Journal of Solid Mechanics
Volume:13 Issue: 3, Summer 2021

Since the temperature or stress distribution in some advanced machines such as modern aerospace shuttles and craft develops in two or three directions, the need for a new type of FGMs is felt whose properties vary in two or three directions. On the other hand, dynamic buckling behavior of structures is a complicated phenomenon which should be investigated through the response of equations of motion. In this paper, dynamic response of beams composed of bi-directional functionally graded materials (BDFGMs) rested on visco-Pasternak foundation under periodic axial force is investigated. Material properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions based on the two types of analytical functions (e.g. exponential and power law distributions). Hamilton's principle is employed to derive the equations of motion of BDFGMs beam according to the Euler-Bernoulli and Timoshenko beam theories. Then, the generalized differential quadrature (GDQ) method in conjunction with the Bolotin method is used to solve the differential equations of motion under different boundary conditions. It is observed that a good agreement between the present work and the literature result. Various parametric investigations are performed for the effects of the gradient index, length-to-thickness ratio and viscoelastic foundation coefficients on the dynamic stability region of BDFGMs beam. The results show that the influence of gradient index of material properties along the thickness direction is greater than gradient index along the longitudinal direction on the dynamic stability of BDFGMs beam for both exponential and power law distributions.

In this study, a new periodic structure with special vibration band gap properties is introduced. This structure consists of a main beam and several cantilever beam elements connected to this main beam in the branched shape. Two models with different number of beam elements and geometrical parameters are considered for this periodic structure. The transverse vibrations of beams are solved using the generalized differential quadrature rule (GDQR) method to calculate the first four band gaps of each model. Investigating the influences of geometrical parameters on the band gaps shows that some bands are close to each other for specific ranges of geometrical parameters values. Furthermore, as the number of beam elements increases, the number of close band gaps increases. Having more than two close band gaps means that this periodic structure has a relatively wide band gap in total. Furthermore, this wide band can move to low frequency ranges by changing the geometrical parameters. Absorbing vibrations over a wide band gap at low frequency ranges makes this periodic structure a good vibration absorber. Verification of the analytical method using ANSYS software shows that the GDQR method can be used for vibration analysis of beam-like structures with high accuracy.

The article presents the study of the stress state of a two-layer composite with a cylindrical cavity located parallel to the surfaces of the layers. Displacements are set on the cavity and the upper and lower boundaries of the upper and lower layers, respectively. The three-dimensional elasticity solution has been obtained by the analytical-numerical generalized Fourier method with respect to the system of Lame equations in local cylindrical coordinates associated with cavity and Cartesian coordinates associated with boundaries of the layers. The infinite systems of linear algebraic equations resulting from satisfying the boundary conditions are solved by the reduction method. As a result, displacements and stresses have been obtained at various points of the elastic body. We have compared the stress-strain state of a two-layer structure with a cylindrical cavity located in either of the layers. The analysis included various geometrical parameters and boundary functions; the results obtained were compared with a single-layer holed structure.

The present study analyzes the free vibration of multi-layered composite cylindrical shells and perforated composite cylindrical shells via a modified version of Reddy’s third-order shear deformation theory (TSDT) under simple support conditions. An advantage of the proposed theory over other high-order theories is the inclusion of the shell section trapezoidal form coefficient term in the displacement field and strain equations to improve the accuracy of results. The non-uniform stiffness and mass distributions across reinforcement ribs and the empty or filled bays between the ribs in perforated shells were addressed via a proper distribution function. For integrated perforated cylindrical shells, the results were validated by comparison to other studies and the numerical results obtained via ABAQUS. The proposed theory was in good consistency with numerical results and the results of previous studies. It should be noted that the proposed theory was more accurate than TSDT.

An analytical framework is developed for the thermoelastic analysis of annular sector plate whose boundaries are subjected to elastic reactions. The exact expression for transient heat conduction with internal heat sources is obtained using a classical method. The fourth-order differential equation for the thermally induced deflection is obtained by developing a new integral transformation in accordance with the simply supported elastic supports that are subjected to elastic reactions. Here it is supposed that the movement of the boundaries is limited by an elastic reaction, that is, (a) shearing stress is proportional to the displacement, and (b) the reaction moment is proportional to the rate of change of displacement with respect to the radius. Finally, the maximum thermal stresses distributed linearly over the thickness of the plate are obtained in terms of resultant bending momentum per unit width. The calculation is obtained for the steel, aluminium and copper material plates using Bessel's function can be expressed in infinite series form, and the results are depicted using a few graphs.

This paper experimentally and numerically investigated the impact of a blunt projectile to perforated steel targets. In this study, projectiles were made of AISI 52100 and perforated plates were made of AISI 1045. In order to investigate the effect of the hole diameter on the projectile, three different diameters of the hole were considered, along with the effect of the projectile overlap with the hole. After examining different hitting states, the projectile was deviated from its movement direction after hitting the hole and changed from vertical hit to skew. The deviation of the projectile increased when the diameter of the hole increased or the amount of projectile overlap with the hole increased. Then, numerical modeling of impacting the projectile was performed by ABAQUS software and the results were compared with experimental results and the accuracy of the model was confirmed. And this model was used to investigate the effect of initial projectile speed on deviation of the projectile, accordingly, an increase in the initial velocity of the impact led to an increase in the deviation of the projectile.

As long as there is the need for disposal of  household  waste there will be the need to understand  the phenomena taking place in storage facilities for nonhazardous waste (municipal solid waste landfill). The understanding of landfill technology is of great importance because of its ever-changing state, whether mechanical, chemical or hydrological. In this context, there is a need to better understand the stress-strain behavior evolution with time of the landfilled waste. Based on triaxial and oedometric compression tests of municipal solid waste samples  ranging from fresh  to degraded waste, a viscoplastic constitutive model (Burgers creep-viscoplastic model) is used to describe the behavior of the municipal solid waste under loading. This model is able to adequately capture the stress-strain and pore water pressure response of the municipal solid waste at different ages. To illustrate its applicability, settlements due to the incremental loading of waste with time are predicted for a typical municipal solid waste landfill. The proposed model predicts the total settlement of a storage facilityin a range similar to results published in the literature. An extension of the studied municipal solid waste landfill was also investigated.

In this article, using memory-dependent derivative (MDD) on three-phase-lag model of thermoelasticity, a new generalized model of thermoelasticity theory with time delay and kernel function is constructed. The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function are applied to two dimensional problem of an isotropic plate. The two dimensional equations of generalized thermoelasticity with MDD are solved using state space approach. Numerical inversion method is employed for the inversion of Laplace and Fourier transforms. The displacements, temperature and stress components for different thermoelastic models are presented graphically and the effect of different kernel and time delay on the considered parameters are observed.