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31.
James K. Knowles 《Mechanics Research Communications》2003,30(6):581-587
In uniaxial tension, the stress–strain curve for rubber changes curvature from concave to convex as the strain increases. For sudden tensile loading of a bar, a one-dimensional model that reflects this behavior leads to an under-determined problem reminiscent of that arising in materials capable of undergoing phase transitions. In the latter setting, adding the kinetic relation underlying the phase change to the conventional statement of the problem removes the indeterminacy; the same is true when such a relation is used in a formal way in the problem for rubber. This presents a physical question: What is the evolutionary process at the microscale whose kinetics are needed in the dynamics of rubber? 相似文献
32.
33.
Zirka A. I. Malezhik M. P. Chernyshenko I. S. Sheremet G. P. 《International Applied Mechanics》2004,40(7):810-813
The stress wave field and the behavior of waves near the free boundary in an orthotropic plate and at the interface between two anisotropic media are studied. The results presented were obtained using the dynamic photoelastic method and optically sensitive fibrous models. Experimental data for impulsively loaded plates with various boundary conditions are analyzed 相似文献
34.
35.
For axially symmetric deformations of the perfectly elastic neo-Hookean and Mooney materials, formal series solutions are
determined in terms of expansions in appropriate powers of 1/R, where R is the cylindrical polar coordinate for the material coordinates. Remarkably, for both the neo-Hookean and Mooney materials,
the first three terms of such expansions can be completely determined analytically in terms of elementary integrals. From
the incompressibility condition and the equilibrium equations, the six unknown deformation functions, appearing in the first
three terms can be reduced to five formal integrations involving in total seven arbitrary constants A, B, C, D, E, H and k
2, and a further five integration constants, making a total of 12 integration constants for the deformation field. The solutions
obtained for the neo-Hookean material are applied to the problem of the axial compression of a cylindrical rubber tube which
has bonded metal end-plates. The solution so determined is approximate in two senses; namely as an approximate solution of
the governing equations and for which the stress free and displacement boundary conditions are satisfied in an average manner
only. The resulting load-deflection relation is shown graphically. The solution so determined, although approximate, attempts
to solve a problem not previously tackled in the literature.
相似文献
36.
弹性地基上四边自由的各向异性矩形板 总被引:4,自引:2,他引:4
通过叠加法得到了弹性地基上的各向异性矩形板的一般解。每个叠加解被展成重傅立叶级数,其自身或其一阶导数在边界上的值被展成单傅立叶级数。利用控制微分方程和一些边界条件,每个叠加解被简化成用边界值的级数的系数表示的傅立叶级数。文后给出了弹性地基上的方板的挠曲面图。 相似文献
37.
In this paper, we use the complex function method for solving the problem of interaction of plane SH-waves and circular cavity
surfaced with lining in anisotropic media. Anisotropic media can be used to simulate the conditions of the geology. This problem
can be handled by using the method similar to that incorporated in Ref. [5] to define the scattering waves in media, added
with the given boundary condition of the circular cavity.
In this paper, as illustrated in the examples, the results and discussions of numerical studies have been done for the interaction
of plane SH-waves and two kinds of circular cavities, surfaced with lining made up of different materials, in anisotropic
media. 相似文献
38.
39.
According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed. 相似文献
40.