In the variational equation, there is only line integral.
在变分方程中，只存在线积分，没有面积分。
Finally, based on the total variational equation, the finite element method of these problems is also discussed.
最后讨论了利用全变分方程建立有限元的方法。
In this paper, large amplitude variational equation of conical shallow thin shells is derived according to the principle of minimal action quantity.
本文首先用最小作用量原理推导出扁薄锥壳大振幅的变分方程。
The variational equation for general resonant cavities is used to derive the characteristic formula for the resonant frequency of the arbitrarily planar reso aators.
本文应用一般型谐振腔的变分方程，推导了平面型谐振腔谐振频率的特征方程。
According to the stress and Galerkin's variational principles, the mixed variational equations for the laminated shell are presented, from which the state equation is obtained.
根据应力变分原理和伽辽金变分原理，导出叠层圆柱壳的混合变分方程，并将其转换成状态方程。
From studying some kind of quite complex variational equation problems and applying the conclusion, we prove that the optimal control of new model is existent and characterize its structure.
通过对一类相当复杂的变分方程问题的研究并利用其有关结论，我们证明了新模型最佳控制的存在性并刻划出其结构。
The complete Euler equation set contains all kinds of Euler equations of the variational problems.
该方程组涵盖了变分问题的各种欧拉方程。
The partial differential equation of flow in porous medium has been studied with variational finite element method.
用变分有限元方法对描述地下流体渗流的偏微分方程进行了分析。
By means of the variational approach, in a condition weaker than(AR) the existence of infinitely many solutions of fourth-order elliptic equation is discussed.
在比（AR）条件更弱的一类超线性条件之下，利用变分方法讨论了一类超线性四阶椭圆方程的无穷多解的存在性。
When energy equation for element was built, variational method was used to get ordinary differential equation.
在建立单元的能量方程后，对方程进行变分得到墙元的常微分方程。
In this paper, we mainly study equivariant harmonic maps, the theorem of reduction, the equivariant variational formula, and the harmonic equation.
在本文中我们主要研究了等变调和映照、及其约化定理和等变变分公式，得到了等变调和映照的调和性方程。
A power-like equation, a Virial-like theorem, an integral variational principle and a differential variational principle for the system are deduced by using the time-integral identity.
给出系统的时间积分等式，并由此等式导出类能量方程、类维里定理、一个积分变分原理和一个微分变分原理。
Based on the theory of variational inequality, a direct solution method of one-dimensional problem is developed which efficiently solves the Reynolds equation.
基于变分不等方程理论，雷诺方程采用一维直接解法求解。
Short term optimization of hydroelectric generation is a procedure problem and should be solved by the variational method of functional extreme value, i. e. , the famous Eulerian equation.
短期水电优化是过程问题，应该用泛函极值的变分法即欧拉方程求解。
According to the variational principle for wave propagation, the elastic wave equation and the compressional and shear wave equations in a vertically inhomogeneous medium are developed.
本文由波传播问题的变分原理导出了垂向不均匀介质中的弹性波波动方程及纵波和横波波动方程。
By the variational method, the governing equation of the plate non-linear theory is solved, and he relationship between load and deformation of a single spring leaf is obtained.
应用薄板非线性理论的变分方法求解基本方程，得到了单片碟形弹簧的载荷和变形关系以及应力分布及其计算公式。
In this paper, the mathematical theory of the nodal expansion method for 2nd order elliptical equation including variational principle and error estimate is established.
本文建立了二阶椭圆方程节点展开法数学理论，包括变分原理和误差估计等。
The equilibrium equation and thew-equation, an idealized typhoon field and variational adjustment scheme are used for initialization of the typhoon model.
平衡方程和方程，理想台风场和变分调整方案被用于台风模式初始化。
Finite Elemnent-Linear Complementary Equation is established for analysis of elastoplastic thin plate-bending problems based on variational inequality principle.
从变分不等式出发，结合有限元，建立了按增量求解薄板弹塑性弯曲问题的线性互补方程。
Conversion relations between two variational functionals that take respectively same equation as their constrain condition and Euler's equation are obtained.
指出了以同一方程作为约束条件及欧拉方程的两个泛函之间的转换关系。
The interaction between two optical soliton is derived from nonlinear Schrodinger equation by variational approach.
本文利用变分原理，通过非线性薛定谔方程，导出光纤中传输的光学孤子相互作用。
The negative plastic hinge line in the plate was evaluated by using variational approach, then an equation for calculating the ultimate load carrying capacity was developed.
首先利用变分原理确定板的负塑性铰线方程，继而推导出极限承载力的表达式。
By making use of variational methods, we obtain two positive solutions ofp(x)-Laplace equation, which generlizes the corresponding relusts of Laplace equation.
利用凸性分析方法，在方程具有边界条件和正初始能量情况下得到整体解不存在的充分条件。
A variational formula combining mixed finite element method with discontinuous finite element method is derived for solving the two-group neutron diffusion equation in 2d.
构造了求解二维两群中子扩散方程的混合间断有限元格式，研制了相应的计算程序。
This papar deals with the problem of solution's existence about elliptic equation under limiting exponents and free boundary problem by variational evaluation methods.
本文是采用变分估计方法考虑一类椭圆方程在临界指数和自由边界条件下解的存在性问题。
The complete Euler equation set contains all kinds of Euler equations of the variational problems.
通过两个算例验证了完全欧拉方程组的正确性。
The variational method is utilized for the discretization of the governing transient conduction-convection equation, with heat transfer coefficients adaptively determined by the actual mill data.
生产应用中，采用短时、长时自学习方法对换热系数进行在线修正，进一步提高模型的预测精度和稳定性。
The variational method is utilized for the discretization of the governing transient conduction-convection equation, with heat transfer coefficients adaptively determined by the actual mill data.
生产应用中，采用短时、长时自学习方法对换热系数进行在线修正，进一步提高模型的预测精度和稳定性。
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