Journal of Solid Mechanics
Volume:8 Issue: 2, Spring 2016

In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal elasticity and the effects of nonlocal forces from adjacent and non-adjacent elements on deflection are considered. The Eringen’s theory is utilized due to its capability to consider the size effect. Based on Hamilton’s principle, motion equations as well as boundary conditions are derived and solved by means of hybrid analytical-numerical method. It is believed that the presented general foundation model offers an exact and effective new approach to investigate vibration characteristics of this kind of structures embedded in an elastic medium. The results of this investigation may provide a useful reference in controlling systems in nano-scale.

This paper presents a finite element formulation for the dynamics analysis of the steady and transient states of a nonlinear piezoelectric beam. A piezoelectric beam with damping is studied under harmonic excitation. A numerical method is used for this analysis. In the paper, the central difference formula of four order is used and compared with the central difference formula of two order in the time response of the structure. The NPBDA program is developed with Matlab software. In this program, the Newmark technique for dynamic analysis is used, the Newton-Raphson iterative and Simpson methods are used for the nonlinear solution. To verify the NPBDA results, the experimental results of Malatkar are used for the nonlinear vibration analysis of a beam without piezoelectric properties. Then, the piezoelectric effect on the frequency mode values and the time response are obtained. Afterwards, the modulation frequency in the nonlinear beam and the piezoelectric effect in this parameter are verified.

The buckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates resting on Winkler-Pasternak elastic foundations under in-plane loads for various temperatures is investigated using element-free Galerkin (EFG) method based on first-order shear deformation theory (FSDT). The modified shear correction factor is used based on energy equivalence principle. Carbon nanotubes (CNTs) are embedded in polymer matrix and distributed in four types of arrangements. The temperature-dependent material properties of an FG-CNTRC plate are assumed to be graded along the thickness direction of the plate and estimated through a micromechanical model based on the extended rule of mixture. Full transformation approach is employed to enforce essential boundary conditions. The modified shear correction factor is utilized based on energy equivalence principle involving the actual non-uniform shear stress distribution through the thickness of the FG-CNTRC plate. The accuracy and convergency of the EFG method is established by comparing the obtained results with available literature. Moreover, the effects of elastic foundation parameters are investigated for various boundary conditions, temperatures, plate width-to-thickness and aspect ratios, and CNT distributions and volume fractions. Detailed parametric studies demonstrate that the elastic foundation parameters, CNT distributions along the thickness direction of the plate and the temperature change have noticeable effects on buckling behavior of carbon nanotube-reinforced composite (CNTRC) plates.

The bending behavior of composites sandwich plates with multi-layered laminated face sheets has been investigated, using a new four-nodded rectangular finite element formulation based on a layer-wise theory. Both, first order and higher-order shear deformation; theories are used in order to model the face sheets and the core, respectively. Unlike any other layer-wise theory, the number of degrees of freedom in this present model is independent of the number of layers. The compatibility conditions as well as the displacement continuity at the interface ‘face sheets–core’ are satisfied. In the proposed model, the three translation components are common for the all sandwich layers, and are located at the mid-plane of the sandwich plate. The obtained results show that the developed model is able to give accurate transverse shear stresses directly from the constitutive equations. Moreover, a parametric study was also conducted to investigate the effect of certain characteristic parameters (core thickness to total thickness ratio, side-to-thickness ratio, boundary conditions, plate aspect ratio, core-to-face sheet anisotropy ratio, core shear modulus to the flexural modulus ratio and degree of orthotropy of the face sheet) on the transverse displacement variation. The numerical results obtained by our model are compared favorably with those obtained via analytical solution and numerical/experimental, results obtained by other models. The results obtained from this investigation will be useful for a more comprehensive understanding of the behavior of sandwich laminates.

In this research, a control feedback system is used to study the free vibration response of rectangular plate made of magnetostrictive material (MsM) for the first time. A new trigonometric higher order shear deformation plate theory are utilized and the results of them are compared with two theories in order to clarify their accuracy and errors. Pasternak foundation is selected to modelling of elastic medium due to considering both normal and shears modulus. Also in-plane forces are uniformly applied on magnetostrictive nano-plate (MsNP) in x and y directions. Nonlocal motion equations are derived using Hamilton’s principle and solved by differential quadrature method (DQM) considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, elastic medium, compression and tension loads and small scale effect on vibration behaviour of MsNP especially the controller effect of velocity feedback gain to minimizing the frequency. These finding can be used to active noise and vibration cancellation systems in micro and nano smart structures.

The cause of crack initiation turbine blade had initially cracked by a fatigue mechanism over a period of time and then fractured by the overload at the last moment. Experimental procedure consists of macroscopic inspection, material verification, microscopic examination, and metallographic analysis and finally FE. And for these procedures, some specimens were prepared from a fractured blade. Using ICP and energy dispersive X-ray fluorescence, the chemical composition of the blade was carefully analyzed. The segregated area of Ti and Mo, caused generally by inappropriate manufacturing process, is found by the microstructure and EDX analysis of the blade. The fracture blade which installed on the third stage rotor of the turbojet was fractured at about 6 cm distance from the hub of proposed blade. The non-linear finite element method (FEM) was utilized in order to define the stress state of the disc or blade segment under operating conditions. High stress zones were found at the region of the lower fir-tree slot, where the failure occurred. A computation were also achieved with excessive rotational speed. The aim of this study is devoted to the mechanisms of damage of the turbine disc, and furthermore the critical high stress areas.

In this paper the capability of Gurson-Tvergaard-Needleman (GTN) model in the prediction of ductile damage in 7075-T651 aluminum alloy is investigated. For this purpose, three types of specimens were tested: Standard tensile bars, Round notched bar (RNB) specimens and compact tension (C(T)) specimens. Standard tensile bar tests were used to obtain the mechanical properties of the material and to calibrate the independent parameters of GTN model. RNB and C(T) specimen test results were used for validation of the calibrated parameters. Finite element analyses were carried out using ABAQUS commercial software for two purposes; calibration of the GTN model parameters and validation of the model predictions. The comparison between the finite element analyses and the test results suggested that the GTN model is capable of damage prediction in notched specimens, but not a good in cracked specimens. Finally, To show the applicability of the model in industry-level problems, the model is used for damage predictions of internal pressure vessels made of 7075-t651 aluminum alloy.

This paper deals with free vibration analysis of thick Laminated curved panels with finite length, based on the three-dimensional elasticity theory. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. The material properties vary continuously through the layers thickness according to a three-parameter power-low distribution. It is assumed that the inner surfaces of the FG sheets are metal rich while the outer surfaces of the layers can be metal rich, ceramic rich or made of a mixture of two constituents. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG panels are investigated. The obtained results show that the outer FGM Layers have significant effects on the vibration behavior of cylindrical panels. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated curved panels.

This paper aims at presenting a new efficient element for free vibration and instability analysis of Axially Functionally Graded Materials (FGMs) non-prismatic beams using Finite Element Method (FEM). Using concept of Basic Displacement Functions (BDFs), two- node element extends to three-node element for obtaining much more exact results using FEM. First, BDFs are introduced and computed using energy method such as unit-dummy load method. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions; free vibration and instability analysis of the FGM beam are studied using finite element method for all types of AFGM beams and the convergence of FEM has been studied. The results from both free vibration and instability analysis are in perfect agreement with those of previously published.

In this paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function. The general solution of the equation of motion is obtained, which satisfies the required radiation condition. The appropriate traction free boundary conditions are also satisfied by the solution to obtain the required secular equation for the Rayleigh wave speed. Iteration method is used to compute the numerical values of non-dimensional speed of Rayleigh wave. The dependence of the non-dimensional wave speed on non-dimensional material parameter is illustrated graphically. Effect of transverse isotropy is observed on the Rayleigh wave speed.

Polypropylene is one of the most common, fastest growing and versatile thermoplastics currently used to produce tanks and chemical piping systems. Even at room temperature creep is considerable for polypropylene products. The creep behavior of strains, stresses, and displacement rates is investigated in a thick-walled cylinder made of polypropylene reinforced by functionally graded (FG) multi-walled carbon nanotubes (MWCNTs) using Burgers viscoelastic creep model. The mechanical properties of the composite are obtained based on the volume content of the MWCNTs. Loading is composed of an internal pressure and a uniform temperature field. Using equations of equilibrium, stress-strain and strain-displacement, a constitutive differential equation containing total creep strains is obtained. Creep strain increments are accumulated incrementally during the life of the vessel. Creep strain increments are related to the current stresses and the material uniaxial Burgers creep model by the well-known Prandtl-Reuss relations. A semi-analytical solution using Prandtl-Reuss relation has been developed to determine history of stresses, strains and displacements. The results are plotted against dimensionless radius for different volume content of MWCNTs. It has been found that the creep radial and circumferential strains of the cylinder reduce with increasing content of carbon nanotubes. It has also been concluded that the uniform distribution of MWCNTs reinforcement does not considerably influence on stresses.

On the ground of manufacturing, sheet metal parts play a key role as they cover about half of the production processes. Sheet metals are commonly obtained from rolling and forming processes which causes misalignment of micro structure resulting obvious anisotropic characteristics and micro cracks. Presence of micro cracks poses serious attention, when stresses at the tip reach to the critical value. Present research deals with a thin anisotropic plate, containing an edge crack subjected to mode-I condition. To predict the nature of crack propagation, anisotropic triaxiality is formulated with special reference to Lankford’s coefficient and degree of anisotropy. The distribution of magnitude of anisotropic triaxiality is shown with respect to polar angle at crack tip supplemented by plastic zone shapes. Numerical evaluation has been carried out by considering five different cases of plane stress condition using Hill-von Mises yield criteria. Critical values so obtained apropos respective cases, as traced on the yield locus had been used to predict the location of crack propagation in sheet metal. It is revealed that the angle through which the crack propagate do not remain invariable for all combinations of Lankford’s coefficient and degree of anisotropy but it shifts for two of the five cases taken into consideration.

The permeability of the preform composite materials used in liquid molding processes such as resin transfer molding and structural reaction injection molding is a complex function of weave pattern and packing characteristics. The development of tools for predicting permeability as a function of these parameters is of great industrial importance. Such capability would speed process design and optimization and provide a step towards establishing processing-performance relations. In this study, both normal and parallel permeability of fibrous media comprised of ordered arrays of elliptical cylinders is studied analytically. A novel scale analysis technique is employed for determining the normal permeability of arrays of elliptical fibers. In this technique, the permeability is related to the geometrical parameters such as porosity, elliptical fiber diameters, and the tortuosity of the medium. Following a unit cell approach, compact relationships are proposed for the first time for the normal permeability of the studied geometries. A comprehensive analysis is also performed to determine the permeability of ordered arrays of elliptical fibers over a wide range of porosity and fiber diameters. The developed compact relationship is successfully verified through comparison with the present results. As a result of assuming an elliptical cross section for the fibers in this analytical analysis, an extra parameter comes to play; therefore, the present analytical solution will be more complicated than those developed for circular fiber type in the literature.

In this paper, two kinds of vibrations are considered for a composite Timoshenko rotor: longitudinal-torsional vibration and two plane transverse one. The kinetic and potential energies and virtual work due to the gyroscopic effects are calculated and the set of six governing equations and boundary conditions are derived using Hamilton principle. Differential quadrature method (DQM) is used as a strong numerical method and natural frequencies and mode shapes are derived. Effects of the rotating speed and the lamination angle on the natural frequencies are studied for various boundary conditions; meanwhile, critical speeds of the rotor are determined. Two kinds of critical speeds are considered for the rotor: the resonance speed, which happens as rotor rotates near one of the natural frequencies, and the instability speed, which occurs as value of the first natural frequency decreases to zero and rotor becomes instable.

Many liquid storage tanks around the world have affected by earthquakes. This structure can store dangerous chemical liquids. Hence dynamic behavior of ground supported rectangular storage tanks is very important due to their applications in industrial facilities. In current research, the seismic behavior of two water storage rectangular concrete tanks is examined. For this purpose, these tanks are modeled in FEM software for analyzing. These tanks are analyzed under four type of analysis: static, modal, response-spectrum and time-history analysis. Time history analysis can take all the nonlinear factors into the analysis, so it is used to estimate the exact amount of structural response. In time history analysis, earthquake accelerograms of Tabas, Kobe and Cape Mendocino have been applied to tanks. Finally, it is resulted that Displacement, base shear and wave height obtained from time history analysis are more than those of response spectrum analysis, indicating insufficiency of response spectrum analysis. In time history analysis, the maximum displacement is achieved in highest part of the tanks. It is due to the wave height which created in earthquake. By increasing in dimension, the wave height is also increased.

The basic governing equations in anisotropic elastic material under the effect of porous piezothermoelastic are presented. Biot [1], Lord & Shulman [4] and Sherief et al. [5] theories are used to develop the basic equations for porous piezothermoelastic with mass diffusion material. The variational principle, uniqueness theorem and theorem of reciprocity in this model are established under the assumption of positive definiteness of elastic, porousthermal, chemical potential and electric field.