On stability and non-uniqueness of the dilatation states of a compressible isotropic unit cube subjected to dead loading

This paper considers a unit elastic cube, made of compressible isotropic material, with its faces subjected to certain dead-load tractions that produce a possible equilibrium state of non-uniform dilatation. It is seen that, at the considered equilibrium state, the cube material acquires properties of pseudo-transverse isotropy. Conditions are obtained for the stability of such an equilibrium state with respect to superimposed pure homogeneous deformations having principal directions parallel to the cube edges. The problem of non-uniqueness of the cube dilatation states is also addressed, and non-uniqueness is illustrated in an example application dealing with an isotropic cube made of the Blatz-Ko material. The nature and the stability features of these equilibrium states are studied in depth.     

Stresses in a tubular bone exposed to heat radiation from a distant heat source

The paper deals with the development of a mathematical model for studying the distribution of stresses generated in a long tubular bone specimen due to a radiating heat source situated at a very large distance. The model is particularly suitable for examining the effect of solar radiation on long bones. The expressions for the radial and circumferential stresses derived on the basis of the mathematical analysis are computed numerically for a particular bone specimen and the variation of the stress-components with radial and angular distances are studied.     

浸没的球面各向同性球壳的自由振动

本文引入三个们移函数并用球面调和函数展开，可将球面各向同性弹性力学的基本方程转化成一个独立的二阶常微分方程和另一个耦合的二阶常微分方程组，采用液动压力表示流体与壳的相互作用，可以把无限大不可压缩流体中任意厚度球面各向同性球壳的自由振动频率计算归结为一个代数循征值问题，文中计算了若干种情况下球壳的频率，在各向同性情形与有关文献作了比较。     

Isotropy of 5-dimensional quadratic forms over the function field of a quadric in characteristic 2

We complete a classification of quadratic forms over a field of characteristic 2 of type (1,3) that become isotropic over the function field of a quadric.     

Solution for plane strain forward and backward extrusions with a fractional reductionR=0.5 by the integartion depending on a parameter

A parameter t is introduced to boundary slip line of rigid regions for plane strain and indirect extrusions with a fractional reduction R=0.5. Integration by substitution has been used along the boundary slip line in order to obtain the extrusion pressure. By the integration depending on a parameter, the following results are obtained, and die pressure is 5.14k for backward extrusion; and pad average pressure is 2.57k for forward extrusion. All the results from this method are the same as those of the conventional solution.     

分析土壤半无限域的一种有限层方法(Ⅰ)——一般理论

本文研究了一种用于横观各向同性体动力学的有限层法.将土壤介质半无限域视为一个横观各向同性半空间体,介质的材料函数沿深度变化,将介质沿深度方向分成若干层,在每一层内材料函数用一个指数函数来模拟.这样,使求解问题的方程得到简化,利用Fourier变换我们得到了各层处“节点”力与位移的关系.这种有限层法实际上是一种半解析法.具有一般半解析法所具备的数据前后处理量少及计算量小等优点.本文所研究的这种有限层法为分析土壤与结构相互作用问题提供了一条新途径.     

非线性横观各向同性弹性材料的本构方程及其势函数

研究了非线性Green弹性材料弹性张量独立分量,归纳推导出横观各向同性Green弹性材料、各向同性非线性弹性材料独立的弹性常数个数.从张量函数出发,用含有高阶弹性张量的张量多项式,推导出四阶非线性横观各向同性,各向同性材料Green弹性材料本构方程及其势函数.并将本构方程及其势甬数用张量不变量,标量不变量表示.证明了方程是完备的,不可约的,满足张量函数表示定理.     

横观各向同性压电功能梯度旋转圆盘的三维解析解

从横观各向同性压电弹性力学轴对称问题基本方程出发,采用直接位移法将位移分量展开成径向坐标,的幂函数线性组合形式,其中含有7个待定的位移函数,它们是坐标z的函数,由基本方程导出关于位移函数的控制方程,结合相应的边界条件,可以积分得到位移函数,并确定积分常数,从而给出横观各向同性压电功能梯度旋转圆盘的三维解析解．并通过相应算例展示了一种特殊形式的压电功能梯度材料的梯度指标对应力场、位移场和电场的影响．     

Anti-plane Shear Deformations in Compressible Transversely Isotropic Materials

Anti-plane shear deformations in a compressible, transversely isotropic hyperelastic material are under investigation. The displacement is assumed to be along the direction of the symmetry axis and is independent of the axial position. The resulting equations of equilibrium form an overdetermined system of partial differential equations for which solutions do not exist in general. Necessary and sufficient conditions are derived for such materials to sustain anti-plane shear deformations in the sense that every solution to the axial equation automatically satisfies the other two in-plane equations. Comparison is made with results for isotropic materials. A weaker version of the conditions specialized to axisymmetric anti-plane shear deformations is also obtained.     

Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with cylindrical hole

This paper investigates the influences of higher order viscoelasticity and the inhomogeneities of the transversely isotropic elastic parameters on the disturbances in an infinite medium, caused by the presence of a transient radial force or twist on the surface of a cylindrical hole with circular cross section. Following Voigt＇s model for higher order viscoelasticity, the nonvanishing stress components valid for a transversely isotropic and higher order viscoelastic solid medium have been deduced in terms of radial displacement component. Considering the power law variation of elastic and viscoelastic parameters, the stress equation of motion has been developed. Solving this equation under suitable boundary conditions, due to transient forces and twists, radial displacement and relevant stress components have been determined in terms of modified Bessel functions. The problem for the presence of transient radial force has been numerically analysed. Modulations of displacement and stresses due to different order of viscoelasticity and inhomogeneity have been graphically depicted. The numerical study of the disturbance caused by the presence of twist on the surface may be similarly done but is not pursued in this paper.