Showing papers on "Functionally graded material published in 2010"

Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory

Abstract: In this paper, an analysis on the nonlinear dynamics and chaos of a simply supported orthotropic functionally graded material (FGM) rectangular plate in thermal environment and subjected to parametric and external excitations is presented. Heat conduction and temperature-dependent material properties are both taken into account. The material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on the Reddy’s third-order share deformation plate theory, the governing equations of motion for the orthotropic FGM rectangular plate are derived by using the Hamilton’s principle. The Galerkin procedure is applied to the partial differential governing equations of motion to obtain a three-degree-of-freedom nonlinear system. The resonant case considered here is 1:2:4 internal resonance, principal parametric resonance-subharmonic resonance of order 1/2. Based on the averaged equation obtained by the method of multiple scales, the phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions of the orthotropic FGM rectangular plate. It is found that the motions of the orthotropic FGM plate are chaotic under certain conditions.

Bending Analysis of Functionally Graded Sandwich Plates Under the Effect of Mechanical and Thermal Loads

Abstract: The bending response of sandwich plates subjected to thermo-mechanical loads is studied. The sandwich plate faces are assumed to have isotropic, two-constituent (metal-ceramic) material distribution through the thickness, and the modulus of elasticity, Poisson's ratio, and thermal expansion coefficient of the faces are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used, taking into account the symmetry of the plate and the thickness of each layer. Field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. Exact solutions for functionally ...

Application of functionally graded material for reducing electric field on electrode and spacer interface

Abstract: For the size reduction and the enhancing reliability of electric power equipment, the electric field stress around solid insulators should be considered enough. For the relaxation of the field stress, the application of FGM (Functionally Graded Materials) with spatial distribution of dielectric permittivity (?-FGM) can be an effective solution. In this paper, we investigated the applicability of ?-FGM for reducing the electric field stress on the electrode surface with contact to the solid dielectrics, which was one of the important factors dominating a long-term reliability of the insulating spacer. Firstly, we carried out numerical simulation of electric field to confirm the reduction of the electric stress by U-shape permittivity distribution. Secondly, we investigated the fabrication feasibility of ?-FGM with the U-shape distribution. Thirdly, we estimated the longterm electrical insulation performance of the ?-FGM. Finally, we verified the applicability and the fabrication technique of the ?-FGM to solid dielectrics for improvement of the electric stress and the long-term insulation performance in electric power equipment.

Thermal buckling analysis of functionally graded material beams

Abstract: Buckling of beams made of functionally graded material under various types of thermal loading is considered. The derivation of equations is based on the Euler–Bernoulli beam theory. It is assumed that the mechanical and thermal nonhomogeneous properties of beam vary smoothly by distribution of power law across the thickness of beam. Using the nonlinear strain–displacement relations, equilibrium equations and stability equations of beam are derived. The beam is assumed under three types of thermal loading, namely; uniform temperature rise, nonlinear, and linear temperature distribution through the thickness. Various types of boundary conditions are assumed for the beam with combination of roller, clamped and simply-supported edges. In each case of boundary conditions and loading, a closed form solution for the critical buckling temperature for the beam is presented. The formulations are compared using reduction of results for the functionally graded beams to those of isotropic homogeneous beams given in the literature.

A higher-order theory for static and dynamic analyses of functionally graded beams

Abstract: The higher-order theory is extended to functionally graded beams (FGBs) with continuously varying material properties. For FGBs with shear deformation taken into account, a single governing equation for an auxiliary function F is derived from the basic equations of elasticity. It can be used to deal with forced and free vibrations as well as static behaviors of FGBs. A general solution is constructed, and all physical quantities including transverse deflection, longitudinal warping, bending moment, shear force, and internal stresses can be represented in terms of the derivatives of F. The static solution can be determined for different end conditions. Explicit expressions for cantilever, simply supported, and clamped-clamped FGBs for typical loading cases are given. A comparison of the present static solution with existing elasticity solutions indicates that the method is simple and efficient. Moreover, the gradient variation of Young’s modulus and Poisson’s ratio may be arbitrary functions of the thickness direction. Functionally graded Rayleigh and Euler–Bernoulli beams are two special cases when the shear modulus is sufficiently high. Moreover, the classical Levinson beam theory is recovered from the present theory when the material constants are unchanged. Numerical computations are performed for a functionally graded cantilever beam with a gradient index obeying power law and the results are displayed graphically to show the effects of the gradient index on the deflection and stress distribution, indicating that both stresses and deflection are sensitive to the gradient variation of material properties.

Nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick fgm cylinders with temperature-dependent material properties

Abstract: In the present paper, nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick-walled cylinders made of functionally graded materials with temperature-dependent properties are performed. In contrast to researches accomplished so far, a third-order Hermitian finite element formulation is employed to guarantee both radial displacement and normal stress continuities, improve the accuracy, and prevent virtual wave source formations at the mutual boundaries of the elements. Stress wave propagation, reflection, and interference under impulsive mechanical loads in thermal environments are also studied. In contrast to the common procedure, the cylinder is not divided into isotropic sub-cylinders. Therefore, artificial wave reflections from the hard interfaces are avoided. Time variations of the temperatures, displacements, and stresses due to the dynamic loads are determined by solving the resulted highly nonlinear governing equations using an updating iterative time integration scheme and over-relaxation and under-relaxation techniques. A comprehensive sensitivity analysis includes effects of the volume fraction indices, dimensions, and temperature-dependency of the material properties is performed. Results reveal the significant effect of the temperature-dependency of the material properties on the transient stress distribution and elastic wave propagation and reflection phenomena. Interesting phenomena are noticed; among them the oblique wave formations during the wave propagation. Since examples of the present field are rare in literature, the extracted results may serve as reference results for future comparisons.

Variable kinematic models applied to free-vibration analysis of functionally graded material shells

Abstract: Closed-form solutions of free-vibration problems of simply supported multilayered shells made of Functionally Graded Material have been examined in the present paper. A variable kinematic shell model, which is based on Carrera’ sU ni fied Formulation is extended, in this work, to dynamic shell cases. Classical shell theories are compared to refined ones as well as to layer-wise kinematics and mixed assumptions based on the Reissner mixed variational theorem. A comparison with the few results available in the open literature is presented and conclusions are drawn regarding the accuracy of classical and advanced shell modeling to evaluate lower and higher vibration modes as well as the behavior of these modes in the shell thickness direction.

Thermomechanical Bending Response of Functionally Graded Nonsymmetric Sandwich Plates

Abstract: The thermomechanical bending response of nonsymmetric sandwich plates of uniform thickness (constant depth) is studied. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The nonsymmetric sandwich plate faces are made of isotropic, two-constituent (ceramic-metal) material distribution through the thickness. The core layer is still homogeneous and made of an isotropic metal material. The modulus of elasticity, Poisson's ratio of the faces and the thermal expansion coefficient are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. Several kinds of nonsymmetric sandwich plates are presented. Field equations for functionally graded nonsymmetric sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement and stress functions of the plate for different values of the power-law exponent and thickness-to-side ratios are presented. The results of the shear deformation theories are compared together. Numerical results for deflections and stresses of functionally graded metal-ceramic plates are investigated.

Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov-Galerkin (MLPG) method

Abstract: In this paper, a version of meshless local Petrov–Galerkin (MLPG) method is developed to obtain three-dimensional (3D) static solutions for thick functionally graded (FG) plates. The Young's modulus is considered to be graded through the thickness of plates by an exponential function while the Poisson's ratio is assumed to be constant. The local symmetric weak formulation is derived using the 3D equilibrium equations of elasticity. Moreover, the field variables are approximated using the 3D moving least squares (MLS) approximation. Brick-shaped domains are considered as the local sub-domains and support domains. In this way, the integrations in the weak form and approximation of the solution variables are done more easily and accurately. The proposed approach to construct the shape and the test functions make it possible to introduce more nodes in the direction of material variation. Consequently, more precise solutions can be obtained easily and efficiently. Several numerical examples containing the stress and deformation analysis of thick FG plates with various boundary conditions under different loading conditions are presented. The obtained results have been compared with the available analytical and numerical solutions in the literature and an excellent consensus is seen.

Refined and Advanced Models for Multilayered Plates and Shells Embedding Functionally Graded Material Layers

Abstract: The present work investigates the static response problem of multilayered plates and shells embedding functionally graded material (FGM) layers. Carrera's unified formulation (CUF) is employed to obtain several hierarchical refined and advanced two-dimensional models for plates and shells. The refined models are based on the principle of virtual displacements. The advanced models, based on Reissner's mixed variational theorem, permit the transverse shear and normal stresses to be “a priori” modelled. Refined and advanced models are developed in both equivalent single layer and layer wise multilayer approaches. CUF is also employed to describe the continuous variation of elastic properties in the thickness direction for the embedded FGM layers. The numerical results, which are restricted to simply supported plates/shells loaded by a harmonic distribution of transverse pressure, show that the use of refined and advanced models, based on CUF, is mandatory with respect to the classical theories that are widel...

Large Deflections of a Non-linear Cantilever Functionally Graded Beam

Abstract: The analysis of the large deformation of a non-linear cantilever functionally graded material (FGM) beam is made. When subjected to an end moment, explicit expressions for deflection and rotation are derived for a functionally graded beam with work hardening of power law. The effects of the gradient distribution of Young’s modulus and the material non-linearity parameter on the deflections of the FGM beam are analyzed. Our results show that depth-dependent Young’s modulus and material non-linearity have a significant influence on the deflections of the beam, and a FGM beam can bear larger applied load than a homogeneous beam. Moreover, to determine an optimal gradient distribution, an optimum design of a beam of a lighter weight and larger stiffness is given. The influence of the geometric non-linearity of the beam is also studied. Large and small deformation theories predict nearly the same deflections with 5% error when rotation is less than 45°, and the predictions based on the small deformation theory...