Journal of Solid Mechanics
Volume:6 Issue: 3, Summer 2014

In this paper, the reflection and refraction of longitudinal wave from a plane surface separating a micropolar viscoelastic solid half space and a fluid saturated incompressible half space is studied. A longitudinal wave (P-wave) impinges obliquely at the interface. Amplitude ratios for various reflected and transmitted waves have been obtained. Then these amplitude ratios have been computed numerically for a specific model and results thus obtained are shown graphically with angle of incidence of incident wave. It is found that these amplitude ratios depend on angle of incidence of the incident wave as well as on the properties of media. A particular case when longitudinal wave reflects at free surface of micropolar viscoelastic solid has been deduced and discussed. From the present investigation, a special case when fluid saturated porous half space reduces to empty porous solid has also been deduced and discussed with the help of graphs.

In the present study, the effects of arrangement and distribution of multifarious types of defects on fundamental frequency of carbon nanotubes are investigated with respect to different chirality and boundary conditions. Interatomic interactions between each pair of carbon atoms are modeled using two types of non–linear spring–like elements. To obtain more information about the influences of defects; the effects of location, number and distribution (gathered or scattered defects) of two most common types of defects (vacancy and Stone–Wales defects) are examined on vibrational behavior of carbon nanotubes. Obtained results are in good agreement with the results reported in other literature. The results show that, gathered vacancy defects cause to a reduction in natural frequency of nanotubes, especially in the case of fix–fix boundary condition. It is also observed that the effect of defects depends on chirality intensively. In addition, the influence of the first vacancy defect is significantly more than the first Stone–Wales defect.

The use of intelligent nanocomposites in sensing and actuation applications has become quite common over the past decade. In this article, electro-thermo-mechanical nonlinear dynamic buckling of an orthotropic piezoelectric nanocomposite (PNC) cylindrical shell conveying viscous fluid is investigated. The composite cylindrical shell is made from Polyvinylidene Fluoride (PVDF) and reinforced by zigzag boron nitride nanotubes (BNNTs) where characteristics of the equivalent PNC being determined using micro-mechanical model. The poly ethylene (PE) foam-core is modeled based on Pasternak foundation. Employing the charge equation, Donnell''s theory and Hamilton''s principle, the four coupled nonlinear differential equations containing displacement and electric potential terms are derived. Harmonic differential quadrature method (HDQM) is applied to obtain the critical dynamic buckling load. A detailed parametric study is conducted to elucidate the influences of the geometrical aspect ratio, in-fill ratio of core, viscoelastic medium coefficients, material types of the shell and temperature gradient on the dynamic buckling load of the PNC cylindrical shell. Results indicate that the dimensionless critical dynamic buckling load increases when piezoelectric effect is considered.

In this paper, low cycle fatigue life of CK45 steel and SS316 stainless steel under strain-controlled loading are experimentally investigated. In addition, the impact of mean strain and strain amplitude on the fatigue life and cyclic behavior of the materials are studied. Furthermore, it is attempted to predict fatigue life using energy and SWT damage parameters. The experimental results demonstrate that increase in strain amplitude decreases fatigue life for both materials, strain amplitude has a remarkable effect on fatigue life, and the impact of mean strain is approximately negligible. Furthermore, the energy damage parameter provides more accurate prediction of fatigue life for both materials.

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differential equation. Then Homotopy Analysis Method is employed to obtain an analytic expression for nonlinear natural frequencies. Effects of design parameters including axial force and slenderness ratio on nonlinear natural frequencies are studied. Moreover, effects of factors of nonlinear terms on the general shape of the time response are taken into account. Combined Homotopy-Pade technique is used to reduce the number of approximation orders without affecting final accuracy. The results indicate increased speed of convergence as Homotopy and Pade are combined. The obtained analytic expressions can be used for a vast range of data. Comparison of the results with numerical data indicated a good conformance. Having compared accuracy of this method with that of the Homotopy perturbation analytic method, it is concluded that Homotopy Analysis Method is a very strong method for analytic and vibration analysis of structures.

A model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the material change. The problem is solved using two separate techniques. Primary, by applying Laplace and Fourier transformation, the governing equation for the crack problem is converted to the solution of a singular integral equation system. Then, finite element technique is employed to analyze this problem by considering quadrilateral eight nodded singular element near the crack tips. The effects of material non-homogeneity and crack length on the stress intensity factor are studied and the results of two methods are judged against each other.

In the current research with novel first and second differentiations of a yield function, Euler forward along with Euler backward with its consistent elastic-plastic modulus are newly implemented in finite element program in rate-independent plasticity. An elastic-plastic internally pressurized thick walled cylinder is analyzed with four famous criteria including both pressure dependent and independent. The obtained results are in good agreement with experimental results. The consistent/continuum elastic-plastic moduli for Euler backward method are also investigated.

Ring rolling is one of the most significant methods for producing rings with highly precise dimensions and superior qualities such as high strength uniformity, all accomplished without wasting any materials. In this article, we have achieved analytical formulas for calculating the pressure and shear friction over the contact arcs between the rollers and ring in the ring rolling process for the material in general nonlinear hardening property. We have also asserted the best mathematical model to predict friction for rolling processes. The method we use is based on calculating the analytical stress distribution. In other words, by using of Saint-Venan principal the stress components are calculated as analytical functions. Once that is accomplished, the pressure and shear traction over the rollers are able to be analyzed. The crucial characteristics which set apart this study from other studies are the investigation of the effects of the speed with which rollers are fed, and resulting ring velocity. With normal and shear friction, those characteristics cannot be investigated by other methods such as the slab method, upper bound, etc. Also, results show the effects of material hardening properties, radius of rollers and thickness reduction under pressure, and shear friction distributions.