形函数

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 .

其中形函数的确定、单跨平衡方程的求解以及多跨FGM板的传递都采用了状态空间法，提高了计算效率。

To improve the efficiency of calculations , the state space method is adopted to derive the shape function and solve the equations governing the FGM plate deformation .

C°连续有限元形函数的系统公式

The Systematic Formulas of the Shape Functions for C ° - continuity Finite Element

本文给出构造C°连续有限元形函数的系统方法。

The systematic method for forming the shape functions of the C ° - continuity element is given .

在此基础上用正弦函数的高次幂作为光栅的槽形函数编写了介质膜光栅衍射效率计算程序，数值计算结果表明了C方法在计算介质膜光栅衍射效率的可行性。

The feasibility of calculating the diffraction efficiency of dielectric reflection grating with C method are proved with computation results .

基于股线的参数，建立了S形函数连接的BP神经网络模型。

Based on the parameters of plied yarn , a modeling of Neural Network is determined .

在小变形条件下，用Green应变张量得到了柔性体的耦合形函数。

The coupling shape function is obtained by Green 's strain tensor the assumption of small deformation of the arbitrary flexible body .

本文以非等距B＿3样条函数为基函数分别建立了旋转壳子午向和环向形函数，其中环向形函数满足周期性条件。

In this paper , the unequdistant B_3-spline function is used for establishing the meridional and circumferential shape function , and the circumferential shape function satisfies the periodic condition .

设n为正整数且n≥2，h为凸形函数，考虑如下n阶线性微分从属关系：并确定此微分从属的最佳控制。

Let n bc an integer number with n ≥ 2 , this paper considers the nth-order linear differential subordination and determines the best dominant of this differential subordination .

Meyer小波构造中S形函数的多项式实现

The construction of polynomial S - function for Meyer wavelet designing

通过递推的方式，由低次单元的形函数导出高次单元的形函数，从而使C°连续有限元形函数的构造过程系统化、程序化。

By way of recurrence , the shape functions of high-order element are obtained from those of low-order element . The course for forming the shape functions of the C ° - continuity element is systemized .

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 ) .

对多边形单元上平均值插值的误差进行分析，利用平均值插值形函数的性质和二元函数的Taylor展开式，证明平均值插值的误差估计不等式。

With shape functions of mean value interpolation and a bivariate Taylor expression , error estimation of mean value interpolation within polygonal elements is analyzed .

当技术新颖性高时，团队授权和创新速度之间呈线性关系，而当技术动态性高时，二者呈反U形函数关系。

Under conditions of high technological novelty a linear relationship between empowerment and speed was found , but under conditions of high technological turbulence the relationship was reverse U-shaped .

与其他判别训练算法不同，MSR算法直接使用阶梯形函数作为其损失函数。

Unlike other discriminative methods , MSR directly takes a step function as its loss function .

高次变节点Serendipity等参单元的形函数通用公式

The general formulas of shape functions for the higher serendipity isoparametric elements with variable nodes

首先利用径向基函数构造形函数逼近空间导数，然后在此基础上，对二维Euler方程进行了无网格离散，利用显式Runge-Kutta格式推进求解。

The spatial discretization is estimated using radial basis functions . The paper adopts explicit four-steps Runge-Kutta scheme for time discretization to solve the discrete form for Euler equations .

用该方法构造的形函数具有Kroneckerδ-函数属性，方便了位移边界条件的处理。

The shape functions constructed by the proposed method have the property of Kronecker δ - function which made the essential boundary conditions be easily implemented .

着重介绍了p型自适应有限元法的基本概念、典型算法、单元形函数特点及误差估计方法，并利用ANSYS软件提供的p单元时机车从动车轮的静强度进行了自适应分析。

The basic concept , typical algorithm , unit function characteristics and error estimation method is introduced for the p-version adaptive finite element method . The adaptive analysis is made to the static strength of the driving and driven wheel of locomotive with p unit supplied by ANSYS software .

主要分析了无网格伽辽金法（EFGM）节点不良分布以及采用一般高次多项式基构造形函数时，致使形函数中矩阵A（X）病态，从而导致全局数值解振荡的原因。

It was showed that the shape matrix A ( X ) was ill conditioned when Element Free Galerkin method ( EFGM ) used high order polynomial basis and the nodes were ill distributed .

在求解过程中，利用成熟的Delaunay三角形剖分技术，采用FEM三节点三角形单元的形函数作为权函数，可以减少域积分中被积函数的阶次，提高了计算效率。

In the implementation , based on the well established Delaunay triangulation , the FEM shape functions of three nodes triangular are taken as test functions , which reduce the order of integrands involved in domain integrals and improves the computational efficiency of the method .

然后运用运动影响系数（KIC）方法，通过对位形函数直接求导，得到系统的一、二阶运动影响系数矩阵，从而描述了机构各部件的运动关系；

Then , by using Kinematics Influence Coefficients ( KIC ) method , the first and second order of Kinematics Influence Coefficients matrix which can describe each part motion are given .

在模态空间内，利用Chebyshev正交多项式作为响应和荷载的时间有限元形函数，基于加权残值法，建立了移动荷载识别的时间元模型。

In the modal space , the Chebyshev orthogonal polynomial is taken as the time finite element shape function of responses and forces , and the time finite element model for moving load identification is established based on the weighted-residual method .

介绍了基于六面体单元的三维数值流形方法的基本理论，并在六面体单元中采用了有限元中C8型等参单元的形函数作为流形元中的覆盖函数。

In this paper , three-dimensional numerical manifold method ( NMM ) based on hexahedron element is proposed and the shape functions of C8 isoparametric element are used as the cover weight functions .

最后通过反透视投影算法和灰度插值算法，将失真的QR码符号有效地校正过来。再次，针对印制在曲面物体上的QR码图像，提出了一种基于有限元形函数的校正算法。

At last , the inverse perspective transformation and gray level interpolation are performed to correct the distorted QR code image . Thirdly , a correction algorithm for the QR images printed on the curved objects is proposed based on the finite element shape function .

本文通过在Newmark模型中引入翘曲形函数来描述楼板纵向位移的横向非均匀分布，然后采用虚余功原理建立了考虑剪力滞后效应的钢-混凝土组合梁力法单元。

By introducing a warping shape function into Newmark 's model accounting for the non-uniform transverse distribution of longitudinal displacements in the concrete slab , a force-based formulation is proposed for steel-concrete composite beams with shear lag by use of the principle of virtual complementary work .

给出了振动圆柱体边界周围节点移动的算法和采用虚拟控制单元的算法，求解EFM形函数的空间导数使其适用于较高雷诺数的流场。

Givens the algorithm of move nodes around the vibration cylinder boundary , and used the " virtual control unit " to solve the spatial derivative of EFM shape functions so that to deal with the high Reynolds number flow field .

以点插值方法构造形函数，推导了一种适合于求解工程电磁场瞬态涡流问题的边界点型无单元方法（BMFM），进行了详细的理论分析。

A boundary nodes-type mesh-free method ( BMFM ) for transient eddy based on point interpolation method ( PIM ) was presented , and the theoretical analysis of the BMFM given .

使用1阶或1阶以上最小滑动二乘法（MLS）形函数的无网格伽辽金法（EFGM），它们的主要缺点是形函数构造复杂、计算费用十分昂贵。

The major shortcoming of the Element free Galerkin method ( EFGM ), which are based on the use of one or more order moving least square ( MLS ) approximation , has been that the complexity of the shape functions and the high cost of computational time .

通过数值计算验证了所提方法的合理性与有效性。（3）离散铺设角度的变刚度层合板优化设计及基于广义形函数的参数化方法（GSFP）。

Numerical examples are presented to validate the proposed optimization scheme . ( 3 ) Optimization design of variable stiffness laminated plate with discrete orientation angle and the method of generalized shape function based parameterization ( GSFP ) .