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A Real-Time Transient Analysis of a functionally Graded Material Plate Using Reduced-Basis Methods

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Advances in Linear Algebra & Matrix Theory 2015年第3期5卷 98-108页

作者： Yonghui Huang Yi Huang Sunwoda Electronic Co. Ltd. Guangdong China College of Mechanical and Vehicle Engineering Hunan University Changsha China

Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.

关键词： Reduced-Basis Method Transient Response functionally Graded Material Hybrid Numerical Method Real-Time

Thermal buckling analysis of ceramic-metal functionally graded plates

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Natural Science 2010年第9期2卷 968-978页

作者： Ashraf M. Zenkour Daoud S. Mashat 不详

Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power law form in the thickness direction. Equilibrium and stability equations are derived based on the SPT. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The buckling analysis of a functionally graded plate under various types of thermal loads is carried out. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the SPT, demonstrating its importance and accuracy in comparison to other theories.

关键词： Thermal Buckling Non-Linear Strains functionally Graded Material Sinusoidal Plate

Computer Simulation of Distribution of Reinforced Particles in functionally Graded Materials Fabricated by Centrifugal Casting

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Journal of Harbin Institute of Technology(New Series) 1997年第3期4卷 89-94页

作者：张宝生王建华张永军安阁英

A mathematic model is developed with viscosity of molten matrix,centrifugalforce,casting temperature,mold temperature and other parameters taken intoconsideration for preditction of the distribution of reinforced particles during centrifugalcasting of FGM,and the simulation of distribution of reinforced particles and thesolidification process during centrifugal casting is performed with the aid of ***_p/A356 FGM is fabricated by centrifugal *** results of computersimulation of distribution of reinforced particles are in good agreement with experimentalobservations.

关键词： functionally graded materials(FGM) centrifugal casting mathematical model computer simulation

Experimental analysis for thermal stress in functionallygradient material

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Chinese Science Bulletin 1998年第10期43卷 827-829页

作者： Yilan Kang Qianjun Xu Shouwen Yu Tianjin Univ Dept Mech Tianjin 300072 Peoples R China Tsing Hua Univ Dept Engn Mech Beijing 100084 Peoples R China

Studies of displacement fields and stress concentration, due to uniform temperature change in a functionally gradient material (FGM) specimen and bimaterial (NFGM) specimen, have been made by Moire interferometry and finite element method. Results show that the thermal stresses concentration has been effectively reduced, and the distribution of the thermal deformations and thermal strains have also been relaxed and improved by transition layer of FGM.

关键词： functionally gradient material (FGM) Moire interferometry concentration of thermal stress.

Vibration analysis of FG annular sector in moderately thick plates with two piezoelectric layers

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Applied Mathematics and Mechanics(English Edition) 2019年第6期40卷 783-804页

作者： S.AZARIPOUR M.BAGHANI School of Mechanical Engineering College of Engineering University of Tehran

Free vibration of functionally graded (FG) annular sector plates embedded with two piezoelectric layers is studied with a generalized differential quadrature (GDQ) method. Based on the first-order shear deformation (FSD) plate theory and Hamilton’s principle with parameters satisfying Maxwell’s electrostatics equation in the piezoelectric layers, governing equations of motion are developed. Both open and closed circuit (shortly connected) boundary conditions on the piezoelectric surfaces, which are respective conditions for sensors and actuators, are accounted for. It is observed that the open circuit condition gives higher natural frequencies than a shortly connected condition. For the simulation of the potential electric function in piezoelectric layers, a sinusoidal function in the transverse direction is considered. It is assumed that properties of the FG material (FGM) change continuously through the thickness according to a power distribution law. The fast rate convergence and accuracy of the GDQ method with a small number of grid points are demonstrated through some numerical examples. With various combinations of free, clamped, and simply supported boundary conditions, the effects of the thicknesses of piezoelectric layers and host plate, power law index of FGMs, and plate geometrical parameters (e.g., angle and radii of annular sector) on the in-plane and out-of-plane nat-ural frequencies for different FG and piezoelectric materials are also studied. Results can be used to predict the behaviors of FG and piezoelectric materials in mechanical systems.

关键词： free vibration annular sector piezoelectric functionally graded material (FGM) first-order shear deformation (FSD)

Rotating sandwich cylindrical shells with an FGM core and two FGPM layers: free vibration analysis

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Applied Mathematics and Mechanics(English Edition) 2019年第4期40卷 563-578页

作者： R.KARROUBI M.IRANI-RAHAGHI Department of Solid Mechanics Faculty of Mechanical Engineering University of Kashan

The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material(FGM) shell, and it is surrounded by two piezoelectric layers. Considering piezoelectric materials to be functionally graded(FG),the material properties vary along the thickness direction as one innovation of this *** the first-order shear deformation theory(FSDT), the equations of motion of this electromechanical system are derived as the partial differential equations(PDEs) using Hamilton's principle. Then, the Galerkin procedure is used to discretize the governing equations, and the present results are compared with the previously published results for both isotropic and FGM shells to verify the analytical method. Finally, the effects of FGM and functionally graded piezoelectric material(FGPM) properties as well as the thickness ratio and the axial and circumferential wave numbers on the natural frequencies are studied. Moreover, the Campbell diagram is plotted and discussed through the governing equations. The present results show that increasing the non-homogeneous index of the FGM decreases the natural frequencies on the contrary of the effect of non-homogeneous index of the FGPM.

关键词： vibration sandwich structure rotating shell functionally graded material(FGM) functionally graded piezoelectric material(FGPM)

Bending Solutions of FGM Reddy-Bickford Beams in Terms of Those of the Homogenous Euler-Bernoulli Beams

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Acta Mechanica Solida Sinica 2019年第4期32卷 499-516页

作者： You-Ming Xia Shi-Rong Li Ze-Qing Wan School of Civil Science and Engineering Yangzhou UniversityYangzhou 225127 China

In this paper, correspondence relations between the solutions of the static bending of functionally graded material (FGM) Reddy-Bickford beams (RBBs) and those of the corresponding homogenous Euler-Bernoulli beams are presented. The effective material properties of the FGM beams are assumed to vary continuously in the thickness direction. Governing equations for the titled problem are formulated via the principle of virtual displacements based on the third-order shear deformation beam theory, in which the higher-order shear force and bending moment are included. General solutions of the displacements and the stress resultants of the FGM RBBs are derived analytically in terms of the deflection of the reference homogenous Euler- Bernoulli beam with the same geometry, loadings and end conditions, which realize a classical and homogenized expression of the bending response of the shear deformable non-homogeneous FGM beams. Particular solutions for the FGM RBBs under specified end constraints and load conditions are given to validate the theory and methodology. The key merit of this work is to be capable of obtaining the high-accuracy solutions of thick FGM beams in terms of the classical beam theory solutions without dealing with the solution of the complicated coupling differential equations with boundary conditions of the problem.

关键词： functionally graded material beams Reddy-Bickford beam theory Euler- Bernoulli beam theory Bending solution Shear deformation

Axial compressive behavior of Moso Bamboo and its components with respect to fiber-reinforced composite structure

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Journal of Forestry Research 2019年第6期30卷 2371-2377页

作者： Xuexia Zhang Zixuan Yu Yan Yu Hankun Wang Jinghao Li Department of Biomaterials International Center for Bamboo and RattanBeijing 100102People’s Republic of China SFA and Beijing Co-built Key Laboratory of Bamboo and Rattan Science and Technology State Forestry AdministrationBeijing 100102People’s Republic of China Forest Products Laboratory U.S.Forest ServiceWisconsinWI 53726USA

Bamboo is a unique fiber-reinforced bio-composite with fibers embedded into a parenchyma cell *** conducted axial compression tests on bamboo blocks prepared from bottom to top,and from inner to outer portions of the *** apparent Young’s modulus and compressive strength of whole thickness bamboo blocks exhibited slight increases with increasing height along the culm,due to slight increases of fiber volume fraction(Vf)from 28.4 to 30.4%.Other blocks showed a significant increase in apparent Young’s modulus and strength from the inner to outer part of the culm wall,mainly owing to a sharp increase of Vf from 17.1 to 59.8%.With a decrease of fiber fraction volume there was a transition from relatively brittle behavior to very ductile behavior in bamboo *** indicated that stiffness and strength of bamboo was primarily due to fiber in compression,and ductility of bamboo was provided by the parenchyma cell matrix acting as a natural fiber-reinforced composite.

关键词： Bamboo Axial compressive behavior functionally grade structure

Light-induced nonhomogeneity and gradient bending in photochromic liquid crystal elastomers

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Science China(Physics,Mechanics & Astronomy) 2006年第5期49卷 553-563页

作者： JIN Lihua JIANG Xin HUO Yongzhong Department of Mechanics and Engineering Science Fudan UniversityShanghai 200433China Department of Mechanics and Engineering ScienceFudan UniversityShanghai 200433China Department of Mechanics and Engineering ScienceFudan UniversityShanghai 200433China

The recently reported opto-mechanical effect of some photochromic liquid crystal elastomers (LCEs) is studied. It is found that in such LCEs, material parameters such as the Young’s modulus and the stress-free strains will become nonhomogeneous under light irradiations. One may call them the light-induced functionally gradient materials. Analytical expressions for the dependence of the material parameters on the space varia- ble and possibly on the time variable are obtained. Exponential dependence can be derived under certain approximations. As an example, the light-induced bending of a beam is studied. Two neutral planes are found in the beam. Thus, along the thickness of the beam, there are extensions in the upper and lower parts and contractions in the middle.

关键词： opto-mechanical effect material nonhomogeneity functionally gradient materials light-induced bending