Search results for: functionally graded sandwich beam

Authors: Saeed Kamarian, Mahmoud Shakeri

Abstract:

Sandwich structures are used in a variety of engineering applications including aircraft, construction and transportation where strong, stiff and light structures are required. In this paper, frequency maximization of Functionally Graded Sandwich (FGS) beams resting on Pasternak foundations is investigated. A generalized power-law distribution with four parameters is considered for material distribution through the thicknesses of face layers. Since the search space is large, the optimization processes becomes so complicated and too much time consuming. Thus a novel meta–heuristic called Imperialist Competitive Algorithm (ICA) which is a socio-politically motivated global search strategy is implemented to improve the speed of optimization process. Results show the success of applying ICA for engineering problems especially for design optimization of FGM sandwich beams.

Keywords: sandwich beam, functionally graded materials, optimization, imperialist competitive algorithm

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Authors: Nasim Abuali Galehdari, Thomas J. Ryan, Ajit D. Kelkar

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In recent years, nanotechnology has played an important role in the design of an efficient radiation shielding polymeric composites. It is well known that, high loading of nanomaterials with radiation absorption properties can enhance the radiation attenuation efficiency of shielding structures. However, due to difficulties in dispersion of nanomaterials into polymer matrices, there has been a limitation in higher loading percentages of nanoparticles in the polymer matrix. Therefore, the objective of the present work is to provide a methodology to fabricate and then to characterize the functionally graded radiation shielding structures, which can provide an efficient radiation absorption property along with good structural integrity. Sandwich structures composed of Ultra High Molecular Weight Polyethylene (UHMWPE) fabric as face sheets and functionally graded epoxy nanocomposite as core material were fabricated. A method to fabricate a functionally graded core panel with controllable gradient dispersion of nanoparticles is discussed. In order to optimize the design of functionally graded sandwich composites and to analyze the stress distribution throughout the sandwich composite thickness, a finite element method was used. The sandwich panels were discretized using 3-Dimensional 8 nodded brick elements. Classical laminate analysis in conjunction with simplified micromechanics equations were used to obtain the properties of the face sheets. The presented finite element model would provide insight into deformation and damage mechanics of the functionally graded sandwich composites from the structural point of view.

Keywords: nanotechnology, functionally graded material, radiation shielding, sandwich composites, finite element method

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Authors: Saeed Kamarian

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In this paper, free vibrations of Functionally Graded Sandwich (FGS) beams reinforced by randomly oriented Single-Walled Carbon Nanotubes (SWCNTs) are investigated. The Eshelby–Mori–Tanaka approach based on an equivalent fiber is used to investigate the material properties of the structure. The natural frequencies of the FGS nanocomposite beam are analyzed based on various Higher-order Shear Deformation Beam Theories (HSDBTs) and using an analytical method. The verification study represents the simplicity and accuracy of the method for free vibration analysis of nanocomposite beams. The effects of carbon nanotube volume fraction profiles in the face layers, length to span ratio and thicknesses of face layers on the natural frequency of structure are studied for the different HSDBTs. Results show that by utilizing the FGS type of structures, free vibration characteristics of structures can be improved. A comparison is also provided to show the difference between natural frequency responses of the FGS nanocomposite beam reinforced by aligned and randomly oriented SWCNT.

Keywords: sandwich beam, nanocomposite beam, functionally graded materials, higher-order beam theories, Mori-Tanaka approach

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Authors: A. R. Nezamabadi, M. Veiskarami

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This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: functionally graded beam, free vibration, elastic foundation, Engesser-Timoshenko beam theory

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Authors: R. Bennai, H. Ait Atmane, Jr., A. Tounsi

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In this work, a new analytical approach using a refined theory of hyperbolic shear deformation of a beam was developed to study the free vibration of graduated sandwiches beams under different boundary conditions. The effects of transverse shear strains and the transverse normal deformation are considered. The constituent materials of the beam are supposed gradually variable depending the height direction based on a simple power distribution law in terms of the volume fractions of the constituents; the two materials with which we worked are metals and ceramics. The core layer is taken homogeneous and made of an isotropic material; while the banks layers consist of FGM materials with a homogeneous fraction compared to the middle layer. Movement equations are obtained by the energy minimization principle. Analytical solutions of free vibration and buckling are obtained for sandwich beams under different support conditions; these conditions are taken into account by incorporating new form functions. In the end, illustrative examples are presented to show the effects of changes in different parameters such as (material graduation, the stretching effect of the thickness, boundary conditions and thickness ratio - length) on the vibration free and buckling of an FGM sandwich beams.

Keywords: functionally graded sandwich beam, refined shear deformation theory, stretching effect, free vibration

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Authors: Gholamreza Koochaki

Abstract:

This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.

Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam

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Authors: A. Amiri Delouei

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In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: functionally graded materials, unsteady heat conduction, cylinder, temperature distribution

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Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati

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In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.

Keywords: carbon nanotubes, vibration control, piezoelectric layers, elastic foundation

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Authors: Pejman Daryabor, Kamal Mohammadi

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In the present work, the study of vibration characteristics of a functionally graded thick hollow cylinder is investigated. The cylinder natural frequencies are obtained using Galerkin finite element method. The functionally graded cylinder is assumed to be made from many subcylinders. Each subcylinder is considered as an isotropic layer. Material’s properties in each layer are constant and functionally graded properties result by exponential function of layer radius in multilayer cylinder. To validate the FE results code, plane strain model of functionally graded cylinder are also modeled in ABAQUS. Analytical results are validated for both models. Also, a good agreement is found between the present results and those reported in the literature.

Keywords: natural frequency, functionally graded material, finite element method, thick cylinder

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Authors: A. Selmi

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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: differential transformation method, functionally graded material, mode shape, natural frequency

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Authors: M. Derayatifar, M. Packirisamy, R.B. Bhat

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Role of piezoelectric energy harvesters has gained interest in supplying power for micro devices such as health monitoring sensors. In this study, in order to enhance the piezoelectric energy harvesting in capturing energy from broader range of excitation and to improve the mechanical and electrical responses, bimorph piezoelectric energy harvester beam with magnetic mass attached at the end is presented. In view of overcoming the brittleness of piezo-ceramics, functionally graded piezoelectric layers comprising of both piezo-ceramic and piezo-polymer is employed. The nonlinear equations of motions are derived using energy method and then solved analytically using perturbation scheme. The frequency responses of the forced vibration case are obtained for the near resonance case. The nonlinear dynamic responses of the MEMS scaled functionally graded piezoelectric energy harvester in this paper may be utilized in different design scenarios to increase the efficiency of the harvester.

Keywords: energy harvesting, functionally graded piezoelectric material, magnetic force, MEMS (micro-electro-mechanical systems) piezoelectric, perturbation method

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Authors: Tejeet Singh, Harmanjit Singh

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Creep behavior of thick-walled functionally graded cylinder consisting of AlSiC and subjected to internal pressure and high temperature has been analyzed. The functional relationship between strain rate with stress can be described by the well-known threshold stress based creep law with a stress exponent of five. The effect of imposing non-linear particle gradient on the distribution of creep stresses in the thick-walled functionally graded composite cylinder has been investigated. The study revealed that for the assumed non-linear particle distribution, the radial stress decreases throughout the cylinder, whereas the tangential, axial and effective stresses have averaging effect. The strain rates in the functionally graded composite cylinder could be reduced to significant extent by employing non-linear gradient in the distribution of reinforcement.

Keywords: functionally graded material, pressure, steady state creep, thick-cylinder

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Authors: R. Bennai, H. Ait Atmane, H. Fourne, B. Ayache

Abstract:

In this work, an analytical approach using a refined theory of hyperbolic shear deformation of a beam was developed to study the buckling of graduated sandwiches beams under different boundary conditions. The effects of transverse shear strains and the transverse normal deformation are considered. The constituent materials of the beam are supposed gradually variable depending on the height direction based on a simple power distribution law in terms of the volume fractions of the constituents; the two materials with which we worked are metals and ceramics. The core layer is taken homogeneous and made of an isotropic material; while the banks layers consist of functionally graded materials with a homogeneous fraction compared to the middle layer. In the end, illustrative examples are presented to show the effects of changes in different parameters such as (material graduation, the stretching effect of the thickness, boundary conditions and thickness ratio-length) on the vibration free of an FGM sandwich beams.

Keywords: FGM materials, refined shear deformation theory, stretching effect, buckling

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Authors: Mahmood Heshmati, Farhang Daneshmand

Abstract:

Material scientists and engineers have introduced novel materials with complex geometries due to the recent technological advances and promotion of manufacturing methods. Among them, lattice structures with graded architectures denoted by functionally graded porous materials (FGPMs) have been developed to optimize the structural response. FGPMs are achieved by tailoring the size and density of the internal pores in one or more directions that lead to the desired mechanical properties and structural responses. Also, FGPMs provide more flexible transition and the possibility of designing and fabricating structural elements with complex and variable properties. In this paper, wave propagation in lattice structures with functionally graded (FG) porosity is investigated in order to examine the ability of shock absorbing effect. The behavior of FG porous beams with different porosity distributions under impact load and the effects of porosity distribution and porosity content on the wave speed are studied. Important conclusions are made, along with a discussion of the future scope of studies on FGPMs structures.

Keywords: functionally graded, porous materials, wave propagation, impact load, finite element

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Authors: R. Bennai, M. Nebab, H. Ait Atmane, B. Ayache, H. Fourn

Abstract:

In this work, a study of the stability of a functionally graduated sandwiches beam using a refined theory of hyperbolic shear deformation of a beam was developed. The effects of transverse shear strains and the transverse normal deformation are considered. The constituent materials of the beam are supposed gradually variable depending on the height direction based on a simple power distribution law in terms of the volume fractions of the constituents; the two materials with which we worked are metals and ceramics. In order to examine the present model, illustrative examples are presented to show the effects of changes in different parameters such as the material graduation, the stretching effect of the thickness and thickness ratio –length on the buckling of FGM sandwich beams.

Keywords: FGM materials, refined shear deformation theory, stretching effect, buckling, boundary conditions

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Authors: Trevor Sabiston, Mohsen Mohammadi, Mohammed Cherkaoui, Kaan Inal

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A new micromechanics framework is developed for long fibre reinforced composites using a single fibre surrounded by a functionally graded interphase and matrix as a representative unit cell. The unit cell is formulated to represent any number of aligned fibres by a single fibre. Using this model the elastic response of long fibre composites is predicted in all directions. The model is calibrated to experimental results and shows very good agreement in the elastic regime. The differences between the proposed model and existing models are discussed.

Keywords: computational mechanics, functionally graded interphase, long fibre composites, micromechanics

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Authors: Cagri Mollamahmutoglu, Ali Mercan, Aykut Levent

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Studies concerning the microstructures are becoming more important as the utilization of various micro-electro mechanical systems (MEMS) are increasing. Thus in recent years, thermal buckling and vibration analysis of microstructures have been subject to many investigations that are utilizing different numerical methods. In this study, thermal effects on mechanical response of a functionally graded (FG) Timoshenko micro-beam are presented in the framework of a mixed finite element formulation. Size effects are taken into consideration via modified couple stress theory. The mixed formulation is based on a function which in turn is derived via Gateaux Differential scientifically. After the resolution of all field equations of the beam, a potential operator is carefully constructed. Then this operator is used for the manufacturing of the functional. Usual procedures of finite element approximation are utilized for the derivation of the mixed finite element equations once the potential is obtained. Resulting finite element formulation allows usage of C₀ type simple linear shape functions and avoids shear-locking phenomena, which is a common shortcoming of the displacement-based formulations of moderately thick beams. The developed numerical scheme is used to obtain the effects of thermal loads on the static bending, free vibration and buckling of FG Timoshenko micro-beams for different power-law parameters, aspect ratios and boundary conditions. The versatility of the mixed formulation is presented over other numerical methods such as generalized differential quadrature method (GDQM). Another attractive property of the formulation is that it allows direct calculation of the contribution of micro effects on the overall mechanical response.

Keywords: micro-beam, functionally graded materials, thermal effect, mixed finite element method

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Authors: Mokhtar Bouazza

Abstract:

In this paper, the simplified theory will be used to predict the thermoelastic buckling behavior of rectangular functionally graded plates. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The simplified theory is used to obtain the buckling of the plate under different types of thermal loads. The thermal loads are assumed to be uniform, linear, and non-linear distribution through the thickness. Additional numerical results are presented for FGM plates that show the effects of various parameters on thermal buckling response.

Keywords: buckling, functionally graded, plate, simplified higher-order deformation theory, thermal loading

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

Abstract:

The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Merbouha Barka, K. H. Benrahou, A. Fakrar, A. Tounsi, E. A. Adda Bedia

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This paper presents an analytical investigation on the buckling and postbuckling behaviors of thick functionally graded plates subjected to thermal load .Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. The formulations are based on first order shear deformation plate theory taking into account Von Karman nonlinearity and initial geometrical imperfection. By applying Galerkin method, closed-form relations of postbuckling equilibrium paths for simply supported plates are determined. Analysis is carried out to show the effects of material and geometrical properties, in-plane boundary restraint, and imperfection on the buckling and postbuckling loading capacity of the plates.

Keywords: functionally graded materials, postbuckling, first order shear deformation theory, imperfection

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Authors: Javad Jamali Khouei, Mohammadreza Khoshravan

Abstract:

Considering that application of functionally graded material is increasing in most industries, it seems necessary to present a methodology for designing optimal profile of structures such as plate under mechanical loading which is highly consumed in industries. Therefore, volume fraction variation profile of functionally graded circular plate which has been considered two-directional is optimized so that stress of structure is minimized. For this purpose, equilibrium equations of two-directional functionally graded circular plate are solved by applying semi analytical-numerical method under mechanical loading and support conditions. By solving equilibrium equations, deflections and stresses are obtained in terms of control variables of volume fraction variation profile. As a result, the problem formula can be defined as an optimization problem by aiming at minimization of critical von-mises stress under constraints of deflections, stress and a physical constraint relating to structure of material. Then, the related problem can be solved with help of one of the metaheuristic algorithms such as genetic algorithm. Results of optimization for the applied model under constraints and loadings and boundary conditions show that functionally graded plate should be graded only in radial direction and there is no need for volume fraction variation of the constituent particles in thickness direction. For validating results, optimal values of the obtained design variables are graphically evaluated.

Keywords: two-directional functionally graded material, single objective optimization, semi analytical-numerical solution, genetic algorithm, graphical solution with contour

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Authors: S. H. Abo Sabah, A. B. H. Kueh, M. A. Megat Johari, T. A. Majid

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In a recent study, a new bio-inspired honeycomb sandwich beam (BHSB) mimicking the head configuration of the woodpecker was developed. The beam consists of two carbon/epoxy composite face sheets, aluminum honeycomb core, and rubber core to enhance the repeated low-velocity impact resistance of sandwich structures. This paper aims to numerically enhance the repeated low-velocity impact resistance of the BHSB via optimizing the aluminum honeycomb core thickness. The beam was investigated employing three core thicknesses: 20 mm, 25 mm, and 30 mm at three impact energy levels (13.5 J, 15.55 J, 21.43 J). The results revealed that increasing the thickness of the aluminum honeycomb core to a certain level enhances the sandwich beam stiffness. The beam with the 25 mm honeycomb core thickness was the only beam that can sustain five repeated impacts achieving the highest impact resistance efficiency index, especially at high energy levels. Furthermore, the bottom face sheet of this beam developed the lowest stresses indicating that this thickness has a relatively better performance during impact events since it allowed minimal stress to reach the bottom face sheet. Overall, increasing the aluminum core thickness will increase the height of its cells subjecting it to buckling phenomenon. Therefore, this study suggests that the optimal thickness of the aluminum honeycomb core should be 65 % of the overall thickness of the sandwich beam to have the best impact resistance.

Keywords: sandwich beams, core thickness, impact behavior, finite element analysis, modeling

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Authors: Natural Frequency Analysis of a Porous Functionally Graded Shaft System

Abstract:

The vibration characteristics of a functionally graded (FG) rotor model having porosities and micro-voids is investigated using three-dimensional finite element analysis. The FG shaft is mounted with a steel disc located at the midspan. The shaft ends are supported on isotropic bearings. The FG material is composed of a metallic (stainless-steel) and ceramic phase (zirconium oxide) as its constituent phases. The layer wise material property variation is governed by power law. Material property equations are developed for the porosity modelling. Python code is developed to assign the material properties to each layer including the effect of porosities. ANSYS commercial software is used to extract the natural frequencies and whirl frequencies for the FG shaft system. The obtained results show the influence of porosity volume fraction and power-law index, on the vibration characteristics of the ceramic-based FG shaft system.

Keywords: Finite element method, Functionally graded material, Porosity volume fraction, Power law

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Authors: M. M. Atashi, P. Malekzadeh

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A first known formulation for the out-of-plane free vibration analysis of functionally graded (FG) circular curved beams in thermal environment and with temperature dependent material properties is presented. The formulation is based on the first order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be temperature dependent and graded in the direction normal to the plane of the beam curvature. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle. Differential quadrature method (DQM), as an efficient and accurate numerical method, is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The fast rate of convergence of the method is investigated and the formulations are validated by comparing the results in the limit cases with the available solutions in the literature for isotropic circular curved beams. In addition, for FG circular curved beams with soft simply supported edges, the results are compared with the obtained exact solutions. Then, the effects of temperature rise, boundary conditions, material and geometrical parameters on the natural frequencies are investigated.

Keywords: out of plane, free vibration, curved beams, functionally graded, thermal environment

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

Abstract:

In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

Keywords: non-linear vibrations, annular plates, large amplitudes, functionally graded material

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

Abstract:

The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Gennady M. Kulikov, Svetlana V. Plotnikova

Abstract:

This paper focuses on implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) stress analysis of functionally graded (FG) laminated elastic and piezoelectric shells. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the electric potentials and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed FG piezoelectric shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. As a result, the SaS formulation can be applied efficiently to 3D solutions for FG piezoelectric laminated shells, which asymptotically approach the exact solutions of piezoelectricity as the number of SaS In goes to infinity.

Keywords: electroelasticity, functionally graded material, laminated piezoelectric shell, sampling surfaces method

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Authors: Ali Kurşun, Emre Kara, Erhan Çetin, Şafak Aksoy, Ahmet Kesimli

Abstract:

In this study, thermal elastic stress distribution occurred on long hollow cylinders made of functionally graded material (FGM) was analytically defined under thermal, mechanical and thermo mechanical loads. In closed form solutions for elastic stresses and displacements are obtained analytically by using the infinitesimal deformation theory of elasticity. It was assumed that elasticity modulus, thermal expansion coefficient and density of cylinder materials could change in terms of an exponential function as for that Poisson’s ratio was constant. A gradient parameter n is chosen between - 1 and 1. When n equals to zero, the disc becomes isotropic. Circumferential, radial and longitudinal stresses in the FGMs cylinders are depicted in the figures. As a result, the gradient parameters have great effects on the stress systems of FGMs cylinders.

Keywords: functionally graded materials, thermoelasticity, thermomechanical load, hollow cylinder.

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Authors: Soukaina Ounss, Hamid Mounir, Abdellatif El Marjani

Abstract:

Sandwich materials with composite reinforced skins are mostly required in advanced construction applications with a view to ensure resistant structures. Their lightweight, their high flexural stiffness and their optimal thermal insulation make them a suitable solution to obtain efficient structures with performing rigidity and optimal energy safety. In this paper, the mechanical behavior of a sandwich beam with composite skins reinforced by unidirectional carbon fibers is investigated numerically through analyzing the impact of reinforcements specifications on the longitudinal elastic modulus in order to select the adequate sandwich configuration that has an interesting rigidity and an accurate convergence to the analytical approach which is proposed to verify performed numerical simulations. Therefore, concerned study starts by testing flexion performances of skins with various fibers orientations and volume fractions to determine those to use in sandwich beam. For that, the combination of a reinforcement inclination of 30° and a volume ratio of 60% is selected with the one with 60° of fibers orientation and 40% of volume fraction, this last guarantees to chosen skins an important rigidity with an optimal fibers concentration and a great enhance in convergence to analytical results in the sandwich model for the reason of the crucial core role as transverse shear absorber. Thus, a resistant sandwich beam is elaborated from a face-sheet constituted from two layers of previous skins with fibers oriented in 60° and an epoxy core; concerned beam has a longitudinal elastic modulus of 54 Gpa (gigapascal) that equals to the analytical value by a negligible error of 2%.

Keywords: fibers orientation, fibers volume ratio, longitudinal elastic modulus, sandwich beam

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