变分法

In the present paper, a new adjoint shape sensitivity analysis method for shape optimization of continuum structures is proposed.

新方法弥补了Arora等人所提出的形状优化灵敏度分析变分原理中的缺陷，为采用伴随法进行灵敏度分析提供了新的框架。

In this paper, we propose a simple alternating direction method.

本文提出了一个解线性变分不等式的简单的交替方向法。

Founds three-dimensional analytic model and analyses heat transfer with phase change with the help of numerical simulation software using Euler backward difference.

通过实验分析了冰水两相流在垂直和水平管道流动时的压降特性；建立了冰融解的三维分析模型，采用欧拉向后差分法，利用ANSYS数值模拟软件对冰水相变传热进行了数值模拟分析，得出冰粒大小与融解时间两者的关系曲线。

In this paper, based on variational principle and bilinear coordinate transformation, a spline Kantorovich method using cubic B-spline function is presented to obtain an approximate solution for the free vibration problem of arbitrary quadrilateral plates with various boundary conditions.

本文从变分原理和双线性坐标变换出发，采用基于三次B样条的康托洛维奇法得到了带有各种边界条件任意四边形板自由振动的近似解答。

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 the basic theory, the basic STFEM theory is perfected, the variation principle in form of a convolution included is given and proved.

在时空有限元法的基础理论方面，完善了时空有限元法的基础理论，给出并证明了具有普适意义的含卷积运算的变分定理。

In the chapter 2, based on elastic mechanics and variation principle, the fundamental and process of static and dynamic FEM is presented, placing special emphasis on the modal superposition method.

第二章根据弹性力学和变分原理，系统总结了有限元法求解静力学、动力学问题(包括特征值、动力响应问题等)的基本原理和步骤，并重点对模态叠加法求解动力，响应问题作了阐述。

With finite differential method, the discretization equations are derived by chosing control volume integral method to solve the unsteady one-dimensional heat conduction question with variable physical properties, and the temperature distributinn in ladle lining in preheat is computed.

应用有限差分法，选用控制容积积分法推导出离散化方程组，对一维不稳定态变物性热传导问题进行求解，计算出钢包在预热过程中包衬的温度分布。

The weak formulation permit is satisfied not point by point, finite element method balances only at node neighborhood, in unit balance is not required, in analytical method single check from infinite series does not satisfy the equation, but infinite number of points satisfy the equation, and then the weak formulation of dual system of Hamilton equations was educed.

基于基本方程和边界条件的弱形式，给出相应的广义变分和不同形式的有限元所采用的弱条件，说明弱形式允许不是逐点满足，有限元法只在节点邻域平衡，在单元内不要求平衡，解析法用无穷级数中单取一项也不满足方程，也是无穷多项在积分下满足，进而导出对偶体系弱形式哈密尔顿方程。

The equations of the towed cable motion are based on Ablow and Schechter model and six degree-freedom ordinary differential equations are used in the analysis of the motion of a towed body. The partial differential equations are discretized by finite difference method and the transient values of towed body depth and cable tension are computed by Newton Iteration when the heave compensation system performs and the length of the cable varies.

拖缆动力学模型基于Ablow and Schechter模型，拖体采用水下运载体六自由度方程模拟，运用有限差分法离散偏微分方程组和牛顿迭代法计算变缆长情况下拖体深度与拖缆各点张力的动态取值。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。