is a disadvantage of EFGM as it suffers from problems in the imposition of essential boundary conditions and the application of point loads .

利用罚参数来实现稳态蠕变的不可压缩条件和本质边界条件，能够保证求解过程中刚度矩阵的对称正定性。

The essential boundary conditions and volume incompressible conditions can be realized by employing the penalty parameters , so the symmetric positive definite system stiffness matrix can be yielded .

构造出的位移和孔隙水压力的形函数具有δ函数特性，所以本质边界条件很易处理。

The shape functions of both displacement and pore water pressure constructed by this method possess the delta function property , so the essential boundary conditions can be imposed easily .

分析中，本质边界条件采用罚因子法施加，离散的特征值方程由板稳定控制方程的局部积分对称弱形式中得到。

In the analysis , the essential boundary conditions are enforced by a penalty method . The discrete eigenvalue problem is derived using the local integral symmetric weak form of the governing equation of stability problems .

因为用移动最小二乘法来近似挠度变量，不容易直接施加本质边界条件，所以采用罚因子法施加本质边界条件。

For the moving least square approximation does not possess properties of the Kronecker-delta function , the essential boundary condition can not be enforced directly , the penalty method is used to imposed the essential boundary condition .

把入口、出口及物面边界条件都化为自然边界条件处理，而把上、下游周期性边界条件作为本质边界条件处理。

The boundary conditions of the inlet and outlet and the surface of substance are changed to natural boundary conditions , while the periodical boundary conditions of the inlet and outlet stations are taken as essential boundary conditions in treating .

本文构造的自然邻接插值函数具有δ特性且在电磁场凸域边界上的相邻点之间是严格线性的，这使得自然单元法能方便地施加电磁场的本质边界条件，也可方便地处理其边界面。

The natural neighbor interpolation function is constructed with the δ characteristic , and it is strictly linear on the border of the points in the adjacent , so the NEM can easily impose the essential boundary conditions , also can easily deal with its boundary surface .

EFGM采用移动最小二乘函数近似试函数，并用罚函数法施加本质（位移）边界条件，这是一种与单元划分无关的无网格方法。

It uses the moving least squares method to construct trial function and the essential boundary conditions are imposed by penalty function method . In this method , only nodal data are needed and there is no need to join nodes into elements .