Showing papers on "Functionally graded material published in 2009"

Buckling of functionally graded and elastically restrained non-uniform columns

Abstract: Columns with non-uniform distribution of geometrical or material parameters i.e. functionally graded material distribution, varying cross-sectional area and flexural stiffness provide an economical solution to carry the desired higher compressive loads in engineering structures. In this paper, a low-dimensional mathematical model is presented, which is capable of computing the buckling loads of uniform and non-uniform functionally graded columns in the axial direction. The columns with spatial variation of flexural stiffness, due to material grading and/or non-uniform shape, are approximated by an equivalent column with piecewise constant geometrical and material properties. Such a formulation leads to certain transcendental eigenvalue problems where the matrix elements are transcendental functions. This model is further extended in analyzing some uniform and non-uniform elastically restrained or braced axially graded columns with equal or unequal spans. The mathematical modeling, closed-form transcendental functions and numerical solution technique are described and several examples of estimating buckling loads for various boundary configurations are presented. Some of the results are also validated against available solutions, representing the convergence, effectiveness, accuracy and versatility of the proposed modeling and numerical method. Formulation of such low-dimensional eigenvalue problems can also be extended for analyzing, designing and optimizing the static and dynamic behavior of structural components that are made of functionally graded materials.

Vibration characteristics of FGM circular cylindrical shells using wave propagation approach

Abstract: In this paper, the wave propagation approach is employed to study the vibration characteristics of functionally graded material circular cylindrical shells. Axial modal dependence is approximated by exponential functions. This is a very simple and easily applicable technique. This avoids a large amount of algebraic manipulations. A theoretical analysis of shell natural frequencies are conducted for various boundary conditions. Validity and accuracy of the present method are confirmed by comparing the present results with those available in the literature. A good agreement is observed between the two sets of the results.

Propagation of a stress wave through a virtual functionally graded foam

Abstract: Stress wave propagation through a Functionally Graded Foam Material (FGFM) is analysed in this paper using the finite element method. A finite element model of the Split Hopkinson Pressure Bar (SHPB) is developed to apply realistic boundary conditions to a uniform density foam and is validated against laboratory SHPB tests. Wave propagation through virtual FGFMs with various gradient functions is then considered. The amplitude of the stress wave is found to be shaped by the gradient functions, i.e., the stress can be amplified or diminished following propagation through the FGFMs. The plastic dissipation energy in the specimens is also shaped by the gradient functions. This property of FGFMs provides significant potential for such materials to be used for cushioning structures.

A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

Abstract: The elastic analysis of a pressurized functionally graded material (FGM) annulus or tube is made in this paper. Different from existing studies, this study deals with an axisymmetrical FGM hollow cylinder or disk with arbitrarily varying material properties. A simple and efficient approach is suggested, which reduces the associated problem to solving a Fredholm integral equation. The resulting equation is approximately solved by expanding the solution as series of Legendre polynomials. The stresses and displacements can be represented in terms of the solution to the equation. For radius-dependent Young’s modulus, numerical results of the distribution of the radial and circumferential stresses are presented graphically. Our results indicate that change in the gradient of the FGM tube does not produce a substantial variation of the radial stress, but strongly affects the distribution of the hoop stress. In particular, the hoop stress may reach its maximum at an internal position or at the outer surface when the tube is internally pressurized. The results obtained are helpful in designing FGM cylindrical vessels to prevent failure.

Bio-inspired design of dental multilayers: experiments and model.

Abstract: This paper combines experiments, simulations and analytical modeling that are inspired by the stress reductions associated with the functionally graded structures of the dentin-enamel-junctions (DEJs) in natural teeth. Unlike conventional crown structures in which ceramic crowns are bonded to the bottom layer with an adhesive layer, real teeth do not have a distinct "adhesive layer" between the enamel and the dentin layers. Instead, there is a graded transition from enamel to dentin within a approximately 10 to 100 microm thick regime that is called the Dentin Enamel Junction (DEJ). In this paper, a micro-scale, bio-inspired functionally graded structure is used to bond the top ceramic layer (zirconia) to a dentin-like ceramic-filled polymer substrate. The bio-inspired functionally graded material (FGM) is shown to exhibit higher critical loads over a wide range of loading rates. The measured critical loads are predicted using a rate dependent slow crack growth (RDEASCG) model. The implications of the results are then discussed for the design of bio-inspired dental multilayers.

Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading

Abstract: In this paper a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to impact internal pressure is considered. The axisymmetric conditions are assumed for the 2D-FG cylinder. The finite element method with graded material properties within each element is used to model the structure, and the Newmark direct integration method is implemented to solve the time dependent equations. The time histories of displacements, stresses and 2D wave propagation are investigated for various values of volume fraction exponents. Also the effects of mechanical properties distribution in radial and axial direction on the time responses of the FG cylinder as well as the stress distribution are studied and compared with a cylinder made of 1D-FGM. The achieved results show that using 2D-FGM leads to a more flexible design. To verify the presented method and data, the results are compared to published data.

Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness

Abstract: A thermo elastic analysis is presented for axisymmetric rotating disks made of functionally graded material (FGM) with variable thickness. Material properties are assumed to be temperature-dependent and graded in the radial direction according to a grading index power law distribution. The temperature field considered is assumed to be uniformly distributed over the disk surface and varied in the radial direction. Semi-analytical solutions for the displacement field are given for solid disk and annular disk under free-free and fixed-free boundary conditions. The effects of the thermal field, the material grading index and the geometry of the disk on the displacement and stress fields are investigated. Results of this study emphasize on the crucial role of the temperature-dependent properties in a high temperature environment. A comparison of these results with the reported ones in the literature that is temperature-dependent versus temperature-independent suggests that a functionally graded rotating disk with concave thickness profile can work more efficiently than the one with uniform thickness irrespective of whether the material properties are assumed to be temperature-dependent or temperature-independent.

Torsional buckling and postbuckling of fgm cylindrical shells in thermal environments

Abstract: A postbuckling analysis is presented for a functionally graded cylindrical shell subjected to torsion in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation theory with a von Karman–Donnell-type of kinematic non-linearity. The non-linear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling load and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of twist, perfect and imperfect, FGM cylindrical shells under different sets of thermal fields. The results reveal that the volume fraction distribution of FGMs has a significant effect on the buckling load and postbuckling behavior of FGM cylindrical shells subjected to torsion. They also confirm that the torsional postbuckling equilibrium path is weakly unstable and the shell structure is virtually imperfection–insensitive.

Optimal design of periodic functionally graded composites with prescribed properties

Abstract: The computational design of a composite where the properties of its constituents change gradually within a unit cell can be successfully achieved by means of a material design method that combines topology optimization with homogenization. This is an iterative numerical method, which leads to changes in the composite material unit cell until desired properties (or performance) are obtained. Such method has been applied to several types of materials in the last few years. In this work, the objective is to extend the material design method to obtain functionally graded material architectures, i.e. materials that are graded at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable inside the finite element domain is considered to represent a fully continuous material variation during the design process. Thus the topology optimization naturally leads to a smoothly graded material system. To illustrate the theoretical and numerical approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional material gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of the homogenization method is extended to two dimensions considering a trigonometric material gradation, and a material variation with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally graded material cell design. Finally the influence of material gradation on extreme materials is investigated, which includes materials with near-zero shear modulus, and materials with negative Poisson’s ratio.

Vibration and Stability of Functionally Graded Plates Based on a Higher-order Deformation Theory

Abstract: In this article, the governing equations of motion for a functionally graded material plate (FGP) based on a higher-order deformation theory in a general state of non-uniform initial stress are derived. The properties of FGP are assumed varied continuously along the thickness of the plate, according to a simple power law of volume fractions of constituents. With the derived governing equations, the natural frequencies and buckling loads of ceramic—FGM—metal plates subjected to an initial stress are investigated. The initial stress is taken to be a combination of a uniaxial extensional stress and a pure bending stress. A ceramic—FGM—metal plate can become an all-FGM, all-ceramic plate, or all-metal plate by modifying the value of material parameter and volume fraction index. The effects of various parameters and initial stresses on the natural frequencies and buckling loads of FGPs are studied.

Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

Abstract: A theoretical model for geometrically nonlinear vibration analysis of piezoelectrically actuated circular plates made of functionally grade material (FGM) is presented based on Kirchhoff’s-Love hypothesis with von-Karman type geometrical large nonlinear deformations. To determine the initial stress state and pre-vibration deformations of the smart plate a nonlinear static problem is solved followed by adding an incremental dynamic state to the pre-vibration state. The derived governing equations of the structure are solved by exact series expansion method combined with perturbation approach. The material properties of the FGM core plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. Control of the FGM plate’s nonlinear deflections and natural frequencies using high control voltages is studied and their nonlinear effects are evaluated. Numerical results for FG plates with various mixture of ceramic and metal are presented in dimensionless forms. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FGM plate on vibration characteristics of the smart structure.