然后导出与二维边值问题相应的变分方程；
Second, the variation equation corresponding to the 2-D boundary value problem is derived.
在变分方程中，只存在线积分，没有面积分。
最后讨论了利用全变分方程建立有限元的方法。
Finally, based on the total variational equation, the finite element method of these problems is also discussed.
为了获得该椭圆边值问题的解，推导出了有限元求解变分方程。
The corresponding variation equation has also been derived to solve this problem.
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。
In this paper, large amplitude variational equation of conical shallow thin shells is derived according to the principle of minimal action quantity.
离散后变分方程化为有限元方程组，求解可得口径场的电磁场值。
After dispersing, the calculus of variations equation turn to FEM equation group and solve the equation group to gain the electromagnetic value.
同时，还指出这类变分方程在随机控制的研究中有着重要的理论意义。
Also we point out that this kind of variational equations has a main theoretical meaning in the study of stochastic controls.
另一种处理方法是只对弥散项实施积分变换，应用边界条件，得出变分方程。
The other method is to perform the integration by parts only to dispersion term, then introduce the boundary conditions, and finally obtain the variation equation.
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。
The variational equation for general resonant cavities is used to derive the characteristic formula for the resonant frequency of the arbitrarily planar reso aators.
应用变分原理满足其余边界条件并求解应力强度因子。变分方程中只有线积分。
The stress intensity factors are solved by means of variational method to satisfy the other boundary conditions.
利用哈密顿原理推导出压电结构的变分方程，建立了智能结构的有限元动力方程。
Hamilton's principle is used to derive the equation of piezoelectric thin films and the dynamic finite element equations of intelligent structures.
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。
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.
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。
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.
根据应力变分和伽辽金变分原理，导出混合变分方程，并将其转换成状态方程，使状态空间理论和变分解相结合，给出任意厚度叠层板自振频率的变分解。
Thus, the theory of state space is combined with variational solution, and the variational results for free vibration frequency of the laminates with arbitrary thickness are calculated.
作为哈密顿力学逆问题，从弹性力学基本方程推导出弹性力学中一个新的哈密顿系统及其变分原理。
As an inverse problem of Hamiltonian mechanics, a new Hamiltonian system in elasticity and its variational principle are derived from the basic equations of elasticity.
该方程组涵盖了变分问题的各种欧拉方程。
The complete Euler equation set contains all kinds of Euler equations of the variational problems.
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。
The equilibrium equation and thew-equation, an idealized typhoon field and variational adjustment scheme are used for initialization of the typhoon model.
建立了管道泄漏引起的水力瞬变泄漏数学模型和边界条件，构造了差分方程。
Mathematics model and boundary conditions are proposed for hydraulic transient which is resulted from pipeline leaking while the difference equation is constructed.
根据胜利油田典型地质模型的构造特点，本文提出了变密度声波方程交错网格高阶差分正演方法。
According to structural feature of typical geologic models in Shengli oilfield, the paper presented staggering mesh high-order difference forward simulation of density-variated acoustic equation.
用张量形式通过变分原理导出了无约束物体的动力学普适方程。
An universal dynamic equation for unrestrained body has been derived in the form of tensor by using variation method.
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。
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.
根据离散变分原理建立离散系统的运动方程。
Based on discrete variational principle, the equations of motion for the discrete systems are established.
本文应用哈密顿变分原理较简捷地建立了厚梁横向振动的微分方程。
The differential equation for transverse vibration in thick beam is easily established by applying the Hamilton's variance principle.
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。
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.
运用变分的方法将遥感水汽的非线性方程线性化，讨论了线性化遥感方程的适用范围。
The nonlinear equation for remote sensing of water vapor was linearized by means of variation method. The effective range of linearized equation is examined.
利用变分原理得到平衡微分方程组和相应的边界条件。
By variational principle we obtain a system of differential equations and corresponding boundary conditions.
本文从大气的运动方程出发，利用实测的台风气压场资料和变分调整的方法，计算了进入渤海的台风风场，模拟了台风的不对称结构。
Starting from the motion equations and accepting the technique of numerical variational adjustment, this paper sets up a new model to calculate the typhoon wind field in the Bohai Sea.
本文从大气的运动方程出发，利用实测的台风气压场资料和变分调整的方法，计算了进入渤海的台风风场，模拟了台风的不对称结构。
Starting from the motion equations and accepting the technique of numerical variational adjustment, this paper sets up a new model to calculate the typhoon wind field in the Bohai Sea.
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