In the present study, the boundary value problems in generalized thermodiffusive ELASTIC MEDIUM has been investigated as a result of inclined load. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. As an application of the approach, distributed sources and moving force have been taken. Expressions of displacement, stresses, temperature and concentration in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. Graphical representation due to the response of different sources and use of angle of inclination are shown. Some particular cases are also deduced.

In the present research, stress analysis of a functionally graded material cylindrical pressure vessel subjected to the simultaneous action of thermal loading, rotation and internal pressure is performed. Also it is assumed that vessel in located in an ELASTIC MEDIUM which is designated according to the Winkler model. Except for Poisson’ s ratio, all of the thermomechanical properties of the vessel are assumed to follow a power law model and vary across the radius of the vessel. Heat conduction equation and Navier equation which govern the temperature and radial displacement distribution across the radius of vessel are established and solved analytically. Closed form expressions are obtained for temperature distribution, radial displacement profile, strains and stresses components in the vessel. Parametric studies are provided to explore the effects of rotation and foundation stiffness on the structural responses of the vessel. It is shown that, foundation stiffness, power law index of the properties and angular speed all affect the stresses and displacement components of the vessel, significantly.

Third order shear deformation theory of cylindrical shells is employed to investigate the vibration characteristics of non-homogeneous cylindrical shells surrounded by an ELASTIC MEDIUM. The kinematic relations are obtained using the strain-displacement relations of Donnell shell theory.The shell properties are considered to be dependent on both position and thermal environment. A suitable function through the thickness direction is assumed for the non-homogeneity property.The Winkler-Pasternak ELASTIC foundation is used to model the ELASTIC MEDIUM. Analytical solutions are presented for cylindrical shells with simply supported boundary conditions. From the numerical studies, it is revealed that, the natural frequencies are affected significantly by the ELASTIC foundation coefficients and environmental temperature conditions.

In the process of hydraulic fracture, various physical parameters such as; viscosity, inertia of fluid and toughness of rock do not influence the fracture propagation identically, and it is probable that one or more of the parameters be more pronounced. Therefore, it may persuade one special regime which is named base on dissipation of energy. In an impermeable rock, the two limiting regimes can be identified with the dominance of one or the other of the two energy dissipation mechanisms corresponding to extending the fracture in the rock and to flow of viscous fluid in the fracture, respectively. In the viscosity-dominated regime, dissipation in extending the fracture in the rock is negligible compared to the dissipation in the viscous fluid flow, and in the toughness-dominated regime, the opposite holds. Here, it is supposed that the flow of incompressible fluid in the fracture is unidirectional and laminar. Besides, the fracture is fully fluid-filled at all times and fracture propagation is described in the framework of linear ELASTIC fracture mechanics (LEFM). In this paper, a new semi-analytical method has been introduced for solving the plane-strain fluid-driven fracture propagating in an impermeable MEDIUM in viscosity-toughness dominated (the MK-edge solution). Standard methods of analysis and improvement of diverging series have been applied on the expansion series method to gain the more convergence for the viscosity series diverge due to a nearest (non-physical) singularity on the negative real axis of the viscosity parameter for larger viscosity. For more explanation, Euler transformations have been suggested in terms of small parameter which is a function of viscosity parameter. Compared to the other analytical solution (e. g. Garagash, 2006), the new M-K edge solution represents a significant improvement in term of convergence. In addition to, the results have been compared to the numerical solution (e. g. Adachi, 2000) and it is shown good agreement in the light of quantity and quality. Contrary to numerical methods, the new proposed method can pragmatically be used for the range of M-K edge.

In the present investigation, we study the re ection of plane waves, that is, Longitudinal displacement wave(P-Wave), Thermal wave(T-Wave) and Mass Di, usive wave(MD-Wave) in thermodi, usion ELASTIC-half MEDIUM which is subjected to impedence boundary condition in context of one relaxatioon time theory given by Lord and Shulman theory (L-S) and the Coupled theory (C-T) of thermoELASTICity. The expressions of amplitude ratios are obtained numerically and their variation with angle of incidence is presented graphically for a particular model to emphasize on the impact of impedence parameter, relaxation time and di, usion. Some special cases are also deduced.

In this paper, surface energy and ELASTIC MEDIUM effects on torsional vibrational behavior of nanorods are studied. The surface ELASTICity theory is used to consider the surface energy effects and the ELASTIC MEDIUM is modeled as torsional springs attached to the nanorod. At the next step, Hamilton’ s principle is utilized to derive governing equations and boundary conditions. Then, with the aid of an analytical method, natural frequencies are obtained and effects of various parameters on torsional frequencies are studied in details. It is concluded from the present study that the surface energy can make nanorods unstable depending on the nanorod dimension and frequency number. Results of the present study can be useful in design of nanoelectromechanical systems like drive shafts.

In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal ELASTICity and the effects of nonlocal forces from adjacent and non-adjacent elements on deflection are considered. The Eringen’s theory is utilized due to its capability to consider the size effect. Based on Hamilton’s principle, motion equations as well as boundary conditions are derived and solved by means of hybrid analytical-numerical method. It is believed that the presented general foundation model offers an exact and effective new approach to investigate vibration characteristics of this kind of structures embedded in an ELASTIC MEDIUM. The results of this investigation may provide a useful reference in controlling systems in nano-scale.