Journal of Solid Mechanics
Volume:14 Issue: 1, Winter 2022

In this paper, a numerical solution is presented for static and dynamic stability analysis of carbon nanotube (CNT) reinforced beams resting on Pasternak foundation. The beam is considered to be exposed to compressive axial and follower forces at its free end. The beam is modeled based on the Reddy’s third order shear deformation theory and governing equations and external boundary conditions are derived using Hamilton’s principle. The set of governing equations and boundary conditions are solved numerically using differential quadrature method. Convergence and accuracy of results are confirmed and effect of various parameters on the stability region of the beam is investigated including volume fraction and distribution of CNTs, width and thickness of the beam and elastic and shear coefficients of the foundation.

This article introduces a novel mixed method that combines the Fast Fourier Transform technique and a conventional Finite Element Method for investigating thermo-mechanical behavior of a thick functionally graded cylinder under asymmetric loadings. Material properties are assumed to vary along the radial direction according to a power function. Thermo-elastic governing equations of the cylinder are derived using principle of virtual work in cylindrical coordinates. Plane strain assumption is considered for a long cylinder during the analysis. Fast Fourier Transform technique is utilized in circumferential direction to discretize equations and related boundary conditions. Finite element method is then applied to remaining equations. For convergence study, the results obtained from this method are compared with those extracted from exact and complete FE solutions. It is observed from the results that the method has a super algebraic convergence behavior in circumferential direction. Influence of the mesh refinement is also investigated in the radial direction. According to ability of the mixed FFT-FE method for asymmetric analyzing, two kinds of loadings are considered here and results are presented. In thermo-elastic analyzing of the long cylinder, it’s obvious that the present method benefits from some features such as fast convergence and low computational cost in comparison with FE solution.

In this paper, the behavior of free vibrations of the thick sandwich panel with  multi-layer face sheets and an electrorheological (ER) fluid core using  Exponential Shear Deformation Theory were investigated. For the first time, Exponential shear deformation theory is used for the face sheets while the Displacement field based on the second Frostig's model is used for the core. The governing equations and the boundary conditions are derived by Hamilton’s principle. Closed form solution is achieved using the Navier method and solving the eigenvalues. Primary attention is focused on the effects of electric field magnitude, geometric aspect ratio,and ER core layer thickness on the dynamic characteristics of the sandwich plate. The rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. When an electric field is applied, the damping of the system is more effective. The effects of the natural frequencies and loss factors on the dynamic behaviorof the  sandwich plate are studied.the natural frequency of the sandwich plate increases and the modal loss factor decreases. With increasing the thickness of the ER layer, the natural frequencies of the sandwich plate are decreased.

Engine piston is one of the most complex components among all automotive. The engine can be called the heart of a car and the piston may be considered the most important part of an engine. In fact, piston has to endure thermo-mechanical cyclic loadings in a wide range of operating conditions. This paper presents high cycle fatigue (HCF) life prediction for an aluminum alloy piston using stress gradient approach described in the Forschungskuratorium Maschinenbau (FKM) method. For this purpose, first Solidworks software was used to model the piston. Then Ansys Workbench software was used to determine temperature and stress distribution of the piston. Finally, in order to study the fatigue life of the piston based on HCF approach, the results were fed into the nCode Design Life software. The numerical results showed that the temperature maximum occurred at the piston crown center. The results of finite element analysis (FEA) indicated that the stress and number of cycles to failure have the most critical values at the upper portion of piston pin and piston compression grooves. To evaluate properly of results, stress analysis and HCF results is compared with real samples of damaged piston and it has been shown that critical identified areas, match well with areas of failure in the real samples. The lifetime of this part can be determined through FEA instead of experimental tests.

This paper is presenting the solutions of the one dimension generalized thermo-elastic coupled equations by considering some thermo-elastic constants as interval numbers. As most of the elastic constants are obtained using the experimental methods. Thus there might be some deficiency of exactness to obtain such constants. This kind of deficiency might cause the results on a micro-scale.  L-S model has been considered to study the effect of such an interval parametric approach to generalized thermoelasticity. Laplace transform method applied to obtain a system of coupled ordinary differential equations. Then the vector-matrix differential form is used to solve these equations by the eigenvalue approach in Laplace transformed domain. The solution in the space-time domain obtained numerically. The numerical solutions obtained by using some suitable inverse transformation method. The solutions are graphically represented for different values of the parameter of interval parametric form and the significance of obtained results are described along with the behavior of the solutions.

In this paper, we have studied a model of finite linear Mode-I crack in a thermoelastic transversely isotropic medium under Green Naghdi theory. The crack is subjected to a prescribed temperature and a known tensile stress. The plane boundary surface is considered as isothermal and all the field variables are sufficiently smooth. The heat conduction equation is written under two temperature theory (2TT) for Green Naghdi model which contains absolute temperature as well as conductive temperature. The analytical expressions of displacement components, stress components and temperature variables are obtained by normal mode analysis and matrix inversion method. Comparisons have been made within Green Naghdi (G-N) theory of type I, type II and type III for displacement, stress and absolute temperature variables against the crack width for a transversely isotropic material (Cobalt) by virtues of graphs. Also, Comparison have been made among displacement, thermal stress and absolute temperature for different depths.

In this paper, the torsional free vibration of solid and hollow rotating shafts with non-uniform tapered elements are investigated. To this end, the exact solution and also transfer matrix for the free torsional vibration of a hollow tapered shaft element with uniform thickness and also solid element are firstly obtained. Then, the natural frequencies are determined based on distributed and lumped modeling technique (DLMT). This technique is similar to transfer matrix method (TMM) but the exact solution is employed to obtain the transfer matrixes of the distributed element, therefore, there is no approximation and the natural frequencies and mode shapes are the exact values. To confirm the reliability of the presented method, the simulation results are compared with the results obtained from the other methods such as finite element method. It is shown that the proposed method provides highly accurate results and it can be simply applied to the complex torsional systems.

In this paper, the low-velocity impact response of composite plates in the presence of pre-loads is investigated using three new models for contact force estimation. The boundary conditions are considered as simply supported and the behavior of the material is linear elastic. The equations are based on both classical and first order shear deformation theory and the Fourier series method is used to solve the governing equations. The mass of the impactor is considered to be large mass and therefore the impact response is categorized as quasi-static. In the first impact model, the contact force history is first considered as a half-sine and then the maximum contact force and contact duration are calculated.  In the second model, an improved two degree of freedom (ITDOF) spring-mass system is expressed by calculating the effective contact stiffness using a fast-iterative scheme. In the third model, which is expressed for the first time in this paper, the plate is considered as a series of masses and springs constructing a multi degree of freedom (MDOF) spring-mass system and the average forces applied to springs is introduced as the contact force. Validation of these models is done by comparing the results with the analytical, numerical and experimental results and shows good agreement. Results show that the new MDOF spring-mass system is more accurate for calculating the contact force rather than the ITDOF spring-mass system.