分析静力学的重要原理，又称虚位移原理引，是J.-L.拉格朗日于1764年建立的。其内容为：一个原为静止的质点系，如果约束是理想双面定常约束，则系统继续保持静止的条件是所有作用于该系统的主动力对作用点的虚位移所作的功的和为零。
... principle of virtual displacement虚位移原理 principle of virtual power虚功原理 principle of virtual stress虚应力原理 ...
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... virtual work 虚功 virtual work principle 虚功原理 Castigliano first theorem 卡氏第一定理 ...
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虚功率原理 virtual power theory
According to the principle of virtual work, the finite element equations of the contact problem composed of gap elements are obtained. The calculating procedure with gap element method and the features of it are all presented.
文中给出了间隙元法在空间可动机构接触问题中的应用,推导了其几何边界条件和力学边界条件,利用虚功原理推导了含间隙元弹性接触问题的有限元方程式,给出了其数值解法的迭代步骤,并指出了利用间隙单元进行分析的特点。
参考来源 - 开启式屋盖结构可动部件研究及风振相应分析Firstly, governing equations about contact are educed by node-to-node model and principle of virtual work.
本文首先用节点对模型与虚功原理导出求解的两个粘弹性体接触问题的基本方程组，并直接代入接触边界条件求解。
参考来源 - 粘弹性体接触有限元法及应用研究On this basis, flexibility matrix and static stiffness matrix of the micro-positioning platform’ overall mechanism was worked out respectively according to energy principle and virtual work principle, mapping relationship between the two Jacobian matrixes was derived.
在此基础上根据能量原理和虚功原理分别求出了微定位平台整体机构的柔度矩阵与静刚度矩阵,并得出了两者间的雅可比矩阵映射关系。
参考来源 - 二维平动并联微定位平台的结构设计与参数优化·2,447,543篇论文数据，部分数据来源于NoteExpress
最后运用虚功原理给出了胀形平均液压的解析解。
In the end, the average hydraulic pressure of bulging is given by the principle of virtual work.
而物理模拟虚功原理及余虚功原理是物理模拟能量原理的统一理论。
And the virtual work and complementary virtual work principles for physical simulations are united theories of the energy principles for physical simulations.
本文建立了有限变形弹性理论中的余虚功原理，包括此原理的提出与详细的证明。
This paper puts forward the principle of complementary virtual work in the finite displacement theory of elasticity and provides a detailed proof thereof.
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