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1.前言弹性锥壳的一般弯曲、稳定和振动问题,在实际工程中经常遇到,但对其研究基本上限于轴对称问题且都是以挠度函数和应力函数为基本未知量.我们认为,对于锥壳的特征值问题、弹性地基锥壳以及锥壳组合结构,则宜采用锥壳的位移解法.本文作者之一曾对锥壳一般弯曲问题的位移解法进行了系统的研究,以广义超几何函数给出了一般解.在应用文献[1]结果的基础上,本文通过引入一个广义载荷q_n(s,θ,t),得到了以位移函数U(s,θ,t)表示的弹性锥壳一般弯曲、稳定和振动(包括弹性地基影响)问题的统一型式的控制方程.文献[2]用级数给出了锥壳横向自由振动问题的解,但应指出,由于文献[2]中 相似文献
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基于[1]的弹性曲杆的平衡方程,本文研究了矩形横截面细长杆在轴压下的后屈曲行为。设横截面的边长比为 1:2δ,使用 Poincare-Keller 的打靶法并引进坐标的伸缩变换,研究了δ在 δ_0=1 附近的情形。当δ≠1 时,发现了杆平衡态的二次分叉。我们也给出了原始后屈曲解支及二次分支的渐近表示并分析了各个解支的稳定性。 相似文献
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正交各向异性柱壳的非线性参数共振问题——多频共振问题研究的应用 总被引:2,自引:0,他引:2
弹性结构动力稳定性问题,近年来一直受到各国的重视[1—13]。除研究线性与非线性弹性结构中的参数主共振外,在文献[2,3,4,7,8,13]中,还讨论了参数组合共振问题,在梁、杆、板方面组合共振已有较多的研究,在壳的组合共振问题方面文献较少。本文使用文献[18,19]中的多个快转相位方法和多频共振性质,论证了正交各向异性柱壳中参数主共振与组合共振的存在性和稳定性。 相似文献
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本文通过导出多种情形下的渐近解,采用新的级数求和等方法,对文献[1]中给出的有限封闭含水层系越流问题的精确解进行了具体计算,并研究了降深曲线的形态特点,以及各种地层参数对它的影响。计算结果和Neuman-Witherspooa解作了对比。 相似文献
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本文在[1]的基础上,研究了多层介质中由于双硬币形裂纹引起的对弹性扭转波散射的远场特性.文中应用Hankel积分变换和Abel变换,将问题最后归结为求解一组第二类Fredholm积分方程,并导出了用积分形式给出的散射位移场表达式.最后运用围道积分技术和渐近分析的方法,对散射位移场在远离裂纹时的主要性态进行了分析讨论. 相似文献
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各向异性平板开孔动应力集中问题的研究 总被引:2,自引:0,他引:2
采用各向异性平板弯曲波动理论及摄动方法,对正交各向异性平板开孔弯曲波的散射及动应力集中问题进行了分析研究,得到了此种平板稳态弯曲波动问题的渐近形式的分析解。同时采用保角映射技术,为求解正交各向异性平板开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。 相似文献
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The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by
means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress
waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves
while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated
when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation
due to their different velocities.
Southwest Institute of Structural Mechanics 相似文献
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The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s,θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s,θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S. Vlasov in circular cylindrical shell[5], the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell on the elastic foundation is reduced to find the displacement function U(s,θ).The general solution of the eight-order differential equation is obtained in series form. For the symmetric bending deformation of the conical shell on the elastic foundation, which has been widely usedinpractice,the detailed numerical results and boundary influence coefficients for edge loads have been obtained. These results have important meaning in analysis of conical shell combination construction on the elastic foundation,and provide a valuable judgement for the numerical solution accuracy of some of the same type of the existing problem. 相似文献
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Differential equations of the general theory describing the stress-strain state of conical shells are very complicated, and when computing the exact solution of the problem by analytic methods one encounters severe or even so far insurmountable difficulties. Therefore, in the present paper we develop an approach based on the method of asymptotic synthesis of the stressed state, which has already proved efficient when solving similar problems for cylindrical shells [1, 2]. We essentially use the fourth-order differential equations obtained by Kan [3], which describe the ground state and the boundary effect. Earlier, such equations have already been used to solve problems concerning force and thermal actions on weakly conical shells [4–6]. By applying the asymptotic synthesis method to these equations, we manage to obtain sufficiently accurate closed-form solutions. 相似文献
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谷宇 《应用数学和力学(英文版)》2008,29(3):389-398
Sandwich composite material possesses advantages of both light weight and high strength. Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied, little work has been done in the study of mechanical property, in view of the nonlinear behavior of sandwich composites in the complicated external environments. In this paper, the problem about the bending of the three-layer elastic-plastic rod located on the elastic base, with a compressibly physical nonlinear core, has been studied. The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined. The complicated problem about curving of the three-layer rod located on the elastic base has been solved. The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable. The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis. 相似文献
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T.C.T. Ting 《Journal of Elasticity》1997,49(3):269-284
A material is cylindrically anisotropic when its elastic moduli referred to a cylindrical coordinate system are constants.
Examples of cylindrically anisotropic materials are tree trunks, carbon fibers [1], certain steel bars, and manufactured composites
[2]. Lekhnitskii [3] was the first one to observe that the stress at the axis of a circular rod of cylindrically monoclinic
material can be infinite when the rod is subject to a uniform radial pressure (see also [4]). Ting [5] has shown that the
stress at the axis of the circular rod can also be infinite under a torsion or a uniform extension. In this paper we first
modify the Lekhnitskii formalism for a cylindrical coordinate system. We then consider a wedge of cylindrically monoclinic
elastic material under anti-plane deformations. The stress singularity at the wedge apex depends on one material parameter
γ. For a given wedge angle α, one can choose a γ so that the stress at the wedge apex is infinite. The wedge angle 2α can
be any angle. It need not be larger than π, as is the case when the material is homogeneously isotropic or anisotropic. In
the special case of a crack (2α=2π) there can be more than one stress singularity, some of them are stronger than the square
root singularity. On the other hand, if γ <
there is no stress singularity at the wedge apex for any wedge angle, including the special case of a crack. The classical
paradox of Levy [6] and Carothers [7] for an isotropic elastic wedge also appears for a cylindrically anisotropic elastic
wedge. There can be more than one critical wedge angle and, again, the critical wedge angle can be any angle.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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We study a three-dimensional contact problem on the indentation of an elliptic punch into a face of a linearly elastic wedge.
The wedge is characterized by two parameters of elasticity and its edge is subjected to the action of an additional concentrated
force. The other face wedge is free from stresses. The problem is reduced to an integral equation for the contact pressure.
An asymptotic solution of this equation is obtained which is effective for a given contact region fairly remote from the edge.
Calculations are performed that allow one to evaluate the effect of a force applied outside the contact region on the contact
pressure distribution. The problem under study is a generalization of L. A. Galin’s problem on a force applied outside a circular
punch on an elastic half-space [1, 2]. In a special case of a wedge with an opening angle of 180° and zero contact ellipse
eccentricity, the obtained asymptotic relation coincides with the expansion of Galin’s exact solution in a series. Problems
of indentation of an elliptic punch into a spatial wedge with the face not loaded outside the contact region have been studied
previously. For example, the paper [3] dealt with the case of a known contact region (asymptotic method) and the paper [4]
considered the case of an unknown contact region (numerical method). The solution of Galin’s problem allowed the authors of
[2] to reduce the contact problem on the interaction of several punches applied to a half-space to a system of Fredholm integral
equations of the second kind (Andreikin-Panasyuk method). A topical direction in contact mechanics is the model of discrete
contact as well as related problems on the interaction of several punches [2, 5–8]. The interaction of several punches applied
to a face of a wedge can be treated in a similar manner and an asymptotic solution can be obtained for the case where a concentrated
force is applied at an arbitrary point of this face beyond the contact region rather than on the edge. 相似文献
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Experimental investigations [1] show that when allowance is made for the real properties of a gas it is possible to have a regime of regular reflection of a shock wave from the surface of a wedge in which the reflected shock wave is attached to the tip of the wedge. In the present paper, which uses perturbation theory in a form close to a modified small-parameter method [2], an approximate analytic solution is constructed to the problem of the interaction of a strong shock wave with the surface of a wedge for such a regime. In contrast to the problem considered by the same authors in an earlier paper [3], the half-angle at the tip of the wedge is not assumed to be small.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 92–96, March–April, 1983. 相似文献