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981.
Let u(ε) be a rescaled 3-dimensional displacement field solution of the linear elastic model for a free prismatic rod Ωε having cross section with diameter of order ε, and let u (0) –Bernoulli–Navier displacement – and u (2) be the two first terms derived from the asymptotic method. We analyze the residue r(ε) = u(ε) − (u (0) + ε2 u (2)) and if the cross section is star-shaped, we prove such residue presents a Saint-Venant"s phenomenon near the ends of the rod. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   
982.
A new general constitutive model in terms of the principal stretches is proposed to reflect limiting chain extensibility resulting in severe strain-stiffening for incompressible, isotropic, homogeneous elastic materials. The strain-energy density involves the logarithm function and has the general Valanis–Landel form. For specific functions in the Valanis–Landel representation, we obtain particular strain-energies, some of which have been proposed in the recent literature. The stress–stretch response in some basic homogeneous deformations is described for these particular strain-energy densities. It is shown that the stress response in these deformations is similar to that predicted by the Gent model involving the first invariant of the Cauchy–Green tensor. The models discussed here depend on both the first and second invariants.   相似文献   
983.
吴柏生 《力学学报》1993,25(4):443-451
本文研究弹性基础上受轴向加载的两端铰支杆当其最低两屈曲荷载很近时的后屈曲行为。首先,使用Liapunov-Schmidt约化并借助稳定性分析,揭示了杆的二次屈曲现象;基于分叉方程给出了原始后屈曲分支及二次分支的渐近展开。其次,我们使用作者建立的二次分叉的计算方法对杆的二次屈曲做了数值计算,数值结果与渐近展开符合得很好  相似文献   
984.
The forced oscillations of a submerged elastic jet membrane modelling an axisymmetric counter-flow sound source are analyzed. The dependence of the amplitude-frequency response on the geometrical and hydrodynamic parameters of the membrane is studied. The influence of the properties of the fluid and the hydrodynamic pressure on the amplitude-frequency response is analyzed. The theoretical and experimental results are compared__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 60–65, April 2005.  相似文献   
985.
不同模量理论弹性支承连续梁及框架   总被引:2,自引:0,他引:2  
弹性支承连续梁及框架结构的内力不仅与各杆件的刚度有关,而且与支承结构的刚度有关.当引入拉压不同模量后,各杆件的抗弯刚度EI不再为常数(与经典力学不同),而是内力的函数,使结构内力计算成为非线性问题.用分段积分法推导出不同模量弹性支承连续梁及框架的中性轴公式和内力计算表达式并编制非线性内力计算迭代程序.通过实例计算对比分析不同模量与经典力学相同模量两种方法计算结果的差异,最后提出对该类结构计算的合理建议以及利用不同模量对结构进行优化的结论.  相似文献   
986.
应用Kirchhoff比拟讨论Kovalevskaya情况弹性细杆的平衡稳定性问题.导出Kirchhoff方程的解析积分.对于杆截面的主轴与Frenet坐标轴重合的无扭转杆的特殊情形作定性分析,讨论其平衡状态的稳定性与分岔.证明了判断受拉扭作用的圆截面直杆平衡稳定性的Greenhill公式也适用于Kovalevskaya情形的非圆截面杆.  相似文献   
987.
将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$\acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$\acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学.  相似文献   
988.
In this paper we study the problem of rectilinear shear of a slab of transversely isotropic incompressible non-linearly elastic material. In particular, the material under consideration is a base neo-Hookean model augmented with a function that accounts for the existence of a unidirectional reinforcement. The slab is of infinite length in two dimensions and finite thickness in the other one and is clamped to two rigid plates. Closed form analytic solutions are found for this problem. It is shown that, depending on the reinforcement strength and the fiber orientation in the undeformed configuration, weak solutions, i.e. solutions for which the smoothness required by the differential equations is relaxed, are to be expected. These solutions give rise to fiber kinking. It is shown that: (i) both sides of the kink involve fiber contraction; (ii) a suitable intermediate deformation between the two conjoined kink deformation states is non-elliptic.  相似文献   
989.
An asymptotic analysis of the plane problem of reptation motion of animals in a fluid is performed in a long-wave approximation. Turbulent motion is considered. Asymptotic estimates are obtained for the axial and shear forces, expended energy, and motion trajectory. Results of numerical analysis are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 60–69, March–April, 2006.  相似文献   
990.
A technique has been developed to assess elasticity in extension of fluids which are weakly elastic. The technique is based on stretching a fluid sample held between two small closely spaced co-axial disks until the fluid bridge or filament breaks. The distance between the disks on breakup, ‘the breaking length’, is measured. When the fluid is elastic, this length is greater than that of an equivalent inelastic fluid. An inelastic baseline was established by measuring the breaking lengths of a wide variety of Newtonian fluids. Measurements with weakly elastic fluids reveal that the extra breaking length increases with polymer type and concentration and with the rate of stretching, the expected behavior for elastic liquids. The breaking lengths of model paper coatings were measured and found to correlate with the degree of misting in a roll coating machine, indicating that droplet formation is related to extensional elasticity.  相似文献   
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