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

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。     

Sudden tensile loading of a rubberlike bar

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?     

ANISOTROPIC EFFECTS OF QUASI-ISOTROPIC COMPOSITES(I)──MODELLING

Experimental observations show that quasi-isotropic materials, such as N-axial fibre-reinforced composites and woven materials, exhibit various degrees of anisotropy in elasticity and strength, and the anisotropy in strength is normally stronger than that in elasticity. In view of some available experimental data and based on the general formulation of the constitutive equations and failure criteria of quasi-isotropic materials established by using the theory of representations for tensor functions, we postulate several applicable models of the constitutive equations and strength for 3-and 4-axial quasi-isotropic materials to reveal the anisotropic effects. In a continued work (Part II), the anisotropic effect in strength of an infinitely large plate with a single elliptical hole or crack is studied, and the proposed stiffness and strength models are verified in terms of micro-mechanical analyses.Project supported by the National Natural Science Foundation of China and the State Education Commission Foundation of China     

The interaction of plane SH-waves and circular cavity surfaced with lining in anisotropic media

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.     

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

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.     

白桦材断裂韧度的各向异性性质

木材可视为正交各向异性材料，表征木材抵抗裂纹扩展能力的断裂韧度硒。是木材的基本力学性质之一，它具有明显的各向异性．对白桦材试样断裂韧度硒。测试结果表明，LT试样的断裂韧度明显高于TL，TR试样的断裂韧度，TL和TR试样的断裂韧度相接近．无论哪种试样类型，起裂均发生在裂纹尖端．TL，TR试样裂纹扩展方向与原裂纹初始方向一致，LT试样与前两不同，裂纹沿着几乎平行于纤维的方向扩展．并且含水率对各个方向木材断裂韧度的影响趋势是一致的．     

Asymptotic Axially Symmetric Deformations for Perfectly Elastic Neo-Hookean and Mooney Materials

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.      

Surface tensor estimation from linear sections

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n‐dimensional Euclidean space. The estimators are based on one‐dimensional linear sections. In a design based setting we suggest three types of estimators. These are based on isotropic uniform random lines, vertical sections, and non‐isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting.     

Gap formulas for closed linear relations

A classical formula for the gap between two densely defined closed operators in a Hilbert space is extended to the case of linear relations. Copyright © 2014 John Wiley & Sons, Ltd.