Journal of Solid Mechanics
Volume:6 Issue: 4, Autumn 2014

One of the most promising materials in nanotechnology such as sensors, actuators and resonators is annular Boron Nitride sheets (ABNSs) due to excelled electro-thermo-mechanical properties. In this study, however, differential quadrature method (DQM) and nonlocal piezoelasticity theory are used to investigate the nonlinear vibration response of embedded single-layered annular Boron Nitride sheets (SLABNSs). The interactions between the SLABNSs and its surrounding elastic medium are simulated by nonlinear Pasternak foundation. A detailed parametric study is conducted to elucidate the influences of the nonlocal parameter, elastic medium, temperature change and maximum amplitude on the nonlinear frequency of the SLABNSs. Results indicate that with increasing nonlocal parameter, the frequency of the coupled system becomes lower. The results are in good agreement with the previous researches.

In this paper, the influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based functionally graded materials (FGM) cylindrical shells under combined loadings is investigated. The equations of motion are obtained by using the principle of Hamilton and Maxwell''s equations and the Navier''s type solution used to solve these equations. Material properties are changed according to power law in the direction of thickness. In this study, the effects of Pasternak elastic foundation coefficients and also the effects of material distribution, geometrical ratios and loading conditions on the natural frequencies are studied. It is observed that by increasing Pasternak elastic medium coefficients, the natural frequencies of functionally graded piezoelectric materials (FGPM) cylindrical shell always increases. The mode shapes of FGPM cylindrical shell has been shown in this research and the results show that the distribution of the radial displacements is more significant than circumferential and longitudinal displacements.

A semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonable order of convergence. It is assumed that material properties except Poisson’s ratio are graded through the thickness direction of the sphere according to an exponential distribution. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and von Mises equivalent stress, as a function of radial direction, are obtained. A numerical solution, using finite element method (FEM), is also presented. Good agreement was found between the semi-analytical results and those obtained through FEM.

Stable ductile crack growth in 3 mm thick AISI 304 stainless steel specimens has been investigated experimentally and numerically. Multi-linear Isotropic Hardening method coupled with the Von-Mises yield criterion was adopted for modeling elasto-plastic behavior of the material. Mode-I CT fracture specimens have been tested to generate experimental load-displacement-crack growth data during stable crack growth. The critical fracture energy (JIc) was then determined using the finite elements results in conjunction with the experimental data. The effect of in-plane constraints on the numerical-experimental JIc calculation was then investigated. The results of finite element solution were used to tailor an exponential CZM model for simulation of mode-I stable crack growth in CT specimens. It is found that the adopted CZM is generally insensitive to the applied constraints to the crack tip stress state and thus it can effectively be used for simulating crack growth in this material.

In the present study, the analysis of nonlinear vibration for a simply-supported flexible beam with a constant velocity carrying a moving mass is studied. The amplitude of vibration assumed high and its deformation rate is assumed slow. Due to the high amplitude of vibrations, stretching is created in mid-plane, resulting in, the nonlinear strain-displacement relations is obtained, Thus, Nonlinear terms governing the vibrations equation is revealed. Modified homotopy equation is employed for solving the motion equations. The results shown that this method has high accuracy. In the following, analytical expressions for nonlinear natural frequencies of the beams have been achieved. Parametric studies indicated that, due to increasing of the velocity concentrated mass, the nonlinear vibration frequency is reduced. On the other hand, whatever the mass moves into the middle of beam, beam frequency decreases.

In this paper, a six-stage interactive model is presented for the perforation of metallic plates using blunt deformable projectiles when plastic wave propagation in both target and projectile is considered. In this analytical model, it is assumed that the projectile and target materials are rigid – plastic linear work hardened. The penetration of the projectile into the target is divided into six stages and governing equations are derived. The analytical model shows that residual velocity, diameter of the flattening area of the projectile, and ballistic limit velocity, show close agreement with the data from experiment.

In this paper, edge crack problems under mechanical loads have been analysed using extended finite element method (XFEM) as it has proved to be a competent method for handling problems with discontinuities. The XFEM provides a versatile technique to model discontinuities in the solution domain without re-meshing or conformal mesh. The stress intensity factors (SIF) have been calculated by domain based interaction integral method. The effect of crack orientation and interaction under mechanical loading has been studied. Analytical solutions, which are available for two dimensional displacement fields in linear elastic fracture mechanics, have been used for crack tip enrichment. From the present analysis, it has been observed that there is monotonous decrease in the SIF-1 value with the increase in inclination, while SIF-II values first increases then it also decreases. Next study was performed for first edge crack in the presence of second crack on opposite edge. The results were obtained by changing the distance between the crack tips as well as by changing the orientation of second crack. SIFs values decrease with increase in distances between the crack tips for collinear cracks. In next study, for the first crack in presence of inclined second edge crack and it was found that SIFs increase initially with the increase in inclination and decrease after that. It emphasizes the fact that cracks at larger distances act more or less independently. In next study, with the use of level set method crack growth path is evaluated without remeshing for plate with hole, soft inclusion & hard inclusion under mode-I loading and compare with available published results.

In the present article, the reflection and transmission of plane waves at the boundary of thermally conducting micropolar elastic media with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected and transmitted waves at different angles of incident wave are obtained. Dissipation of energy and two temperature effects on these amplitude ratios with angle of incidence are depicted graphically. Some special and particular cases are also deduced.