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浸没的球面各向同性球壳的自由振动 总被引:1,自引:0,他引:1
本文引入三个们移函数并用球面调和函数展开,可将球面各向同性弹性力学的基本方程转化成一个独立的二阶常微分方程和另一个耦合的二阶常微分方程组,采用液动压力表示流体与壳的相互作用,可以把无限大不可压缩流体中任意厚度球面各向同性球壳的自由振动频率计算归结为一个代数循征值问题,文中计算了若干种情况下球壳的频率,在各向同性情形与有关文献作了比较。 相似文献
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1.几何非线性问题的基本方程在本世纪初,Reissner H.和Meissner E.利用在线性薄壳理论中存在的静力-几何比拟关系,将线弹性薄壳轴对称问题,归结为以应力函数和转角为未知量的两个常微分方程。以后,人们利用这两个方程的相似性,引入复未知函数,把一些典型壳体的方程简化为一个二阶变系数常微分方程,为这些问题的求解带来极大的便利。本文将这一方法推广到薄壳大位移问题,导出用复未知函数表示的常子午线曲率壳体轴对称变形的非线性微分方程。从这个一般方程可以直接得到关于柱壳,锥壳,圆球壳,环壳和圆板几何非线性问 相似文献
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针对具有弱界面的叠层压电球壳自由振动,引入两个位移和应力函数,从三维压电弹性理论基本方程出发建立了分别对应于两类振动形式的独立状态方程,并通过球面谐函数展开技术以及近似层合模型将其化为关于径向坐标的常系数状态方程.采用弱界面模型建立状态向量的界面传递关系,与层内传递关系得到球壳内外状态变量的整体传递关系.最后考虑球壳内外边界自由条件,得到了两类振动形式的频率方程.通过与已有精确解的比较验证了论文解的准确性,数值详细表明弱界面弹性柔性系数的大小对叠层球壳自振频率有较大影响,但弱界面导电性的高低对自振频率的影响不大. 相似文献
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提出球壳轴对称弯曲问题共轭二阶挠度微分方程并给出了初等函数解.
球壳微分方程是薄壳理论三大壳之一旋转壳的典型方程. 共轭二阶挠度微分方程是球
壳中微分方程形式最简单的, 是人们最喜爱的挠度微分方程. 挠度微分方程满足边
界条件非常简单, 使球壳的计算得到很大的简化. 相似文献
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1. 引言本文对受内压的复合材料球壳应用经典层合理论进行应力应变的分析。由一般球形壳体理论的五个平衡方程、六个几何方程及由层合理论导出的六个物理方程,共有十七个独立的方程可求解十七个未知函数,它们是三个中面位移、三个中面应变、三个曲面的曲率变化、五个应力合力、三个合力矩。应用球形壳体的应力函数U以后,得到二个基本微分方程。如为对称铺设此二基本微分方程可以简化。本文用有限差分法解此二基本微分方程。2. 基本方程的推导球壳的平衡方程如下: 相似文献
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板壳问题解的上边界与下边界朱宝安(天津,天津大学分校,300192)关键词加权残值法,数学规划,单调性1引言若微分方程问题存在解u(;,x。,…,x.)及两个近似解w;(xl,z:,…,。)和w(。。,。。,…,X.),关于。的凸集大一(X;,X。,... 相似文献
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复合材料层合开顶扁球壳的非线性动态屈曲 总被引:10,自引:0,他引:10
研究了复合材料层合开顶扁球壳的非线性动态屈曲问题。建立了对称层合圆柱正交异性开顶扁球壳考虑横向剪切的非线性振动微分方程,根据突变理论建立了该壳体动态屈曲的突变模型,得到了动态屈曲的临界方程。 相似文献
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采用六模态的中厚壳理论研究了可压缩流体中球面各向同性球壳的自由振动,即在分析中考虑了剪切变形,旋转惯量和横向正应变的影响,引入5个辅助变量可以理到两类振动及其频率方程,对频率方程作了简化并算例进行了相应的探讨。 相似文献
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Two displacement formulation methods are presented for problems of planar anisotropic elasticity. The first displacement method is based on solving the two governing partial differential equations simultaneously/ This method is a recapitulation of the orignal work of Eshelby, Read and Shockley [7] on generalized plane deformations of anisotropic elastic materials in the context of planar anisotropic elasticity.The second displacement method is based on solving the two governing equations separately. This formulation introduces a displacement function, which satisfies a fourth-order partial differential equation that is identical in the form to the one given by Lekhnitskii [6] for monoclinic materials using a stress function. Moreover, this method parallels the traditional Airy stress function method and thus the Lekhnitskii method for pure plane problems. Both the new approach and the Airy stress function method start with the equilibrium equations and use the same extended version of Green's theorem (Chou and Pagano [13], p. 114; Gao [11]) to derive the expressions for stress or displacement components in terms of a potential (stress or displacement) function (see also Gao [10, 11]). It is therefore anticipated that the displacement function involved in this new method could also be evaluated from measured data, as was done by Lin and Rowlands [17] to determine the Airy stress function experimentally.The two different displacement methods lead to two general solutions for problems of planar anisotropic elasticity. Although the two solutions differ in expressions, both of the depend on the complex roots of the same characteristic equation. Furthermore, this characteristic equation is identical to that obtained by Lekhnitskii [6] using a stress formulation. It is therefore concluded that the two displacement methods and Lekhnitskii's stress method are all equivalent for problems of planar anisotropic elasticity (see Gao and Rowlands [8] for detailed discussions). 相似文献
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圆柱型各向异性弹性力学平面问题 总被引:1,自引:1,他引:1
本文对圆柱型各向异性弹性力学平面问题的基本方程进行了改写。在此基础上,导出了应力函数G和位移函数φ,它们满足相同的控制方程,比文〔1〕的应力函数F的控制方程要简单,便于求得特解,并有F=rG的关系。还对若干经典问题进行了求解。 相似文献
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The paper systematically investigates the plane elasticity problems of two-dimensional quasicrystals with noncrystal rotational symmetry. First, applying their independent elastic constants, the equilibrium differential equations of the problems in terms of displacements are derived and it is found that the plane elasticity of pentagonal quasicrystals is the same as that of decagonal. Then by introducing displacement functions, huge numbers of complicated partial differential equations of the problems are simplified to a single or a pair of partial differential equations of higher order, which is called governing equations, such that the problems can be easily solved. Finally, some solving methods of these governing equations obtained are introduced briefly. 相似文献
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Displacement potentials in linear static elasticity consist of three functions which can be regarded as the three components of a vector, e.g., the Galerkin vector. This research note gives an explanation as to why the biharmonic equations govern these functions in isotropic elasticity as opposed to the sixth-order partial differential equations that govern them in anisotropic elasticity. This note also shows that the Eshelby solution in two-dimensional anisotropic elasticity can be derived from the method of displacement potentials. 相似文献
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锥壳固有振动的精确解 总被引:3,自引:1,他引:3
本文从锥壳的Mushtari-Donnell型位移微分方程组出发,通过引入一个位移函数U(s,θ,τ)(在极限情况下,它将退化成对于圆柱壳引入的位移函数),将基本微分方程组化成为一个可解偏微分方程。这个方程的解用级数形式给出。 相似文献
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Symmetry group classification for one-dimensional elastodynamics problems in nonlocal elasticity 总被引:1,自引:0,他引:1
T.
zer 《Mechanics Research Communications》2003,30(6):539-546
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黄义 《应用数学和力学(英文版)》1991,12(2):163-180
In this paper,the displacement solution method of the conical shell is presented.Fromthe differential equations in displacement form of conical shell and by introducing adisplacement function,U(s,θ),the differential equations are changed into an eight-ordersoluble partial differential equation about the displacement function U(s,θ)in which thecoefficients are variable.At the same time,the expressions of the displacement and internalforce components of the shell are also given by the displacement function.As special casesof this paper,the displacement function introduced by V.Z.Vlasov in circular cylindricalshell,the basic equation of the cylindrical shell and that of the circular plate are directlyderived.Under the arbitrary loads and boundary conditions,the general bending problem of theconical shell is reduced to finding the displacement function U(s,θ),and the generalsolution of the governing equation is obtained in generalized hypergeometric function,Forthe axisymmetric bending deformation of the 相似文献
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借鉴流形方法思想,引入广义节点的概念,对传统的无网格法进行了改进,建立了可具有任意高阶多项式插值函数的广义节点无网格方法。同时采用径向插值函数构造具有插值特性的逼近函数;采用配点法建立系统的离散方程。在阐述了这种方法基本原理的同时,针对线弹性力学问题给出了这种方法的数值计算列式。与传统无网格方法相比,这种方法更具有一般性;同时由于采用了配点法而不需要背景积分网格,所以可以认为这种方法是某种真正意义上的无网格法。当选取0阶广义节点位移插值函数时便可得到传统的无网格法;在不增加支持域内节点数目的条件下,通过选取高阶广义节点位移插值函数可以提高计算精度。最后通过算例分析,对0阶、1阶及2阶广义节点无网格法与现有的有关解答进行了对比,论证了其合理性。 相似文献
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IntroductionQuasicrystalasanewstructureofsolidmatter[1,2 ]bringsprofoundnewideastothetraditionalcondensedmatterphysicsandencouragesconsiderabletheoreticalandexperimentalstudiesonthephysicalandmechanicalpropertiesofthematerial,includingtheelasticitytheoryofthequasicrystal,manyvaluableresultsweregiven[3~ 5 ].Defectsinthematerialwereobservedsoonafterthediscoveryofthequasicrystal[6 ,7].Cracksareonetypeofdefects,theirexistencegreatlyinfluencesthephysicalandmechanicalpropertiesofthequasicrystalinem… 相似文献