فهرست مطالب

Solid Mechanics - Volume:11 Issue:3, 2019
  • Volume:11 Issue:3, 2019
  • تاریخ انتشار: 1398/07/08
  • تعداد عناوین: 16
|
  • Kh Lotfy * Pages 486-497
    A general model of the equations of generalized thermoelasticity   for an infinite space weakened by a finite linear opening Mode-I crack is solving. The material is   homogeneous and has isotropic properties of elastic half space. The crack is subjected to prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, the Lord-Şhulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and micro-stress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the three theories.
    Keywords: Mode-I crack, (L-S) theory, (G-L) theory, Thermoelasticity
  • A. R Golkarian, M Jabbarzadeh *, Sh Dastjerdi Pages 498-512
    This study is the first report of numerical solution of nonlinear bending analysis for annular and circular plates based on 3D elasticity theory with asymmetric boundary conditions using semi-analytical polynomial method (SAPM). Orthotropic annular and circular plates are subjected to transverse loading and 3D bending analysis in the presence of symmetric and asymmetric boundary conditions is studied. For asymmetry cases, the plate boundaries are divided to two or three parts and various boundary conditions such as clamped, simply-supported and free edges are defined for each part. The asymmetry in one and two directions is studied. The influence of elastic foundations, mechanical and thermo-mechanical loadings are examined. Regarding this fact that no study has been done in the case of asymmetric boundary conditions, the obtained results are compared with FEM results by ABAQUS. The results show good agreement with the literatures and FEM results, which it shows that the presented method can use to analyze the 3D bending of plates under asymmetric conditions. Also, it is observed that 3D elasticity estimates some higher deflections than other theories. But, the obtained results by 3D elasticity theory and those obtained by FEM analysis in the case of asymmetric conditions are so close.
    Keywords: 3D elasticity, SAPM, Annular plates, Nonlinear bending, Asymmetry
  • S Gupta, P Pati *, B Prasad Pages 513-522
    The present paper deals with the generation of Love waves in a layer of finite thickness over an initially stressed heterogeneous semi-infinite media. The rigidity and density of the layer are functions of temperature, i.e. they are temperature dependent.  The lower substratum is an initially stressed medium and its rigidity and density vary linearly with the depth. The frequency relation of Love waves has been acquired in compact form. Numerical calculations are accomplished and a number of graphs for non-dimensional phase velocity versus non-dimensional wave number are plotted to display the influence of intrinsic parameters like initial stress and inhomogeneity factors on the generation of Love waves. It is initiated that the non-dimensional phase velocity of Love wave decreases with increase in the non-dimensional wave number and is strongly influenced by the initial stress of the substratum and the inhomogeneity factors of the layer and the substratum. This study may provide effective information in the field of industrial engineering, civil engineering as well as geophysics and seismology.
    Keywords: Love waves, Heterogeneity, Temperature-dependent properties, Initial-stress
  • H Ahmadi *, K Foroutan Pages 523-534
    A semi-analytical method is used to study the effects of the multi vibration absorbers on the nonlinear functionally graded (FG) Euler-Bernoulli beam subjected to periodic load. The material properties of the beam are assumed to be continuously graded in the thickness direction. The governing equations of functionally graded beam are obtained based on the Hamilton's principle and these equations are solved by using the Rayleigh-Ritz method. To validate the results, comparisons are made with the available solutions for the natural frequencies of isotropic beam. The effects of the multi vibration absorbers and material parameters on the vibration response of functionally graded beamare investigated. For case study the effect of two symmetrical vibration absorbers is considered, these absorbers are applicable in some of the mechanic systems. In those systems, two absorbers are used close to the beginning and end of the structures instead of using them in the middle of these structures. By considering the industrial applications, it is shown that using the two symmetrical vibration absorbers with lower mass is close to the end of functionally graded beam is better than the middle of one. Also, the effect of different numbers of the vibration absorbers on the nonlinear functionally graded beam with simply supported boundary condition is considered. The results shown that increasing the number of vibration absorbers leads to decreasing the maximum deflection.
    Keywords: Functionally graded beam, Vibration absorbers, Vibration response, Periodic load
  • A.A Jafari, P Jamshidi * Pages 535-549
    In this paper, the nonlinear vibration behavior of a rotor with asymmetric shaft considering misalignment is studied. The system consists of a rectangular shaft and a disk which is connected to a motor through a flexible coupling. In order to consider higher order deformations, nonlinear Bernoulli beam is used for modeling the shaft. Gibbons’ equations are utilized to apply misaligned coupling forces. The equations of motion of the system are derived using the Lagrangian method and then discretized by the Rayleigh-Ritz method. In order to solve nonlinear equations and hence obtaining nonlinear responses, multiple scales method is used. The vibration behavior of the system near the resonance frequencies is studied by taking into account various parameters including unbalance forces and the effect of the asymmetry of cross section of the shaft. The analytical results are consistent with those of numerical method with a good accuracy. In addition, the effects of variations of the system parameters on the rotor vibration behavior have been shown graphically. In the end, the changes in the various parameters of the system and their effects on the rotor vibration response are discussed.
    Keywords: Nonlinear vibration, Rotor dynamics, Asymmetric shaft, Misalignment
  • B Mirzavand *, M Bohlooly Pages 550-569
    This article provides a fully analytical approach for nonlinear equilibrium path of rectangular sandwich plates. The core of structure is made of symmetric cross-ply laminated composite and the outer surfaces are piezoelectric actuators which perfectly bonded to inner core. The structure is subjected to electro-thermo-mechanical loads simultaneously. One side of plate is rested on Pasternak type elastic foundation. The equilibrium equations of plate are derived based on the higher-order shear deformation theory of Reddy taking into account initial geometrical imperfection, nonlinear strain-displacement relations of von-Karman, temperature dependent properties, and different types of boundary conditions. Some numerical examples are presented to verify the accuracy of the proposed formulation. The effects of various parameters such as voltage on actuators, elastic foundation, imperfection, and pre-load condition on the buckling and postbuckling behaviors are studied. As an important finding of current research, there may be exists bifurcation point for imperfect plates by applying voltage on actuators.
    Keywords: Imperfection, Sandwich, Elastic foundation, Galerkin, HSDT
  • A Mandi *, S Kundu, P Chandra Pal, P Pati Pages 570-580
    In this work, attempts are made to study the dispersion of Love waves in dry sandy layer sandwiched between fiber reinforced layer and inhomogeneous half space.Inhomogeneity in half space associated with density and rigidity and considered in exponential form. Displacement components for fiber reinforced layer, dry sandy layer and inhomogeneous half-space have been obtained by using method of separable variables. Boundary conditions are defined at the free surface of the fiber reinforced layer and at the interfaces between layers and half space. The dispersion equation has derived in closed form. Numerical calculations for dispersion equation are performed. The study results show the effect of parameters on the velocity of Love waves and presented graphically. Graphs are plotted between wave number and phase velocity to show the effect of reinforced parameter, sandiness parameter and inhomogeneity on the phase velocity of Love waves. From the graphs it can be concluded that phase velocity decreases with respect to wave number.
    Keywords: Love waves, Reinforced parameter, Sandiness parameter, Inhomogeneity, Wave number, Phase velocity
  • R Kumar, Sh Devi * Pages 581-592
    The problem treated here is to determinethe viscosity effect on stresses, temperature change and chemical potential in a circular plate. The mathematical formulation is applied to two theories of thermoelastic diffusion developed by Sherief et al. [27] with one relaxation time and Kumar and Kansal [9]with two relaxation times. Laplace and Hankel transform techniques are used to obtain the expression for the displacement components, stresses, temperature change and chemical potential. The resulting quantities are computed numerically and depicted graphically by using numerical inversion technique for a particular model. Effect of viscosity is shown in the normal stress, tangential stress, temperature change and chemical potential. Some particular cases of interest are also deduced. Viscoelastic materials play an important role in many branches of engineering, technology and, in recent years, biomechanics. Viscoelastic materials, such as amorphous polymers, semicrystalline polymers, and biopolymers, can be modelled in order to determine their stress or strain interactions as well as their temporal dependencies.
    Keywords: Viscothermoelastic, Thick circular plate, Laplace, Hankel transforms, Viscosity
  • P Alam *, M.K Singh Pages 593-605
    A mathematical model is presented to investigate the effects of sandiness, irregular boundary interfaces, heterogeneity and viscoelasticity on the phase velocity of Love waves. Geometry of the problem is consisting of an initially stressed viscoelastic layer with corrugated irregular boundaries, which is sandwiched between heterogeneous orthotropic semi-infinite half-space with initial stress and pre-stressed dry sandy half-space. Heterogeneity arises in the upper half-space is due to trigonometric variation in elastic parameters of the orthotropic medium. Inclusion of the concept of corrugated irregular viscoelastic layer clamped between two dissimilar half-spaces under different physical circumstances such as initial stress and heterogeneity brings a novelty to the existing literature related to the study of Love wave. Dispersion equation for Love wave is obtained in closed form. The obtained dispersion relation is found to be in well agreement with classical Love wave equation. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, internal friction, wave number and amplitude of corrugations on the phase velocity of Love waves.
    Keywords: Corrugation, Orthotropic, Heterogeneity, Phase velocity, Initial stress
  • A Boussaha *, R Makhloufi, S Madani Pages 606-614
    This work consists in a numerically evaluation of elastic fields distribution, caused by intrinsic dislocation networks placed at a nanometric trilayers interfaces, in order to estimate their influence on the surface topology during heterostructure operation. The organization of nanostructures is ensured by the knowledge of different elastic fields caused by buried dislocation networks and calculated in the case of anisotropic elasticity. The influence of elastic fields generated by induced square and parallel dislocation networks at CdTe / GaAs / (001) GaAs trilayer interfaces was investigated. By deposition, the nanostructures organization with respect to the topology was controled.
    Keywords: Interface, Network, Nanometric, Dislocation, Elastic field, Anisotropic elasticity
  • M Babaei, K Asemi *, P Safarpour Pages 615-634
    In this paper, natural frequencies and dynamic response of thick beams made of saturated porous materials resting on viscoelastic foundation are investigated for the first time. The beam is modeled using higher-order beam theory. Kelvin-voight model is used to model the viscoelastic foundation. Distribution of porosity along the thickness is considered in two different patterns, which are symmetric nonlinear and nonlinear asymmetric distributions. The relationship between stress and strain is based on the Biot constitutive law. Lagrange equations are used to express the motion equations. Finite element and Newark methods are used to solve the governing equations. The effect of different boundary conditions and various parameters such as porosity and Skempton coefficients, slenderness ratio as well as stiffness and damping coefficients of viscoelastic foundation on natural frequency and transient response of beam have been studied. Results show that in a drained condition, beam has smallest fundamental frequency and by increasing the Skempton coefficient, the fundamental frequency of the beam increases.
    Keywords: Saturated porous beam, Functionally graded, Third order beam theory, Dynamic analysis, Viscoelastic foundation, Biot model
  • S Doddamani *, M Kaleemulla Pages 635-643
    This research work presents the study on fracture behavior of Al6061 with graphite particulate composite produced by the stir casting technique. The materials selected for the proposed work is Al6061 and graphite particles. Compact tension (CT) specimens were utilized to determine fracture toughness for different thickness of composite. In the present work, optimizing the parameters of the compact tension specimens is carried out using Taguchi method. Four parameters and two factors are considered to optimize the parameters. Factors considered are material composition and a/W ratio. From the Taguchi analysis, on compact tension specimens, Al6061-9%graphite is the optimized composition and fracture toughness is maximum for a/W ratio = 0.45. All the compact tension specimens of different thickness (B = 4, 5, 7, 10, 12, 15, 18 and 20mm) of a/W=0.45 were tested to find the fracture toughness. From the results, it was observed that the Kq reduces with increment in thickness to width (B/W) proportions and found to stay consistent for B/W≥0.3. This consistent estimation of Kq for B/W≥0.3 prevail the plane strain fracture toughness (KIc) of the composite.
    Keywords: Al6061-graphite, MMC, fracture toughness, CT Specimens, Taguchi analysis
  • M Hosseini *, F Karami Pages 644-656
    The aim of this paper is to determine the critical buckling load for simply supported thin shallow spherical shells made of functionally graded material (FGM) subjected to uniform external pressure. A metal-ceramic functionally graded (FG) shell with a power law distribution for volume fraction is considered, where its properties vary gradually through the shell thickness direction from pure metal on the inner surface to pure ceramic on the outer surface. First, the total potential energy functional is obtained using the first-order shell theory of Love and Kirchhoff, Donnell-Mushtari-Vlasov kinematic equations and Hooke''''''''''''''''s Law. Then, equilibrium equations are derived through the minimization of the total potential energy functional by employing the Euler equations. The stability equations are derived by application of the adjacent - equilibrium criterion. As the nonlinear strain-displacement relations are employed, so the presented analysis is nonlinear with high accuracy. The Galerkin method is used to determine the critical buckling load. The present problem is also analyzed numerically by simulating it in Abaqus software. For validation, the present analytical results are compared with the present numerical results and with the known data in the literature. Also, the effects of some important geometrical and mechanical parameters on the hydrostatic buckling pressure are investigated.
    Keywords: Buckling, Spherical shell, FGM, External hydrostatic pressure
  • M.M.H Mirzaei, A Loghman *, M Arefi Pages 657-669
    Thermoelastic behavior of temperature-dependent (TD) and independent (TID) functionally graded variable thickness cantilever beam subjected to mechanical and thermal loadings is studied based on shear deformation theory using a semi-analytical method. Loading is composed of a transverse distributed force, a longitudinal distributed temperature field due to steady-state heat conduction from root to the tip surface of the beam and an inertia body force due to rotation. A successive relaxation (SR) method for solving temperature-dependent steady-state heat conduction equation is employed to obtain the accurate temperature field. The beam is made of functionally graded material (FGM) in which the mechanical and thermal properties are variable in longitudinal direction based on the volume fraction of constituent. Using first-order shear deformation theory, linear strain–displacement relations and Generalized Hooke’s law, a system of second order differential equation is obtained. Using division method, differential equations are solved for every division. As a result, longitudinal displacement, transverse displacement, and consequently longitudinal stress, shear stress and effective stress are investigated. The results are presented for temperature dependent and independent properties. It has been found that the temperature dependency of the material has a significant effect on temperature distribution, displacements and stresses. This model can be used for thermoelastic analysis of simple turbine blades.
    Keywords: Cantilever beam, Temperature dependency, Functional graded materials (FGM), First-order shear deformation theory (FSDT), Division method, Thermoelastic
  • S.K Jalali *, M.J Beigrezaee Pages 670-677
    In the present study, potential of finite element based molecular structural mechanics (MSM) for evaluating stress concentration factor of single-layered graphene sheets (SLGSs) with elliptical vacancies is successfully addressed. The MSM approach mimics the interatomic forces of the nanostructure by defining an equivalent frame structure containing beam elements. To obtain the mechanical and cross sectional properties of the equivalent beam, the potential energies of chemical bonds between carbon atoms in the hexagonal lattice of SLGSs are equaled to the strain energies of the beams. This novel proposed approach accurately predicts the stress concentration in graphene sheets with significantly less computational effort in comparison to computational physics methods. Both armchair and zigzag configurations are considered. Furthermore, a comparison between the results obtained by presented MSM approach and theory of elasticity for thin infinite panels having elliptical holes is presented. Influence of chirality, and geometry of elliptical vacancies are investigated in details. Results reveal that MSM approach can successfully predicts stress concentration factor phenomena in nano structures, especially SLGSs. It is seen that chirality has a significant effect on the stress concentration factor so that armchair SLGSs show a larger value of stress concentration.
    Keywords: Defected grapheme, Elliptical vacancies, Molecular structural mechanics, Stress concentration factor, Finite Element Method
  • P Jalali, S Varahram, R Hassannejad *, M.H Sadeghi Pages 678-689
    According to the great importance of safety in aerospace industries, identification of dynamic parameters of related equipment by experimental tests in operating conditions has been in focus. Due to the existence of noise sources in these conditions the probability of fault occurrence may increases. This study investigates the effects of noise in the process of modal parameters identification by Output only Modal Analysis (OMA) method using Singular Value Decomposition (SVD) algorithm. The study case is the horizontal tailplane of the aircraft; therefore, at first, the modal parameters of the tailplane are obtained numerically. Then a cantilever beam is used to perform experimental tests with regard to the high aspect ratio of the modeled tailplane. The modal parameters of the beam are obtained nonparametrically by Experimental Modal Analysis (EMA) and OMA. In order to investigate the effects of noise in a controlled manner, the artificial excitation namely the shaker with the random force is used. Then, the effects of noisy measurements on the specifications of the system in EMA and OMA methods are investigated. The results indicate that: 1. The OMA method has more resistance against the noise for extracting natural frequencies. 2. The results of the Modal Assurance Criterion (MAC) values by EMA method, in the condition of noise existence in output data, are worse than the noise existence in input data. 3. The average of MAC values in general condition of EMA method by noisy input & output data is worse than the OMA method.
    Keywords: Output only modal analysis, Frequency domain decomposition, Finite Element, Singular value, Noise measurement