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精确积分
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  exact integral
     Exact Integral Manifold Controller Design of Maglev Systems
     磁悬浮系统的精确积分流形控制设计
短句来源
     The normal integrals are popularly calculated by exact integral, and the singular integrals by the Gauss numerical integral.
     奇异积分一般采用精确积分 ,非奇异积分采用Guass数值积分。
短句来源
     This paper presents the exact integral equation of Hertz's contact problem, which is obtained by taking into account the horizontal displacement, of points in the contacted surfaces due to pressure.
     本文给出Hertz接触问题的精确积分方程,也就是将压力作用下接触面中各点的水平位移也考虑在内而得到的积分方程.
短句来源
     An exact integral expression of finite sum of sequence of a continuously differentiable function has been given, which can be used in approximate calculation with arbitrary accuracy.
     对通项为连续可微函数的函数列,给出了其有限和的精确积分表示; 可用于任意精度要求的近似计算.
短句来源
  accurate integration
     Accurate Integration of 3D Constant Potential Boundary Element
     三维常数势边界元中的精确积分
短句来源
     A Study on the Accurate Integration of Stiffness Matrices in Finite Element Method of Axisymmetric Problem
     关于轴对称有限元刚度矩阵的精确积分
短句来源
     By using generalized function, an accurate integration method is developed to get the explicit formulation of the matrixes involved. This can improve the accuracy and efficiency of the method.
     利用广义函数给出了一种精确积分方法 ,可以得到有关矩阵的显式表达 ,得到提高了求解精度和效率。
短句来源
  exact integration
     Exact Integration of Constant Element of Elastomer in Boundary Element Method
     三维弹性体边界元常单元的精确积分计算
短句来源
     EXACT INTEGRATION OF CONSTITUTIVE EQUATIONS OF KINEMATIC HARDENING MATERIAL AND ITS EXTENDED APPLICATIONS
     运动硬化材料本构关系的精确积分及其推广应用
短句来源
     Computing the Flux of Collocation Point with Exact Integration for Two-dimensional Potential Problems
     二维位势问题中边界点位势法向导数的一种精确积分解法
短句来源
     Secondly, the exact integration formula of BER for fading channel is presented, moreover, by using the Maclaurin series expansion of MPSK conditional Symbol Error Rate (SER), the simplified BER approximations for BPSK and QPSK are derived over AWGN, Nakagami-m fading and Rayleigh fading channel.
     然后给出了衰落信道中误比特率的精确积分式,并利用MPSK条件误符号率的麦克劳林级数形式,推导了AWGN,Nakagami-m衰落和瑞利衰落信道中BPSK,QPSK误比特率的简化逼近式。
短句来源
     By using an exact integration instead of the approximate integration formula in instantaneous optimal control algorithm,the precise instantaneous optimal control algorithms integration are proposed herein,which includes the precise instantaneous optimal open-loop control,precise instantaneous optimal closed-loop control,and precise instantaneous optimal closed-open-loop control.
     通过在瞬时最优控制算法中用精确积分代替以往采用的近似积分公式,从而给出了精细瞬时最优控制算法,包括精细瞬时闭环最优控制,精细瞬时开环最优控制和精细瞬时开闭环最优控制。
短句来源
  “精确积分”译为未确定词的双语例句
     According to the scalar diffraction theory,the accurate integral expressions ofthe circular aperture diffraction are derived with the plane wave incidence.
     用标量衍射理论导出了平行光入射时,圆孔衍射的精确积分表达式。
短句来源
     Based on the Mindlin-Reissner plate theory, a new 4-nodes plate bending element with ac-cureately integrated stiffness matrix has been derived through a new isoparametric transformation of a quadrilateral parent element together with the associated shape function.
     本文从Mindlin/Reissner理论出发,采用一种新的平行四边形母单元和相应的形函数推导四结点板弯曲单元刚度矩阵的精确积分解。
短句来源
     The exact integrations have been suggested by some authors for the calculation of rigidity matrix.
     也有用精确积分计算刚度矩阵的.
短句来源
     In this program,the integral on central axis is calculated with accurateformulas of integration,the nonlinearity of the problem is treated by themethod of incremental variable stiffness and the error therein is appropriate-ly corrected.
     此程序的特点是,中心轴线上的积分用精确积分公式计算,非线性处理用增量变刚度法分段线性化,其偏差采用修正办法修正。
短句来源
     During the above iteration, the stress resultants of the concrete in the cross section are evaluated by integrating the concrete stress-strain curve over the compression zone, while those of the structural steel and the steel reinforcement (if any) are obtained using the fiber element method.
     迭代计算过程中混凝土的截面抗力通过对混凝土的应力-应变曲线在截面上的精确积分求得,而型钢和钢筋部分的截面抗力则采用纤维元方法求得。
短句来源
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  exact integral
A method for designing microstructured optical fibers that is based on exact integral equations for the transverse components of the magnetic field of the mode is proposed.
      
Assuming the loop axis to be aligned with an external static magnetic field, exact integral equations are formulated for the current distribution on the antenna, when it is subject to the excitation of a slice voltage generator.
      
An exact integral-differential equation is derived for SIT with inhomogeneous broadening, incoherent losses and chirping.
      
Calculations are also performed using exact integral boundary conditions for the vector potential, as given by the standard electromagnetic field approach, taking into account the effects of both exciting and induced currents.
      
The exact integral equation of Hertz's contact problem
      
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  accurate integration
What's more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.
      
All the strongly singular integrals are computed directly through highly accurate integration techniques.
      
Accurate integration of phasic signals with frequencies above 0·1 Hz is obtained.
      
Accurate integration of geostationary orbits with Burdet's focal elements
      
In this approach several different formulae are applied in a well defined cyclic order to produce highly accurate integration schemes with infinite regions of absolute stability.
      
更多          
  exact integration
Through properly manipulating to the double integration appeared in PO, the exact integration of polygon surfaces could be obtained with independence of frequencies, which is vital for the RCS prediction in the Terahertz band.
      
In this so called NNCA (NN-Correlation Approximation) the transfer-integral (TI) method allows an exact integration ofΨ2 over the coordinates in all cubic planes but one, leading to the probability-densityP for this plane.
      
It is difficult to obtain the rigidity matrix by exact integration, and instead, the method of approximate integration is used.
      
The exact integration have been suggested by various authors for the calculation of rigidity matrix.
      
This work deals with the exact integration of a Fokker-Planck equation for the mass distribution in heavy ion collisions.
      
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In this paper are presented integral expressions precise enough for computing the internal forces and vertical displacements of double curvature shallow shells under the action of a concentrated load over a certain distance from the boundary according to the moment theory of shells. In case of shallow shells of equal curvatures, these expressions can be easily integrated into formulae which are exactly the same as those given by E. Reissner, but for shallow shells of unequal curvatures, the solution is given...

In this paper are presented integral expressions precise enough for computing the internal forces and vertical displacements of double curvature shallow shells under the action of a concentrated load over a certain distance from the boundary according to the moment theory of shells. In case of shallow shells of equal curvatures, these expressions can be easily integrated into formulae which are exactly the same as those given by E. Reissner, but for shallow shells of unequal curvatures, the solution is given in the form of series composed of Thomson functions, the convergence of which is considered to be quite good in the ordinary scope of application (1 < k1/k2≤2). Furthermore, formulae for the internal forces and vertical displacements of shallow shells of equal curvatures under the action of circular line loads and circular ring loads as well as their exact values at the point of a concentrated load for shallow shells of unequal curvatures are also given in the paper.

本文按有矩理论对作用在双曲扁壳并距离边界超过一定距离的集中載荷所引起的內力和位移值提出了具有足够精确度的积分表达式。在等曲率双曲扁壳的情况下,这些积分表达式可以很簡便地积出与E.Reissner相同的計算公式;对不等曲率双曲扁壳,本文則根据积分表达式給出了由Thomson函数組成的級数解,其收斂情况在常用的范围內(1精确积分值。

Linear form functions are commonly used in a long time for a toroidal volume element swept by a triangle revolved about the symmetrical axis for general axisymmetrical stress problems. It is difficult to obtain the rigidity matrix by exact integration, and as approximations close to the symmetrical axis, the accuracy of this approximation deteriorates very rapidly. The exact integrations have been suggested by some authors for the calculation of rigidity matrix. However, it is shown in this paper that these...

Linear form functions are commonly used in a long time for a toroidal volume element swept by a triangle revolved about the symmetrical axis for general axisymmetrical stress problems. It is difficult to obtain the rigidity matrix by exact integration, and as approximations close to the symmetrical axis, the accuracy of this approximation deteriorates very rapidly. The exact integrations have been suggested by some authors for the calculation of rigidity matrix. However, it is shown in this paper that these exact integrations can only be used for those axisymmetric elastic bodies with central hole. For solid axisymmetric body, it can be proved that the calculation fails due to the divergent property of rigidity matrix integration. In this paper, a new form function is suggested. In this new form function,the radial displacement u vanishes as radial coordinates r approach to zero. The calculated rigidity matrix is convergent everywhere, including these triangular toroidal element closed to the symmetrical axis. This kind of elenent is useful for the calculation of axisymmetric elastic body problem.

轴对称弹性力学问题的有限元分析长期以来都是采用三角圆环有限元和线性形状函数。由于积分困难,常用近似积分求得刚度矩阵,这种近似积分对于靠近旋转对称轴的元素,误差很大,所以,长期以来,被认为不满意的办法。也有用精确积分计算刚度矩阵的.但本文指出,这种积分只适用于有中孔的轴对称体。对于实心的轴对称体而言,这种刚度矩阵都不收敛,计算是无效的.本文提出了一种新的形状函数,当径向座标r接近于零时,这种形状函数的径向位移u自然地接近于零。如果用这种新的形状函数,则由此计算求得的刚度矩阵,不论三角圆环有限元的位置是否靠近轴线.都是存在的。这种有限元,就能用于计算实心的轴对称体的问题。

In analysis of stress of axisymmetric elastic bodies using finite element method, the mathematical expression for elements of stiffness matrix of triangular elements is a complicated double integration. In order to avoid the complicated calculations the approximate calculation is often preferred in engineering and this results in certain errors inevitably. Beginning with the general integral expression, this paper establishes the error formula in precise and approximate integration and then finds the errors...

In analysis of stress of axisymmetric elastic bodies using finite element method, the mathematical expression for elements of stiffness matrix of triangular elements is a complicated double integration. In order to avoid the complicated calculations the approximate calculation is often preferred in engineering and this results in certain errors inevitably. Beginning with the general integral expression, this paper establishes the error formula in precise and approximate integration and then finds the errors of the elements of stiffness matrix for the element bodies at different distances from the axis of symmetry and for the areas of elements of different sizes. After a large number of numerical evaluations the relation is found between this error and the distenee of the element from the axis of symmetry and the area of element. Approximate formula is given to help the user to choose the right area of element or to see that the divided area of element meets the precision requirements.This paper also compares several methods of approximate calculation for your reference.

用有限元法解答轴对称弹性体的应力分析时,其三角形单元刚阵元素的数学表达式,是一个较复杂的二重积分。为避免复杂的数学运算,工程上常常采用近似的计算方法。这就必然导致一定的误差。本文从它的一般积分表达式出发,建立了它的精确积分与近似积分的误差公式。然后对于距对称轴不同距离的单元体及不同大小的单元面积,求出各单元体所对应的刚阵元素的误差。经过大量的数值计算,从中找出这项误差与单元面积及单元到对称轴的距离的关系。并给出一近似公式。以便使用者选择恰当的单元面积,或检查已划分好的单元面积是否能满足精度要求。同时本文又从该项误差的要求出发,分析了几种近似计算方法的优缺点,供读者参考。

 
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