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Acta Mechanica Sinica 2018年第6期34卷 1124-1135页

作者： Nuttawit Wattanasakulpong Arisara Chaikittiratana Sacharuck Pornpeerakeat Department of Mechanical Engineering Mahanakom University of TechnologyNongchokBangkok 10530Thailand Department of Mechanical and Aerospace Engineering King Mongkut’s University of Technology North BangkokBangkok 10800Thailand Department of Teacher Training in Civil Engineering King Mongkut’s University of Technology North BangkokBangkok 10800Thailand Research Centre for Advanced Computational and Experimental Mechanics(RACE) King Mongkut’s University of Technology North BangkokBangkok 10800nailand

In this paper,vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation *** beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational *** material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal *** Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle,which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary *** on the numerical experiments,it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.

关键词： functionally graded porous beam Vibration analysis Chebyshev collocation method Elastic boundary condition

Coupling Magneto-Electro-Elastic node-based smoothed radial point interpolation method for free vibration and transient analysis of functionally Graded Magneto-Electro-Elastic structures

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Chinese Journal of Aeronautics 2020年第1期33卷 227-243页

作者： Liming ZHOU Shuhui REN Bin NIE Guikai GUO Xiangyang CUI School of Mechanical and Aerospace Engineering Jilin UniversityChangchun 130025China State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan UniversityChangsha 410082China

A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of functionally Graded Magneto-Electro-Elastic(FGMEE)*** introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were *** on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were *** triangular background elements,the free vibration and transient responses of three numerical examples were *** proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of ***,CM-NS-RPIM could reduce the number of nodes while guaranteeing the ***,triangular elements could be generated automatically even for complex ***,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.

关键词： Coupling Magneto-Electro-Elastic node-based smoothed radial point interpolation method functionally Graded Magneto-Electro-Elastic Gradient smoothing technique Rayleigh damping Transient responses

Free vibration of non-uniform axially functionally graded beams using the asymptotic development method

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Applied Mathematics and Mechanics(English Edition) 2019年第1期40卷 85-96页

作者： Dongxing CAO Yanhui GAO College of Mechanical Engineering Beijing University of Technology Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures

The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary ***, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.

关键词： axially functionally graded(AFG)beam non-uniform natural frequency asymptotic development method

Buckling analysis of functionally graded plates partially resting on elastic foundation using the differential quadrature element method

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Acta Mechanica Sinica 2019年第1期35卷 174-189,I0005页

作者： Arash Shahbaztabar Koosha Arteshyar Department of Ocean Engineering AmirKabir University of TechnologyTehran 15914Iran Department of Mechanical Engineering Islamic Azad UniversityKarajAlborzIran

We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.

关键词： Differential quadrature element method Pasternak elastic support Critical buckling load functionally graded plates

Basic solution of two parallel Mode-I cracks in functionally graded materials

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Science China(Technological Sciences) 2008年第9期51卷 1380-1393页

作者： LIANG Jun Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China Center for Composite Materials and Structures Harbin Institute of Technology Harbin China

The solution of two parallel cracks in functionally graded materials subjected to a tensile stress loading is derived in this paper. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate parallel to the crack. The problem is formulated through Fourier transform into four pairs of dual integral equations, in which the unknown variables are jumps of displace-ments across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces are directly expanded as a series of Jacobi polynomials to obtain the shielding effects of the two parallel cracks in functionally graded materials.

关键词： parallel cracks shielding effects functionally graded materials

The Kantorovich macro-or-mesoscopic refined solution for the heterogeneous functionally gradient material complex structure

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Science China(Technological Sciences) 2003年第1期46卷 1-18页

作者：李永宋健张志民 State Key Laboratory of Automotive Safety and Energy Tsinghua University Center of Mechanics Beijing University of Aeronautics and Astronautics

This paper is a piece of research on the complex structure of functionally gradient mate-rials, which is an applicable triangular cantilever plate structure locally fixed and supported by its round revolving axis. Combined with the generalized Euler equation and the generalized boundary conditions, Kantorovich method and the principle of the two independent variables generalized calculus of variations are adopted to establish the bending governing equation of plates to work out the solution. In comparison with the previous work on the problem, this paper, taking into ac-count three generalized mechanical factors and FGM macro-or-mesoscopic heterogeneity, pro-poses a new concept of translating the issue of theoretical initial value into the problem of semi-analytical boundary value to obtain the refined solution and then researches the joint effect of grads stress fields. Thereby a refined version of Kantorovich macro-or-mesoscopic solution is de-veloped.

关键词： functionally gradient, Kantorovich macro-or-mesoscopic, generalized calculus of variations principle, angular force, joint effect.

Are “Higher-Order” and “Layer-wise Zig-Zag” Plate & Shell Theories Necessary for functionally Graded Materials and Structures?

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Computer Modeling in Engineering & Sciences 2016年第7期112卷 1-32页

作者： Yaping Zhang Qifeng Fan Leiting Dong Satya NAtluri Taizhou Polytechnic College China School of Aeronautic Science and Engineering Beihang UniversityChina Department of Mechanical Engineering Texas Tech UniversityUSA

Similar to the very vast prior literature on analyzing laminated composite structures,“higher-order”and“layer-wise higher-order”plate and shell theories for functionally-graded(FG)materials and structures are also widely popularized in the literature of the past two ***,such higher-order theories involve(1)postulating very complex assumptions for plate/shell kinematics in the thickness direction,(2)defining generalized variables of displacements,strains,and stresses,and(3)developing very complex governing equilibrium,compatibility,and constitutive equations in terms of newly-defined generalized kinematic and generalized kinetic *** industrial applications are thus hindered by their inherent complexity,and the fact that it is difficult for end-users(front-line structural engineers)to completely understand all the newly-defined generalized DOFs for FEM in the higher-order and layer-wise *** an entirely different way,very simple 20-node and 27-node 3-D continuum solid-shell elements are developed in this paper,based on the simple theory of 3D solid mechanics,for static and dynamic analyses of functionally-graded plates and shells.A simple Over-Integration(a 4-point Gauss integration in the thickness direction)is used to evaluate the stiffness matrices of each element,while only a single element is used in the thickness direction without increasing the number of degrees of freedom.A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity in Cartesian as well as cylindrical polar *** numerical results are presented for static and dynamic analyses of FG plates and shells,which agree well,either with the existing solutions in the published literature,or with the computationally very expensive solutions obtained by using simple 3D isoparametric elements(with standard Gauss Quadrature)available in NASTRAN(wherein many 3D elements are used in the thi

关键词： functionally graded plates and shells 20-node hexahedral element 27-node over-integration higher order theory layer-wise

Fracture analysis of a functionally graded interfacial zone between two dissimilar homogeneous materials

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Science China(Physics,Mechanics & Astronomy) 2006年第5期49卷 540-552页

作者： CHENG Zhanqi1,2 & ZHONG Zheng1 1. School of Aerospace Engineering and Applied mechanics, Tongji University, Shanghai 200092, China 2. College of Civil Engineering, Zhengzhou University, Zhengzhou 450002, China School of Aerospace Engineering and Applied mechanics Tongji University Shanghai China College of Civil Engineering Zhengzhou University Zhengzhou China

In this paper the plane elasticity problem for a functionally graded interfacial zone containing a crack between two dissimilar homogeneous materials has been considered. It is assumed that in the interfacial zone the reciprocal of the shear modulus is a linear function of the coordinate, while Possion’s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors are investigated. The numerical results show that the graded parameters, the thickness of interfacial zone, the crack size and location have significant effects on the stress intensity factors.

关键词： functionally graded material interfacial zone fracture stress intensity factor

Complex dynamics of functionally graded plates with thermal load in 1:2 internal resonance

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Science China(Technological Sciences) 2010年第3期53卷 713-719页

作者： DING Ran 1 &WU ZhiQiang 1,2 1 Department of Mechanics,Tianjin University,Tianjin 300072,China 2 State Key Laboratory of Engines,Tianjing 310002,China Department of Mechanics Tianjin University Tianjin China State Key Laboratory of Engines Tianjing China

Complex dynamics of the simply-supported functionally graded(FG)rectangular plates with thermal load is *** on Reddy's third-order shear deformation theory and the von Karman nonlinear strain-displacement relations,ordinary differential equations(ODEs)of the plate's transversal oscillation are derived by using Hamilton's principle and Galerkin's ***'classification of the equations in 1:2 internal resonance is *** results of a simplysupported aluminum-alumina rectangular FG plate are *** of temperature and volume fraction on the responses' stabilities are discussed.

关键词： functionally graded materials thermal load 1 internal resonance solutions’ classification modal interactions

An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

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Science China(Physics,Mechanics & Astronomy) 2008年第2期51卷 165-175页

作者： GAO LiMing WANG Ji ZHONG Zheng DU JianKe College of Aerospace Engineering and Mechanics Tongji UniversityShanghai 200092China Piezoelectric Device Laboratory School of EngineeringNingbo UniversityNingbo 315211China

In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing dif-ferent features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with gen-eral material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grad-ing schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applica-tions of such structures in engineering.

关键词： Rayleigh wave surface acoustic wave vibration plate layered structure functionally graded material (FGM)