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Weiqiu Chen - One of the best experts on this subject based on the ideXlab platform.
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a unified solution for an anisotropic functionally graded piezoelectric beam subject to sinusoidal transverse loads
Journal of Intelligent Material Systems and Structures, 2009Co-Authors: D J Huang, H J Ding, Weiqiu ChenAbstract:The behavior of anisotropic functionally graded piezoelectric beams subject to sinusoidal transverse loads is investigated based on the equations for a generalized Plane Stress Problem. Both the Stress function and electric displacement function are assumed to consist of two parts. One corresponds to a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (z). The other is represented by a linear polynomial of x with unknown coefficients also depending on z. The equations governing these z-dependent functions are presented. The expressions for Stresses, electric displacements, resultant forces, displacements, and electric potential are then deduced, in which the integral constants are determined from the boundary conditions. Analytical solution is derived in the case that material coefficients vary exponentially along the thickness of the beam. Semi-analytical solution is also suggested along with the sub-layer approximation when th...
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analytical solution for functionally graded magneto electro elastic Plane beams
International Journal of Engineering Science, 2007Co-Authors: D J Huang, Haojiang Ding, Weiqiu ChenAbstract:This paper investigates the Plane Stress Problem of generally anisotropic magneto-electro-elastic beams with the coefficients of elastic compliance, piezoelectricity, dielectric impermeability, piezomagnetism, magnetoelectricity, and magnetic permeability being arbitrary functions of the thickness coordinate. Firstly, partial differential equations governing Stress function, electric displacement function and magnetic induction function are derived for Plane Problems of anisotropic functionally graded magneto-electro-elastic materials. Secondly, these functions are assumed in forms of polynomials in the longitudinal coordinate and can be acquired through a successive integral approach. The analytical expressions of axial force, bending moment, shear force, average electric displacement, average magnetic induction, displacements, electric potential and magnetic potential are then deduced. Thirdly, Problems of functionally graded magneto-electro-elastic Plane beams are considered, with integral constants being completely determinable from boundary conditions. A series of analytical solutions are thus obtained, including the solutions for beams under tension and pure bending, for cantilever beams subjected to shear force applied at the free end, and for cantilever beams subjected to uniform load. These solutions can be easily degenerated into the solutions for homogenous anisotropic magneto-electro-elastic beams. Finally, a numerical example is presented to show the application of the proposed method.
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elasticity solutions for Plane anisotropic functionally graded beams
International Journal of Solids and Structures, 2007Co-Authors: H J Ding, D J Huang, Weiqiu ChenAbstract:Abstract This paper considers the Plane Stress Problem of generally anisotropic beams with elastic compliance parameters being arbitrary functions of the thickness coordinate. Firstly, the partial differential equation, which is satisfied by the Airy Stress function for the Plane Problem of anisotropic functionally graded materials and involves the effect of body force, is derived. Secondly, a unified method is developed to obtain the Stress function. The analytical expressions of axial force, bending moment, shear force and displacements are then deduced through integration. Thirdly, the Stress function is employed to solve Problems of anisotropic functionally graded Plane beams, with the integral constants completely determined from boundary conditions. A series of elasticity solutions are thus obtained, including the solution for beams under tension and pure bending, the solution for cantilever beams subjected to shear force applied at the free end, the solution for cantilever beams or simply supported beams subjected to uniform load, the solution for fixed–fixed beams subjected to uniform load, and the one for beams subjected to body force, etc. These solutions can be easily degenerated into the elasticity solutions for homogeneous beams. Some of them are absolutely new to literature, and some coincide with the available solutions. It is also found that there are certain errors in several available solutions. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded anisotropic cantilever beam.
D J Huang - One of the best experts on this subject based on the ideXlab platform.
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a unified solution for an anisotropic functionally graded piezoelectric beam subject to sinusoidal transverse loads
Journal of Intelligent Material Systems and Structures, 2009Co-Authors: D J Huang, H J Ding, Weiqiu ChenAbstract:The behavior of anisotropic functionally graded piezoelectric beams subject to sinusoidal transverse loads is investigated based on the equations for a generalized Plane Stress Problem. Both the Stress function and electric displacement function are assumed to consist of two parts. One corresponds to a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (z). The other is represented by a linear polynomial of x with unknown coefficients also depending on z. The equations governing these z-dependent functions are presented. The expressions for Stresses, electric displacements, resultant forces, displacements, and electric potential are then deduced, in which the integral constants are determined from the boundary conditions. Analytical solution is derived in the case that material coefficients vary exponentially along the thickness of the beam. Semi-analytical solution is also suggested along with the sub-layer approximation when th...
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analytical solution for functionally graded magneto electro elastic Plane beams
International Journal of Engineering Science, 2007Co-Authors: D J Huang, Haojiang Ding, Weiqiu ChenAbstract:This paper investigates the Plane Stress Problem of generally anisotropic magneto-electro-elastic beams with the coefficients of elastic compliance, piezoelectricity, dielectric impermeability, piezomagnetism, magnetoelectricity, and magnetic permeability being arbitrary functions of the thickness coordinate. Firstly, partial differential equations governing Stress function, electric displacement function and magnetic induction function are derived for Plane Problems of anisotropic functionally graded magneto-electro-elastic materials. Secondly, these functions are assumed in forms of polynomials in the longitudinal coordinate and can be acquired through a successive integral approach. The analytical expressions of axial force, bending moment, shear force, average electric displacement, average magnetic induction, displacements, electric potential and magnetic potential are then deduced. Thirdly, Problems of functionally graded magneto-electro-elastic Plane beams are considered, with integral constants being completely determinable from boundary conditions. A series of analytical solutions are thus obtained, including the solutions for beams under tension and pure bending, for cantilever beams subjected to shear force applied at the free end, and for cantilever beams subjected to uniform load. These solutions can be easily degenerated into the solutions for homogenous anisotropic magneto-electro-elastic beams. Finally, a numerical example is presented to show the application of the proposed method.
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elasticity solutions for Plane anisotropic functionally graded beams
International Journal of Solids and Structures, 2007Co-Authors: H J Ding, D J Huang, Weiqiu ChenAbstract:Abstract This paper considers the Plane Stress Problem of generally anisotropic beams with elastic compliance parameters being arbitrary functions of the thickness coordinate. Firstly, the partial differential equation, which is satisfied by the Airy Stress function for the Plane Problem of anisotropic functionally graded materials and involves the effect of body force, is derived. Secondly, a unified method is developed to obtain the Stress function. The analytical expressions of axial force, bending moment, shear force and displacements are then deduced through integration. Thirdly, the Stress function is employed to solve Problems of anisotropic functionally graded Plane beams, with the integral constants completely determined from boundary conditions. A series of elasticity solutions are thus obtained, including the solution for beams under tension and pure bending, the solution for cantilever beams subjected to shear force applied at the free end, the solution for cantilever beams or simply supported beams subjected to uniform load, the solution for fixed–fixed beams subjected to uniform load, and the one for beams subjected to body force, etc. These solutions can be easily degenerated into the elasticity solutions for homogeneous beams. Some of them are absolutely new to literature, and some coincide with the available solutions. It is also found that there are certain errors in several available solutions. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded anisotropic cantilever beam.
Zheng Zhong - One of the best experts on this subject based on the ideXlab platform.
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Buckling analysis of functionally graded thin plate with in-Plane material inhomogeneity
Engineering Analysis with Boundary Elements, 2016Co-Authors: Fuyun Chu, Lihua Wang, Zheng ZhongAbstract:Abstract Buckling analysis of functionally graded material (FGM) thin plates with in-Plane material inhomogeneity is investigated based on radial basis functions associated with collocation method. No background mesh is required in the discretization and solution which makes it a truly meshfree method. Two independent Problems raised in the buckling analysis are studied according to the procedure. First, radial basis collocation method (RBCM) is employed to yield the non-uniform pre-buckling Stresses by solving a 2D Plane Stress Problem. Afterwards, based on Kirchhoff assumption and employing the predetermined non-uniform pre-buckling Stresses, Hermite radial basis function collocation method (HRBCM) is proposed to study the buckling loads of FGM thin plates with in-Plane material inhomogeneity. Compared to an over-determined system resulting from the conventional RBCM, HRBCM introducing more degrees of freedom on the boundary nodes can lead to a determined system for the eigenvalue Problem. Convergence and comparisons studies with analytical solutions demonstrate that the proposed method possesses high accuracy and exponential convergence. Numerical examples illustrate that the material inhomogeneity has considerable effects on the buckling loads and mode shapes of thin plates. As a result, material inhomogeneity can be exploited to optimize the in-Plane Stress distribution and prevent the buckling of thin plates.
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analytical solution for a functionally graded beam with arbitrary graded material properties
Composites Part B-engineering, 2013Co-Authors: G J Nie, Zheng Zhong, Shuping ChenAbstract:Abstract The Plane Stress Problem of an orthotropic functionally graded beam with arbitrary graded material properties along the thickness direction is investigated by the displacement function approach for the first time. A general two-dimensional solution is obtained for a functionally graded beam subjected to normal and shear tractions of arbitrary form on the top and bottom surfaces and under various end boundary conditions. For isotropic case explicit solutions are given to some specific through-the-thickness variations of Young’s modulus such as exponential model, linear model and reciprocal model. The influence of different grade models on the Stress and displacement fields are illustrated in numerical examples. These analytical solutions can serve as a basis for establishing simplified theories and evaluating numerical solutions of functionally graded beams.
Shuping Chen - One of the best experts on this subject based on the ideXlab platform.
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analytical solution for a functionally graded beam with arbitrary graded material properties
Composites Part B-engineering, 2013Co-Authors: G J Nie, Zheng Zhong, Shuping ChenAbstract:Abstract The Plane Stress Problem of an orthotropic functionally graded beam with arbitrary graded material properties along the thickness direction is investigated by the displacement function approach for the first time. A general two-dimensional solution is obtained for a functionally graded beam subjected to normal and shear tractions of arbitrary form on the top and bottom surfaces and under various end boundary conditions. For isotropic case explicit solutions are given to some specific through-the-thickness variations of Young’s modulus such as exponential model, linear model and reciprocal model. The influence of different grade models on the Stress and displacement fields are illustrated in numerical examples. These analytical solutions can serve as a basis for establishing simplified theories and evaluating numerical solutions of functionally graded beams.
S Peravali - One of the best experts on this subject based on the ideXlab platform.
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numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under Plane Stress conditions
International Journal for Numerical Methods in Engineering, 2009Co-Authors: A Zolochevsky, S Sklepus, T H Hyde, A A Becker, S PeravaliAbstract:A constitutive model for describing the creep and creep damage in initially isotropic materials with characteristics dependent on the loading type, such as tension, compression and shear, has been applied to the numerical modeling of creep deformation and creep damage growth in thin plates under Plane Stress conditions. The variational approach of establishing the basic equations of the Plane Stress Problem under consideration has been introduced. For the solution of two-dimensional creep Problems, the fourth-order Runge–Kutta–Merson's method of time integration, combined with the Ritz method and R-functions theory, has been used. Numerical solutions to various Problems have been obtained, and the processes of creep deformation and creep damage growth in thin plates of arbitrary shape have been investigated. The influence of tension–compression asymmetry on the Stress–strain state and damage evolution, with time, in thin plates of arbitrary shape, has been discussed. Copyright © 2009 John Wiley & Sons, Ltd.