变分方程

Based on the principle of variation, boundary value problem of pressure partial differential equation was transformed into the extreme value problem of fonctionelle and finite element equation of flow model was deduced for calculating the simulation result.

根据变分原理，将压力微分方程的边值问题转化为泛函的极值问题，建立了渗流模型的有限元方程。

Firstly, the article expatiates the concept of fuzzy reliability and the relation between random and fuzzy. It presents a list of random-finite element formula that is suitable for the reliability analysis for mechanical rigid frame system. Secondly, it presents two arrangements' reliability analysis methods that fit for component and fabric system. Finally, according to the characteristic of engineering mechanical, the article first brings forward half random-half fuzzy"stress-intensity intermeddle model"for mechanical intensity analysis, and according to Gerber equation for weariness intensity calculation, the article presents fuzzy number's calculating principle and the fuzzy reliability analysis method for engineering structure weariness intensity.

首先阐述了模糊可靠性概念、随机性与模糊性的关系；在导出摄动随机有限元法随机变量的变分原理、随机有限元控制方程和递归方程组基础上，给出了适合于工程机械刚架系统可靠性分析的随机有限元列式；给出了构件和结构体系两个层次的可靠性分析方法；根据工程机械的特点，首次提出机械强度分析的半随机半模糊"应力-强度干涉模型"，并依据疲劳强度计算的Gerber方程，给出了模糊强度的模糊数运算法则及工程结构疲劳强度模糊可靠性分析计算方法，该方法具有简便实用的特点和普遍意义。

By the principle of penalt function, the irrotational fluid field is constrained, and author has proposed the Difference Method for distinguishing fluid vortex modes among the natural modes of coupled systems. Author has calculated the real frequencies with the extra deductive method, and discussed the influence of the numerical solution due to the irrotational constraint.

对于流体有限扰动时的非线性耦合系统的有限元分析作了一些探讨，给出了非线性系统的基本方程、变分原理及有限元方程，并具体地导出了三维几何非线性流体单元的切线刚度公式，采用增量形式的Newmark预报——校正逐步积分法计算系统的动力响应，由Newton-Raphson迭代法及其修正方法求解系统的非线性方程组，还列出了不平衡力余量检查和位移迭代增量检查等迭代收敛判断准则。

First of all, in the study from magnetohydrodynamics equilibrium equations describe the plasma derived from the balance of the Grad-Shafranov equation of the theory of expression, and to analyze its borders in a fixed way to solve the region;then we solved the equation with Variational method in given pressure, and the exact numerical value of poloidal magnetic flux and the profile of the magnetic flux surfaces contours in the definite error range are given.At last, the poloidal and toroidal magnetic field with D-shaped is obtained.

在研究中首先从磁流体力学平衡方程出发推导出描述等离子体平衡问题的Grad-Shafranov方程的理论表达式，并分析其在固定边界区域内的求解途径；然后在给定的压强分布情况下采用基于能量形式的变分法对其进行了数值计算，并在一定的误差范围内得到了极向磁通的大致图像以及等离子体的平衡位形分布；最后求出了D-型截面下的极向磁场以及环向磁场分布。

Based on the Timoshenko-Mindlin hypothesis and the Hamilton Principle, a set of governing equations of motion for the laminated non-circular cylindrical thick shells were founded.Using the Galerkin procedure,the Mathieu equation only with time variable was obtained,and this equation was solved by the method of increase harmonic balance.

基于Timoshenko-Midlin假设及Hamilton变分原理，建立了层合中厚非圆柱壳的非线性运动控制方程，采用伽辽金技术，得到仅含时间参数的Mathieu型方程，然后应用增量谐波平衡法进行求解。

By using saddle point reduction and Morse theory,we obtain an existence theorem of three periodic solutions for this equation.By means of E~+-Morse theory established by A.

本章还首次应用临界点理论研究中立型泛函微分方程的次调和解，在变分泛函中允许含有时滞变量，从而给出了研究这类方程周期解的新途径。

Presents a new formulation of Lagrange s equations by using an augmented Lagrangian function with the first order non linear nonholonomic constraint equations, and offers a unified variational approach to both holonomic and nonholonomic constraints.

采用带有二阶非线性非完整约束方程的扩张性拉氏函数，建立起了拉格朗日方程的又一新公式，该新公式较为规则，它提供了一种完整约束系统和非完整约束系统两者统一的变分方法。

The contents of this paper are as follows:Firstly, we study the following semilinear elliptic equation with Dirichlet boundaryvalue problem:in the subcritical growth case we obtain at least two nontrival solutions by using the three-critical-point theorem and the reduction method.

我们首先研究下面半线性椭圆方程Dirichlet边值问题：在次临界增长情况下，利用变分方法中的归约方法和三临界点定理，得到了方程至少有两个非平凡解。

The main idea is to retain the dimensionality advantages of the BEM, and localize the integration domain to a regular sub-domain, as in the MLBIE, such that no mesh is needed for integration.

利用修正变分原理，进一步将积分方程限制在一些相互独立的局部子域内，最后得到与各个边界节点相联系的边界局部积分方程。

First, we have proved that the constraint of local constant gradient angles is equivalent to the minimization of total variation. Based on this, a stronger continuity constraint of gradient angle is presented. The interpolation formula (a 3-degree-PDE) derived from the constraint can ensure the continuity of level lines and reduce the width of edges. The contrast invariant of the regularizer of the formula is also proved.

首先证明了局部恒定的梯度角约束插值等价于总变分最小化；在此基础上，提出一个具有更强连续性的梯度角约束，由这个约束条件导出的三阶偏微分方程使插值的图像既可以保证水平线方向的连续性，又减小图像边缘的宽度；最后证明了插值方程中正则项的对比不变性。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。