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Power series method is used to analyze the distribution of stresses of the transversely isotropic cylinder under arbitrary axisymmetrical normal load. The stress function and normal load are expanded as the form of Fourier series. Unknown parameters in equations are determined using boundary conditions and final solutions of stress and displacement are obtained accordingly. The analysis of stresses obtained from different material parameters shows that the axial stress is significantly affected by Young's modulus and the circumference stress is sensitive to the variation of Poisson's ratio.

In the present paper, a technique is presented for obtaining estimates for the natural frequencies of axisymmetric vibration for transversely isotropic material. The wave propagation of harmonic waves in hollow cylinder of transversely isotropic materials subjected to certain boundary conditions is studied. The two-dimensional equations of elastodynamic are solved in terms of displacement by using the technique of variables separation. The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained. The natural frequencies are calculated numerically and the effects of rotation is discussed. The numerical results obtained have been illustrated graphically to understand the behavior of natural frequency versus the ratio h. Comparisons are made with the result in the absence of rotation.

The frequency of vibration of thick-walled toroidal shells is studied using a finite element formulation wherein the finite element is derived directly in toroidal coordinates. Hexagonal crystals of thallium and cadmium are used as representative transversely isotropic materials. The shell is assumed to be transversely isotropic with respect to the toroidal radial direction, and results based on that assumption are contrasted to a shell that is transversely isotropic with respect to the circumferential toroidal coordinate. It is established that an analysis based on a toroidal coordinate system is superior to an axisymmetric coordinate system and has some advantages over a commercial finite element code. Tables of results are presented that compare frequency of vibration for the above mentioned transversely isotropic materials and isotropic materials.

This paper investigates the prebuckling dynamics of transversely isotropic thin cylinder shells in the context of propagation and reflection of axial stress waves. By constructing the Hamiltonian system of the governing equation, the symplectic eigenvalues and eigenfunctions are obtained directly and rationally without the need for any trial shape functions, such as the classical semi-inverse method. The critical loads and buckling models are reduced to the problem of eigenvalues and eigensolutions, in which zero-eigenvalue solutions and nonzero-eigenvalue solutions correspond to axisymmetric buckling and nonaxisymmetric buckling, respectively. Numerical results reveal that energy is concentrated at the unconstrained free ends of the shell and the buckling modes have bigger bell-mouthed shapes at these positions.

This paper presents the uniaxial and biaxial buckling analysis of rectangular plates based on new trigonometric shear and normal deformation theory. The theory accounts for the cosine distribution of the transverse shear strain through the plate thickness and on the free boundary conditions on the plate surfaces without using the shear correction factor. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The Navier type solutions for the buckling analysis of simply supported isotropic, transversely isotropic, orthotropic and symmetric cross-ply laminated composite rectangular plates subjected to uniaxial and biaxial compressions are presented. The effects of variations in the degree of orthotropy of the individual layers, side-to-thickness ratio and aspect ratio of the plate are examined on the buckling characteristics of composite plates. The present results are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT) and exact three-dimensional (3D) elasticity theory wherever applicable. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory.

The torsional dynamic response of a pile embedded in transversely isotropic saturated soil is investigated while allowing for the construction of disturbance effect. The dynamic governing equations of soil are established based on Biot’s poroelastic theory. By virtue of the continuous conditions of stress and displacement of adjacent disturbance circle and the boundary conditions of pile-soil coupling system, the circumferential displacement of soil and the shear stress on pile-soil contact surface are derived. Subsequently, a closed-form solution for the torsional dynamic response of a pile is derived in the frequency domain. By using inverse Fourier transform and the convolution theorem, a quasi-analytical solution for the velocity response of the pile head subjected to a semi-sine excitation torque is derived in the time domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Following the present solution, a parameter study is undertaken to portray the influence on the complex impedance, twist angle and torque of pile.

The meniscus is a multifunctional fibrocartilage tissue in the knee joint which stables joint movement, bears load and absorbs impact. Improper collisions will cause damage to meniscus tissue and lose its original functionality. However, it is difficult to fully evaluate the mechanical properties of the meniscus based on static test results alone. In this study, Split Hopkinson Pressure Bar (SHPB) and hydraulic material testing system (MTS) were utilized to examine the quasi-static and dynamic properties of the porcine meniscus along with two different orientations. The results showed that the meniscus is a strain rate sensitive material and its mechanical properties mainly depend on the orientation of collagen fiber bundles in the peripheral direction. The meniscus tissue did not show obvious yield characteristics under quasi-static test conditions. However, the meniscus showed clear yield behavior under dynamic loading. When the strain rate increased, the elastic modulus of the radial meniscus remained around 35 MPa while the elastic modulus of the axial meniscus increased from 30 MPa to 80 MPa. This study demonstrates that the meniscus is sensitive to strain rate at both dynamic and quasi-static conditions, and the meniscus is an anisotropic biological tissue.

This paper deals with propagation of Rayleigh-type waves in nonlocal inhomogeneous transversely isotropic half-space. From the characteristic equation of wave for the nonlocal inhomogeneous transversely isotropic medium, the existence of the number of surface waves depends on the inhomogeneity of the medium through the number of solutions satisfying the damping condition of the characteristic equation discussed. It has also been concluded that there exist cut-off frequency and escape frequency for the wave propagating in size-dependent materials based on the nonlocal theory. Dispersion equation for the propagation of Rayleigh-type surface waves at the free surface has been derived. Based on the obtained dispersion equation, the effects of the inhomogeneity of material and nonlocality parameter on the Rayleigh wave propagation are considered through some numerical examples.

Two transversely isotropics elastically similar semi-infinite solids in partial slip tangential contact are considered in the framework of the Cattaneo–Mindlin theory. The problem of limiting shape of the contacting surfaces due to wear in the slip zone is solved under the assumption of constant normal force and oscillating tangential force with a constant amplitude. It has been shown that both the stick zone and the limiting shape do not depend on the orientation of the tangential force. The novelty of the present study is not only in finding an exact analytical solution to the problem of limiting shape in fretting but also in extending the Cattaneo–Mindlin theory of local tangential contact to transversely isotropic, elastically similar solids.

This paper has the objective of studying the propagation of surface waves in a transversely isotropic medium based on nonlocal strain gradient theory (NSGT). A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory and classical theory. It has also been concluded that there exist escape frequency and cut-off frequency for the wave propagating in size-dependent materials based on the NSGT. Dispersion equation for the propagation of Rayleigh-type waves at the free surface has been derived. The effect of the nonlocal parameter, the strain gradient parameter on the Rayleigh wave propagation is considered through some numerical examples.