虚位移原理

On the basis of the idea of partition of unity, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the displacement interpolation formula to account for discontinuity of the contact surface and stress singularity near the contact surface tip respectively. Governing equations are deduced by virtual work principle and the integral of the discontinuous functions are calculated by Gauss integral through sub-elements cut by discontinuous surface.

该方法基于单位分解思想，在位移插值形式中引入不连续函数和裂尖渐近位移场函数分别反映接触面的不连续性和接触面端点的奇异性；根据虚功原理建立有限元支配方程，接触面不连续函数积分采用分区高斯积分的方法。

Considering that body forces and surface forces were both non-conservative force, the quasi-Hamilton principle and the quasi-complementary Hamilton principle of non-conservative elasto-dynamics systems were established.

按照广义力和广义位移之间的对应关系，将弹性动力学的基本方程乘上相应的虚量，然后积分，代数相加，并考虑到体积力和面积力均为非保守力，建立了非保守弹性动力学系统的拟Hamilton原理和拟余Hamilton原理。

Based on the variational principle of virtual voltage and virtual displacement derived in this thesis and the classical theory of linear laminated plates, and by using the constitutive equations of elastic piezoelectric materials, and the DKQ quadrilateral plate bending element, the finite element modeling for the fabric reinforced laminated plates with nonlinear voltage-electric strain relationship of piezoelectric actuators has been established for the first time in this thesis. And the expressions for the electric loadings with obvious mechanical meaning and convenient for computation are established, which can be used to the deformation analysis of laminated plates with piezoelectric actuators under specified voltages.

以本文直接导出的压电结构的虚电势—虚位移变分原理为基础，依据经典线性层合板理论和压电弹性体的本构方程，采用基于离散法线假设的DKQ四结点任意四边形薄板弯曲单元，首次建立了考虑非线性电压—电应变关系的含压电致动器的纤维增强型层合板的有限元分析模型，并推导建立了力学意义明确、便于计算的电荷载表达式，可用于指定电压条件下纤维增强型叠层合成板的变形分析。

Compared with the existing finite element eigenanalysis method[8]for asymptotic fields near the crack tip, current method has the following several characteristics: The jump-off that educes the virtue work formula is different; when solving the characteristic formula with FEM, the form of the element is non-confirming element; the singular transformation technique is not used in the assumption of displacement fields surrounding the wedge tip.

该方法与过去的有限元特征分析方法[8]相比的显著特点是：导出虚功原理的出发点不同；有限元单元形式为非协调元；楔形体端部邻域内的位移场假定没有采用奇异变换技术。

Based on the visual work principle of structure analysis,a general formula for the displacement calculation is deduced for the static analysis of the beam on elastic foundation.

根据结构分析中的虚功原理推导弹性地基梁位移计算的一般公式，介绍了连续弹性地基梁的静力分析方法。

The first chapter presents a comprehensive study of nonholonomic dynamics. They are studied that the nonlinear problem and un-determinate problem of virtual displacement in nonholonomic system in the second chapter. In chapter 3, they are studied that Chetaev model and Vacco model in nonholonomic system.

第一章对非完整动力学研究的有关现状进行了综合评述；第二章研究了非完整系统虚位移关系的不定性问题与非线性问题；第三章比较研究了一般非完整系统的Chetaev模型和Vacco模型；第四章研究了本质线性非完整系统的Hamilton原理；第五章给出了本文的结论与有关研究的展望。

3 The difficulties if the curriculum: internal force calculation of combined structures; virtual work principle and displacement calculation ; displacement method; analysis of structural matrix analysis; dynamic calculation.

本课程难点：静定组合结构的内力计算，虚功原理和结构位移计算，力法，位移法，结构矩阵分析，结构的动力计算。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。