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近期在对虚功原理(也叫虚位移原理)的讨论中谈到的都是定常系统。如果对非定常系统的情况作一些分析,将对这个讨论有所帮助。本文阐述了非定常系统中虚位移原理的特征、证明的要点、并举例说明应用。1.非定常系统虚位移原理的特征,证明的要点虚位移原理具有理想约束的质点系在某位置平 ... 相似文献
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本文提出了采取分区域混合使用虚力原理和虚位移原理的方法推导有限元杂交模型,并用这种方法具体导出了一种增量型的杂交应力分层三角形板单元.本单元,导出时用了作者们早先给出的正交各向异性体增量型的塑性应力应变关系,并且以E.Reissner 厚板理论为基础,可用于对工程上各种厚度的板(壳)进行弹塑性分析.文中提出的混合使用虚力原理和虚位移原理的方法可使许多无变分原理的问题直接建立杂交模型. 相似文献
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理想约束是分析力学的基本假定, 虚位移原理是分析静力学的基本原理. 本文从经典著作和重要教材中提取一些信息, 期望描述理想约束和虚位移原理的形成和发展, 并发表一些议论. 相似文献
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汉代辛氏《三秦记》中记述:``龙门山,在河东界. 每岁季春,有黄鲤鱼自海及诸川,争来
赴之. 一岁中,登龙门者不过七十二. 初登龙门,则有云雨随之,云火自后烧其尾,乃化为
龙矣. '民间``鲤鱼(Carp)跃龙门'美好的传说一直流传至今. 为什么在传说中选择鲤鱼
去跳龙门呢?不但因为鲤鱼长着``鱼须'酷像``龙须',更重要的是鲤鱼能够较迅速地跃出
水面. 那么鲤鱼是靠什么跃出水面的呢?尾巴!这一定是大家的回答. 答案是肯定的. 从力
学原理的角度上讲,鲤鱼能否跳过龙门取决于它跃出水面的速度和角度. 相似文献
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且前的表述形式能否用于有限元分析在一些有限元文献里,把虚位移原理表述成如下必要性命题形式: 如果变形体在发生虚位移以前是平衡的,则当变形体发生任一虚位移时,外力所作总虚功必等于应力在虚应变上所作的总虚变形功。并以此为据进行有限元的单元和整体分析。 相似文献
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在<关于虚功原理的讨论>中,曾涉及如下一些问题:如何将虚位移分解为刚性虚位移和变形虚位移;切割面内力在刚性虚位移上所作之总功W_(面刚),与该力在变形虚位移上所作之总功W_(面变)之间有何关系;如何理解变形体所接受的总虚变形功W_变,及其与内力总虚变形功W_内之间的关系;等等。下面以梁为例就上述问题发表一些粗浅看法。一、关于虚位移之分解为刚性虚位移和变形虚位移考虑图1(a)所示直梁,在横向分布载荷q与端面力Q_0、M_0、Q_1、M_l的作用下处于平衡状态。现在,使 ... 相似文献
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从虚功原理的要求和静不定结构的受力特点出发,指出将单位力加在静定基上的
本质是构造了原结构的静力许可场,从而论证了``在静定基上加单位力来求静不定结构位
移'这一方法的正确性. 相似文献
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戴天民 《应用数学和力学(英文版)》2002,23(2):119-126
IntroductionSomeauthorsstudiedthecoupledfieldproblemsformicropolarcontinua .Especially ,W .Nowackipublishedaseriesofabout 4 0scientificpapersdealingwiththemicropolarthermoelasticityaswellastheproblemsofdistortion ,thermodiffusion ,thermopiezoelectricityandm… 相似文献
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Dai Tian-min 《应用数学和力学(英文版)》2001,23(2):119-126
Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of
micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is restudied. The reason why it
was restricted to a linear one is analyzed. The rather general principle of virtual work and the new formulation for the virtual
work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established.
From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions
of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously
derived.
Contributed by DAI Tian-min
Foundation item: the National Natural Science Foundation of China (10072024); the International Cooperation Project of the NSFC (10011130235)
and the DFG (51520001); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931-) 相似文献
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The Virtual Fields Method (VFM) and the Eigenfunction Virtual Fields Method (EVFM) are inverse techniques for estimating constitutive properties from full-field experimental data. In these, a set of virtual fields is used in the Principle of Virtual Work (PVW) to yield a system of algebraic equations for the unknown material parameters. In a typical experiment, one does not know the distribution of tractions over the external surface of the specimen, but the total force is generally measured. In order to still enable evaluation of the external virtual work integral that appears in PVW, in all the work to date on Virtual Fields methods, the virtual displacements are restricted to be uniform over the portion of the exterior surface where tractions are prescribed so that the external virtual work is simply the inner product of the known total force vector and the uniform value of the chosen virtual displacement vector. In this work, we show that this constraint can be relaxed to obtain a more flexible version of EVFM. The proposed modification is used to obtain orthotropic elastic constants from a simulated unnotched Iosipescu test, and is shown to yield tighter estimates than previously obtained wherein the boundary virtual displacements were constrained to be uniform. This approach, which is novel to Virtual Fields methods, allows us to include domains in the interior of the specimen and therefore, results in an EVFM formulation capable of dealing with material heterogeneity, missing data and discontinuities in specimen geometry. 相似文献
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微孔压电弹性动力学的能量原理 总被引:6,自引:1,他引:5
根据古典阴阳互补和现代对偶互补的基本思想,通过作者早已提出一条简单而统一的新途径,系统地建立了微孔压电弹性动力学的能量原理,给出一个重要的以卷积表示的积分关系式,可以认为,在力学上它是广义虚功原理的表式,从该式出发,不仅能得到微孔压电弹性动力学的虚功原理和互等定理,而且通过作者所给出的一系列广义Legendre变换,能系统地导出成互补关系的11类变量、9类变量、6类变量和3类变量简化Gurtin型变分原理的泛函,同时,通过这条新途径,还能清楚地阐明这些原理之间的内在联系。 相似文献
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有孔隙的耦合热弹性体动力学的一些基本原理 总被引:4,自引:0,他引:4
根据对偶互补的基本思想,通过作者在文[1]中所提出的一条简单而统一的新途径,系统地建立了有孔隙的耦合热弹性体动力学的一些基本原理.文中首先给出一个重要的以卷积表示的积分关系式,可以认为,在力学上它是一个广义虚功原理的表式.然后从该式出发,不仅可以得到有孔隙的耦合热弹性体动力学的虚功原理和互等定理,而且能系统地导出成互补关系的11类变量、9类交量、6类变量及3类变量简化Gurtin型变分原理.同时,通过这条新途径,还能清楚地阐明这些原理之间的内在联系. 相似文献
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静电梳齿微驱动器因其结构简单、功耗低、灵敏度高、受温度影响小,成为硅微陀螺仪的主要驱动方式。静电梳齿微驱动器通常由活动梳齿和固定梳齿组成。理想情况下,活动梳齿平行地位于两固定梳齿中心位置。但由于加工误差、驱动结构不对称、扰动等因素,使得活动梳齿相对固定梳齿发生偏转。该文应用能量法及虚功原理,建立了梳齿之间的力与力矩平衡方程。得出了非理想情况下,偏离距离和转角的解析表达式,并分析得出了梳齿间的临界电压。经过数值仿真发现,梳齿面内既偏转又转动时的临界电压小于只发生偏转或转动时的临界电压。 相似文献
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Luo En 《Acta Mechanica Sinica》1993,9(2):142-148
According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author[1], some basic principles in dynamic theory of elastic materials with voids can be established systematically. In this paper,
an important integral relation in terms of convolutions is given, which can be considered as the generalized principle of
virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the
reciprocal theorem in dynamic theory of elastic materials with voids, but also to derive systematically the complementary
functionals for the eight-field, six-field, four-field and two-field simplified Gurtin-type variational principles. Furthermore,
with this approach, the intrinsic relationship among various principles can be explained clearly.
The project supported by the Foundation of Zhongshan University Advanced Research Center 相似文献
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马景槐 《应用数学和力学(英文版)》2000,21(2):185-192
IntroductionThecontinuousmediumdamagemechanicshasbeenmoreandmoreappliedinmanyengineeringfieldsinpastyears.Atpresent,thehotpointofdamagemechanicsresearchisthedamageconstitutiverelationofmaterial.Itisratherdeficientinresearchofdamagestructureanalyticpri… 相似文献