Journal of Solid Mechanics
Volume:8 Issue: 3, Summer 2016

In the present work, a study of thermoelastic analysis of a rotating thick truncated conical shell subjected to the temperature gradient and non-uniform internal pressure is carried out. The formulation is based on first-order shear deformation theory (FSDT), which accounts for the transverse shear. The governing equations, derived using minimum total potential energy principle, are solved, using multi-layered method (MLM). The model has been verified with the results of finite element method (FEM) for several tapering angles of the truncated cone. The numerical results obtained are presented graphically and the effects of thermal and mechanical loading, tapering angle of truncated cone, and profile of internal pressure are studied in detail.

In this paper dynamic analysis of multi-directional functionally graded panel is studied using a semi-analytical numerical method entitled the state-space based differential method (SSDQM) and comparative behavior modeling by artificial neural network (ANN) for different parameters. A semi-analytical approach which makes use the three-dimensional elastic theory and assuming the material properties having an exponent-law variation along the axial, radial direction or both directions, the frequency equations of free vibration of multi-directional functionally graded panels are derived. Numerical results are given to demonstrate the convergency and accuracy of the present method. Once the semi-analytical method is validated, an optimal ANN is selected, trained and tested by the obtained numerical results. In addition to the quantitative input parameters is considered as a qualitative input in NN modeling. The results of SSDQM and ANN are compared and the influence of longitude of the panel, material property graded index and circumferential wave number on the non-dimensional natural frequency of functionally graded material (FGM) panels are investigated.

The present study is concerned with the propagation of Lamb waves in a homogeneous isotropic thermoelastic micropolar solid with two temperatures bordered with layers or half spaces of inviscid liquid subjected to stress free boundary conditions. The generalized theory of thermoelasticity developed by Lord and Shulman has been used to investigate the problem. The secular equations for symmetric and skew- symmetric leaky and nonleaky Lamb wave modes of propagation are derived. The phase velocity and attenuation coefficient are computed numerically and depicted graphically. The amplitudes of stress, microrotation vector and temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically. Results of some earlier workers have been deduced as particular cases.

In this paper, vibration of the protein microtubule, one of the most important intracellular elements serving as one of the common components among nanotechnology, biotechnology and mechanics, is investigated using stress and strain gradient elasticity theory and orthotropic elastic shells model. Microtubules in the cell are influenced by internal and external stimulation and play a part in conveying protein substances and taking medications to the intended targets. Therefore, in order to control the biological cell functions, it is important to know the vibrational behavior of microtubules. For this purpose, using the cylindrical shell model which fully corresponds to microtubule geometry, and by considering it as orthotropic which is closer to reality, based on gradient elasticity theory, frequency analysis of the protein microtubule is carried out by considering Love’s thin shell theory and Navier solution. Also, the effect of size parameter and other variables on the results are investigated.

This article focused on the stress analysis of an edge crack in a thin hallow rotating functionally graded material (FGM) disk. The disk is assumed to be isotropic with exponentially varying elastic modulus in the radial direction. A comprehensive study is carried out for various combinations of the crack length and orientation with the different gradation of materials. The effect of non-uniform coefficient of thermal expansion on the distribution of stress intensity factor is also studied. The results which are normalized for the advantage of non-dimensional analysis show that the material gradation, the crack orientation and the crack length have significant influence on the amount of stress intensity factors.

The differential quadrature method (DQM) is one of the most elegant and useful approximate methods for solving initial and/or boundary value problems. It is easy to use and also straightforward to implement. However, the conventional DQM is well-known to have some difficulty in implementing multiple initial and/or boundary conditions at a given discrete point. To overcome this difficulty, this paper presents a simple and accurate differential quadrature methodology in which the higher-order initial conditions are exactly implemented. The proposed methodology is very elegant and uses a set of simple polynomials with a simple transformation to incorporate the higher-order initial conditions at the initial discrete time point. The order of accuracy of the proposed method for solving an rth order ordinary differential equation is “m r – 1,” where m being the number of discrete time points. This is better than the accuracy of the CBCGE (direct Coupling the Boundary/initial Conditions with the discrete Governing Equations) and MWCM (Modifying Weighting Coefficient Matrices) approaches whose order is in general “m – 1.” Some test problems are also provided to highlight the superiority of the proposed method over the CBCGE and MWCM approaches.

Power supply is a bottle-neck problem of wireless micro-sensors, especially where the replacement of batteries is impossible or inconvenient. Now piezoelectric material is being used to harvest vibration energy for self-powered sensors. However, the geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. This paper deduces a remarkably precise analytical formula for calculating the fundamental resonant frequency of V-shaped cantilevers using Rayleigh-Ritz method. This analytical formula, which is very convenient for mechanical energy harvester design based on Piezoelectric effect, is then validated by ABAQUS simulation. This formula raises a new perspective that, among all the V-shaped cantilevers and in comparison with rectangular one, the simplest tapered cantilever can lead to maximum resonant frequency and highest sensitivity.

Predicting the effective elastic properties of carbon nanotube-reinforced nanocomposites is of great interest to many structural designers and engineers for improving material and configuration design in recent years. In this paper, a finite element model of a CNT composite has been developed using the Representative volume element (RVE) to evaluate the effective material properties of nanocomposites. Based on this model, the effects of geometrical characteristics such as the aspect ratio, orientation and volume fraction of the CNTs in conjunction with the interphase behavior on the mechanical properties of the nanocomposites are elucidated and the elastic properties of a complex polymeric nanofibrous structure are determined.

The present work is aimed at analyzing the thermoelastic disturbances in a circular plate of finite thickness and infinite extent subjected to constant initial temperature and axisymmetric heat supply. Integral transform technique is used. Analytic solutions for temperature, displacement and stresses are derived within the context of unified system of equations in generalized thermoelasticity in the Laplace transform domain using potential functions. Inversion of Laplace transforms is done by employing a numerical scheme. Temperature, displacement and stresses developed in the thick circular plate are obtained and illustrated graphically for copper (pure) material.

Herein paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the circular symmetrical sandwich plates bending with isotropic face sheets and the nonlinear elastic core material. The method of constructing an analytical solution of nonlinear differential equations has been described. The perturbation method for differential equations with small parameters is used to represent nonlinear differential equations as a sequence of linear equations. Linear differential equations are reduced to Bessel’s equation. It is compared results of analytical model with results of other researches using two problems: 1) the problem of axisymmetric transverse bending of a circular sandwich plate, 2) the problem of axisymmetric transverse bending of an annular sandwich plate. The effect of accounting nonlinear elastic core material on the strain state of the sandwich plate is described.

In this work, the problem of Rayleigh wave propagation is considered in the context of the theory of thermoelastic diffusion. The formulation is applied to a homogeneous isotropic thermoelastic half space with mass diffusion at the stress free, isothermal, isoconcentrated boundary. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree. The roots of this polynomial equation are verified for not satisfying the original dispersion equation and therefore are filtered out and the remaining roots are checked with the property of decay with depth. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically and depicted graphically. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Some particular cases are also deduced from the present investigation.

The study of vibration response of a turbine blade helps to detect the crack presence in the blade which alters its dynamic characteristics. The change is characterized by changes in the modal parameters associated with natural frequencies. In this paper, study of vibration response is made for turbine blade in the presence of a crack like defect. Turbine blade is initially assumed as a cantilever beam. Modal testing has been carried out for both the beams with different crack depth and crack location ratios using FFT spectrum analyzer and ANSYS software. From the analysis, it has been observed that the crack depth and its location have noticeable effect on the natural frequencies. Later the same cantilever beam was twisted with different angle of twists to validate the cantilever beam model to turbine blade.

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) which is a highly accurate numerical method and a new semi-analytical polynomial method (SAPM). The ordinary differential equations (ODE’s) are converted to the nonlinear algebraic equations applying DQM or SAPM. Then, the Newton–Raphson iterative scheme is applied. The obtained results of DQM and SAPM are compared. It is concluded that although, the SAPM’s formulation is considerably simple in comparison with DQM, however, the results of two methods are so close to each other. The results are validated with available researches. The effects of small scale parameter, the value of van der Waals interaction between the layers, different values of elastic foundation and loading, the comparison between the local and nonlocal deflections and linear to nonlinear analysis are investigated.

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) which is a highly accurate numerical method and a new semi-analytical polynomial method (SAPM). The ordinary differential equations (ODE’s) are converted to the nonlinear algebraic equations applying DQM or SAPM. Then, the Newton–Raphson iterative scheme is applied. The obtained results of DQM and SAPM are compared. It is concluded that although, the SAPM’s formulation is considerably simple in comparison with DQM, however, the results of two methods are so close to each other. The results are validated with available researches. The effects of small scale parameter, the value of van der Waals interaction between the layers, different values of elastic foundation and loading, the comparison between the local and nonlocal deflections and linear to nonlinear analysis are investigated.

In this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the effect of the small scale on natural frequencies of nano scaled plates. Effect of nonlocal parameter, lengths of the nanoplate, aspect ratio, mode number, material properties, boundary condition and in-plane loads on the natural frequencies are investigated. It is shown that the natural frequencies depend highly on the non-locality of the nanoplate, especially at the very small dimensions, higher mode numbers and stiffer edge condition.

In this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the effect of the small scale on natural frequencies of nano scaled plates. Effect of nonlocal parameter, lengths of the nanoplate, aspect ratio, mode number, material properties, boundary condition and in-plane loads on the natural frequencies are investigated. It is shown that the natural frequencies depend highly on the non-locality of the nanoplate, especially at the very small dimensions, higher mode numbers and stiffer edge condition.