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The objective of this study was to analyze the square cup stretching process by using the dynamic explicit finite element analytical program, which was based on the Updated Lagrangian Formulation and elasto-plastic theory. Simulation results included the deformation and crack propagation history, the variation of the work piece thickness, the Forming Limit Diagram, and the relationship between punch load and punch stroke. A set of tools was designed for the square-cup stretching experiment to verify the reliability of the program.

中文摘要本文采用显性动态有限元素法，结合材料弹塑性理论，发展出一套三维增量型之有限元素分析程式，进行金属板材方杯拉伸成形制程及破裂之分析，并探讨方杯拉伸成形历程及裂纹成长历程、工件厚度变化、成形极限图(Forming Limit Diagram， FLD)，及冲头负荷与冲程关系，并设计一组方形冲模来进行方杯拉伸成形实验，以验证程式的可信度。

Based on large strain theory, an analysis model of FEM on the basis of Updated Lagrangian is created.

本文依据大应变理论，建立基于Updated LagrangianU。

The methods applied mainly include Euler method and Lagrangian method, for simulating the fluid phenomena such as smoke, fire, explosion, wave, bubble, free surface etc.

其方法总体上可以分为欧拉法和拉格朗日法，涉及的现象包括烟雾、火焰、爆炸、波浪、气泡以及自由运动界面等。

The methods applied mainly include Euler method and Lagrangian method, for simulating the fluid phenomena such as smoke, fire, explosion, wave, bubble, free surface etc.

本文主要探讨基于物理的流体模拟计算机动画，其中涉及的现象包括烟雾[1]、流体运动界面[23]、波浪[4]、气泡[5]、火焰[67]以及爆炸[8]等。

To solve the problem, the error estimates for multivariate Lagrangian interpolates are given. From this, the upper bound of the rule number for a good multi-input fuzzy controller can be found out. The errors for a fuzzy controller to approximately precise control can be obtained after determining fuzzy rule base.

为讨论此问题，给出了多元Lagrange插值公式的误差估计式，并据此推导出一个好的多输入模糊控制器所需规则个数的上界，当模糊规则库确定之后，可求得用模糊控制器逼近精确控制时的误差。

Analysis of stability of surrounding rock of Shuibuya underground plant by three-dimensional fast Lagrangian method.

三维快速拉格朗日法进行水布垭地下厂房的稳定分析。

In this paper the shallow water equations in the Lagrangian coordinate s were derived and the numerical solutions were found out for shallow water problem with moving boundary by using a 2 order Godunov scheme.

移动边界问题是水力计算中难点之一，本文用拉格朗日坐标系来描述浅水方程，并用二阶Godunov算法求解有移动边界的浅水问题的数值解。

In this paper the shallow water equations in the Lagrangian coordinates were derived and the numerical solutions were found out for shallow water problem with moving boundary by using a 2 order Godunov scheme.

移动边界问题是水力计算中难点之一，本文用拉格朗日坐标系来描述浅水方程，并用二阶Godunov算法求解有移动边界的浅水问题的数值解。

The Lagrangian function is introduced to infer the analytical form of the ME density function.

算例表明，该方法避免了复杂的数值计算，可以满足岩石工程随机可靠性分析的要求。

In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques.

在适当的条件下，我们建立了Hestenes-Powell 增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。