变分问题

Considering the characteristic of dynamic consolidation in soft soil, L'place transformation is carried out on the basis of relaxed resolution problem of dynamic consolidation in saturated soft soil proposed by Zienkiewicz. With calculus of variations as the principal theory, the function of dynamic consolidation equation is constructed, and further, dynamic consolidation equation in matrix forms is deducted.

本文针对软土地基上动力固结法的特点，在Zienkiewicz提出的饱和土体动力固结定解问题的基础上做拉氏变换，以变分原理为基本理论，构造动力固结方程的泛函，进一步推导得到动力固结方程的矩阵形式表达式。

In this chapter, under the penalty functional satisfies the local Lipschitz condition, by using the Ekeland's variational principle and the properties of finite codimension, the Pontryagin's maximum principle of corresponding optimal control problem whose control variable is the harvesting rate and the input rate respectively is obtained.

本章在性能指标泛函满足局部Lipschitz条件下，利用Ekeland变分原理和有限余维的性质，证明了控制变量分别为收获率和输入率的相应控制问题的Pontryagin极大值原理。

First, For the coronary artery stent, two kinds of loads, including the pressure named 〓 derivatively from the balloon and the counterforce named 〓 on the wall edge of the stent, have been taken into account in the analysis of the stent.〓 and 〓 were changing as the stent expanding. So, the expansion process of the stent could be considered as the process composing of many extremely short equilibrium processes, where 〓 and 〓 could be regarded as constants and the stresses, the strains and the displacements were obtained using NFEA in every processes. Then, the stresses, the strains and the displacements obtained in every processes or steps were added up to get the final structure of the coronary stent.

首先，解决了支架有限元分析的载荷非线性问题，认为医用心血管支架受到两种载荷的作用：球囊直接传递的压力〓和球囊对不锈钢支架丝壁边缘的反作用力〓，这两种载荷在支架分析中必须都考虑进去；〓为非线性载荷，随着支架扩张不断变化，处理时将支架扩张的整个过程看成由37个很短的平衡过程组成，在每个过程中取〓为常量，采用有限元法获得应力、应变、位移，最后将各过程的应力、应变、位移迭加起来就获得了不锈钢支架总的应力、应变和位移；本研究用变分法和有限元法模拟杆件拉伸证明了上述方法是合理的。

Based on the superpotentialfunction,the variational principle on different function sets is derived for elastoplasticfrictional contact problems.

利用超势函数概念，导出了在不同函数集上的弹塑性摩擦接触问题的变分原理。

We prove the solvability of the first eigenvalue problem for a class of quasilinear elliptic equations including distance potential with homogeneous Dirichlet boundary condition.

变分原理证明了一类含距离位势的拟线性椭圆方程齐次Dirichlet边界条件下第一特征值问题的可解性。

In part V using Lions' second Concentrate Compactness Lemma andvariational method,we prove the existence of minimal positive solutionof a class of quasilinear elliptic obstacle problems〓in space〓.

第五部分使用Lions的集中紧性原理和变分方法，我们证明了一类非齐次拟线性椭圆型方程对应的障碍问题〓在〓中极小正解的存在性。

For one-dimensional ocean temperature model, we optimally determined the initial and boundary conditions and related model parameters through variational assimilation method along with inverse problem techniques using incomplete and complete observational data,so as to determine the variation of position of epilimnion which has influences on SST.

由于温跃层的变化对海表温度的影响，我们以简单的海温模式为例，采用变分同化技术及反问题的技巧，在局部和整体观测资料下，对初、边值条件和模式参数等进行最优估计，确定温跃层的位置及其变化规律。4。

At present, although finite element methods is a kind of effective measures in analyzing metal plastically forming problems with friction, dynamic friction in the process of metal forming is substituted with static friction and constant frictional force as one of independent constraint conditions is transposed to equivalent node-load or FEM unit is divided into contact unit and inner unit in numerous studys and applications, so that it result in relative bad accuracy and awkward operation. These defects mostly attribute to the fact that FEM bases on the variational equality principles, however frictional constraint will actually result in variational inequality energy functional.

目前，应用于分析金属塑性成形的有限元法是一种有效的处理摩擦效应的定量计算方法，但是许多应用和研究是用常摩擦来代替金属塑性成形过程中的动态摩擦；把常摩擦力作为单独的约束条件移置到等效结点载荷上或把有限元单元划分成接触单元和内单元，这些将导致解的精度相对不高及实际操作不方便等一系列问题，产生这些不足的重要原因之一在于它的理论基础是变分等式原理。

Then we derive first-order necessary optimality conditions for optimization problems with affine variational inequality, which joint upper-level feasible region Z includes a linear inequality constraint and a linear equality constraint.

其次，我们研究Luo的带仿射变分不等式约束优化问题，其中上水平约束Z不仅含有线性不等式约束，而且含有等式约束情形时的一阶最优性条件，同时还给出了Z的切线锥的表达式。

The solution of the linear variational inequality problem is transmuted to an equilibrium point of neural networks.

线性变分不等式问题的解被转化为神经网络的平衡点。

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。