| 1. | Let the junction of the three fracture lines have a virtual displacement .
令三条折断线的相交处有一虚位移。
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| 2. | We recall that the principle of virtual displacements is a statement of equilibrium .
前面已叙述过，虚位移原理是对平衡的一种描述。
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| 3. | The virtual displacement method specifies that the sum of the shaded areas is equal to the sum of the stippled areas .
虚位移法规定阴影面积之和等于点画面积之和。
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| 4. | Principle of virtual displacement
虚位移原理
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| 5. | This dissertation studies the problem of dynamics modeling , dynamical response , and distribution of moving mass for a re - entry vehicle ( mmcrv ) under the background of national natural science fund project “ precision control and guidance for moving mass control of a re - entry vehicle based on the virtual displacement concept ”
本论文以国家自然科学基金项目“基于虚位移概念的变质心再入飞行器精确制导问题研究”为背景,研究基于变质心控制的再入体动力学建模、动力学响应和落点分布等问题。
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| 6. | 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 . a unified form of hamilton principle in intrinsical linear nonholonomic system is studied in chapter 4
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。
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| 7. | The rational spectrums of all kinds of virtual displacement definitions and commutativity of d , ? operations are given and testified in this paper . the research methods of intrinsical linear nonholonomic dynamics are similar to those of holonomic dynamics . the rationality and equivalence of chetaev model and vacco model in the intrinsical linear nonholonomic system are testified from the mathematic and mechanical aspects
本文研究了非完整动力学中使不定性问题确定化的交换关系和将非线性问题线性化的虚位移定义，首次证明并给出了在非完系统中各种虚位移定义与交换关系的合理适用范围，指出完整动力学与本质线性非完整动力学在研究方法上具有相同性。
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| 8. | Moreover , popularizing such system is expected . the following works have been fulfilled within this thesis : first of all , based on the general principle of virtual displacement of nonlinear continuum mechanics , the geometric and material stiffness matrices is presented , several examples show that both of them can give out accurate result
本论文主要完成了以下工作：首先，根据连续介质力学理论构造出的交错桁架结构空间单元的几何刚度矩阵和弹塑性刚度矩阵，算例分析表明这些矩阵能准确地计算出结构的空间二阶效应和空间单元弹塑性杆端力增量，计算结果具有良好的精度。
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| 9. | Based upon virtual displacement method and the updated - lagrangian approach , stiffness matrices for two - dimensional elastic - plastic beam model in large displacement were proposed , in the derivation of which transverse stress was included because it was believed that part of the 2nd order effects of various stresses , which are in equilibrium with each other and with the external loads , will counteract each other and neglecting either part would possibly lead to incorrect results
利用虚位移原理和更新的拉格朗日方法，导出了大位移弹塑性梁单元刚度矩阵的显式表达式，在刚度矩阵推导中引入了截面内非线性剪应力和横向应力的影响，刚度矩阵通过了刚体检验。之所以要引入横向应力的影响，是因为本文认为，保持平衡所需的所有应力，它们各自的二阶效应会相互抵消，因此忽略其中的任何一项都可能导致不正确的结果。
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