计算

The approach of solving mean curvature,Gaussian curvature and principal curvatures of general triangular mesh model was derived.Considering coarse triangular mesh model is often seen,in order to increase the precision of curvatures,combined with Loop subdivision algorithm,the curvature algorithm was further extended.

推导了一般三角形网格模型顶点的平均曲率、高斯曲率和主曲率的计算方法，考虑到经常遇到粗糙三角形网格模型，为提高其曲率计算方法的精度，结合Loop细分曲面算法，进一步拓展了该曲率计算方法。

The minor principal stress of slab, the maximum acceleration in up-down stream direction and permanent deformation of the dam body for three-directional earthquake excitation are obviously different from those for unidirectional and two-directional earthquake loading.

计算表明，多向地震动下的面板峰值小主应力、顺河向峰值加速度及坝体的永久变形均与单向和双向输入时显著不同，实际工程计算时应同时考虑三个方向的地震动；振动型地震激励引起的坝体反应明显大于冲击型地震激励；随着地震动强度的增加，峰值加速度、峰值剪应变、面板应力和周边缝变形等增加；面板刚度对面板的应力值和周边缝的变位具有较大影响，当面板模量取值较低时，计算所得到的"面板"应力集中部位不甚明显，计算结论为新型的"土工膜面板堆石坝"提供了理论依据。

Theoretical formulae are derived from using the cuneafe model and principle of limit equilibrium, and consequently, the equations for practical computation are established.

根据楔形体模型及极限平衡原理推导出理论计算公式并建立了实用的计算公式，计算结果与实验符合良好。

Based on the principle of variation of earth pressures on the culverts under different conditions, including topography, span of culvert, density of fill and the type of structure, and the property of arching action above the culvert, a nonlinear earth pressure theory for culverts beneath high fill is presented, the theory suggests the earth pressure on the culverts beneath high fill can be calculated with the formula σ=ξγH〓 as the fill up to higher height.

把这种方法与其它地下洞室的土压力计算理论进行的对比分析结果表明，非线性土压力理论考虑了填土达到一定高度时在涵洞上方产生的拱效应以及土拱的不稳定性特点，其计算的土压力明显低于不考虑拱效应的低填方涵洞土压力计算值，但高于具有稳定土拱效应的地下洞室土压力理论得到的土压力。

3 Computation of virtual work principle and structural displacement : understand the content about the virtual work principle of deformable body and its application; skillfully master the calculation method of statically determinate structure displacement by loads; master the calculation method statically determinate structure displacement by temperature variation and support movement; know Reciprocal theorems .

虚功原理和结构位移计算：理解变形体虚功原理的内容及其应用，熟练掌握在荷载作用下静定结构位移的计算方法，掌握静定结构在温度变化，支座移动影响下位移的计算方法，了解互等定理。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

In this article, the author compares and analyzes three kind of main calculation formulas of the square grid quadrilateral prismoid field leveling earth volume , and provides a formula to calculate directly total excavation and filling earth volume according to construction altitudes of angular points of square grids.

对场地平整土方量方格网四方棱柱体法的3类主要计算公式进行了对比分析，提出了根据方格角点施工高度直接计算场地总挖、填土方量的计算公式。

By using Visual Basic, based on NASTRAN finite element analysis, this paper developed an efficient and convenient software which can process automatically the result of NASTRAN analysis and establish the database, and compute the failure probability of structural element and system, plot the contour of failure probability.

在NASTRAN有限元分析结果的基础上，以Windows95为开发平台，以VisualBasic为开发工具，开发了一个效率高，使用方便的结构可靠性分析软件该软件可以自动处理NASTRAN的计算结果，建立数据库，计算结构单元和系统的失效概率，绘制结构失效概率分布云图等，为工程人员在有限元计算的基础上进一步进行可靠性分析提供了一个方便、快捷的工具

Through the discussion on the calculating methods for failure probability of element section with the influence of one or more human errors ,a mathematic analytical formula under ideal known conditions is deduced.

通过对单个或任意多个人因差错影响下构件截面失效概率计算方法的分析讨论，推导出在理想已知条件下的数学解析求解公式；在考虑人因差错对结构参数影响程度的空间离散化后，得出了相应的简化计算方法；并以一个单筋梁的正截面为例进行了失效概率计算和人因差错影响程度分析。

We have improved the method to avoid the complicated calculating of probability and numeral integral.

由于原先的方法中需要进行繁琐的数值积分和概率的计算，我们对能量函数的计算进行了改进，避免了这种繁琐的计算，使得算法更加简便、易行。

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。