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101.
点支承四边自由各向异性平行四边形板自由振动、屈曲和弯曲分析 总被引:1,自引:0,他引:1
一个精确的重富立叶级数解析解用于分析四边形自由的点支横观各向异性平行四边形板的自由振动、屈曲和弯曲。解析解用叠加法得到,此解收敛迅速。与现有结果的比较证实了由本法得到的解析解的精确性。文后用图表给出高精度的自由振动、屈曲和弯曲计算结果。 相似文献
102.
本文采用泰勒级数法分析横观各向同性球壳轴对称弯曲问题。将位移沿厚度方向展开成泰勒级数,利用三维弹性方程求得级数中的各阶导数。对于边值问题,用特征函数法满足球面齐次边界条件,并用最小二乘配点法满足端部条件。 相似文献
103.
配点类无网格法需要计算近似函数的二阶导数,因而在移动最小二乘(MLS)近似中至少要采用二次基函数。本文利用Voronoi图对双重点移动最小二乘近似法进行了改进,建立了基于Voronoi图的双重点移动最小二乘近似(VDG),并利用加权最小二乘法离散微分方程,导出了双重点最小二乘配点无网格法(MD GLS)。该方法将求解域用节点离散,并以节点为生成点建立Voronoi图,取Voronoi多边形的顶点为辅助点。近似函数及其二阶导数的计算过程可分解为两个步骤:首先用场函数节点值拟合辅助点处近似函数的一阶导数,再以辅助点处近似函数的一阶导数值拟合节点处近似函数的二阶导数。由于在每一步中只需计算MLS形函数及其一阶导数,这种近似方法需要较少的影响点和较小的影响域。同时借助于Voronoi结构的优良几何性质,可以快速地搜索影响点。研究表明,与基于MLS的加权最小二乘无网格法(MWLS)相比,这种方法可以显著提高计算效率,并且在精度和收敛性方面也有所改善。 相似文献
104.
基于三维弹性理论,导出了带有压电层的圆柱形梯度壳的动力学方程以及相应的边界条件,用幂级数展开法得到了求解该圆柱形梯度壳自由振动的三维精确公式.通过实例模型求解了该壳体的自由振动的固有频率;分析了不同电学边界条件对壳体的振动频率的影响。结果可评估各种近似理论解和数值解的正确性。 相似文献
105.
106.
In this work, experimental determinations are carried out using a home-made device called an erythrodeformeter, which has
been developed and constructed for rheological measurements on red blood cells subjected to definite fluid shear stress. A
numerical method formulated on the basis of the fractal approximation for ordinary and fractionary Brownian motion1 is proposed to evaluate the viscoelastic behavior of mammalian erythrocyte membranes. The diffraction pattern, which is circular
when the mammalian erythrocyte membranes are at rest, becomes elliptical when the cells undergo shear stress. Photometric
readings of light intensity variation along the major axis of the elliptical diffraction pattern are recorded during the creep
and recovery process. These data series are used to calculate, fractal rheological parameters of self-affine Brownian motion
on the erythrocytes, averaged over several millions of cells. Three different parameters over the time dependent process could
be obtained, which are: correlation coefficient <C(t)>, correlation integral, andK
2-entropy, and very different results were obtained. 相似文献
107.
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
108.
G. Bonnet 《Journal of the mechanics and physics of solids》2007,55(5):881-899
A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended for rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites. 相似文献
109.
Diffuse mode bifurcation of soil under plane-strain compression test is shown, by means of an image analysis based on group-theoretic bifurcation theory, to trigger convection-like shear and to precede shear band formation. First digital photos of Toyoura sand specimens are processed by PIV (particle image velocimetry) to gather digitized images of deformation. Next bifurcation from a uniform state is detected by expanding these images into the double Fourier series and finding a predominant harmonic diffuse bifurcation mode based on that theory. This harmonic bifurcation mode, which is the mixture of a few harmonic functions, expresses complex convection-like shear. Last bifurcation from a non-uniform state is detected by decomposing each image into a few images with different symmetries to extract non-harmonic diffuse bifurcation modes. Diffuse modes of bifurcation, which hitherto were hidden behind predominant uniform compressive deformation, have thus been made transparent by virtue of the group-theoretic image analysis proposed. A possible course of deformation suggested herein is the evolution of diffuse mode bifurcation with a convection-like bifurcation mode breaking uniformity and symmetry, followed by the formation of shear bands through localization. 相似文献
110.
A. M. Zenkour 《Archive of Applied Mechanics (Ingenieur Archiv)》2004,74(3-4):262-276
Summary The static and dynamic responses of anisotropic spherical shells under a uniformly distributed transverse load are investigated.
Analytical solutions using the mixed variational formulation are presented for spherical shells subjected to various boundary
conditions. Numerical results of a refined mixed first-order shear deformation theory for natural frequencies, critical buckling,
center deflections and stresses are compared with those obtained using the classical shell theory. A variety of simply-supported
and clamped boundary conditions are considered and comparisons with the existing literature are made. The sample numerical
results presented herein for global structural behaviour of monoclinic spherical shells should serve as references for future
comparisons. 相似文献