Baoyu Ma¹, Guansuo Dui¹, Shengyou Yang², Libiao Xin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.6, pp. 537-554, 2015, DOI:10.3970/cmes.2015.109.537

Abstract This article focuses on the analytical solution for uniform heating of a FGM hollow sphere made of two phase of different materials. It is assumed that the volume fraction of one phase is a function f1=(rn-an)/(bn-an) varied in the radial direction. Based on the Voigt constant strain approximation, analytical solutions of stresses, displacements and the effective coefficient of thermal expansion are obtained. The effects of the volume fraction, Poisson’s ratio, Young’s moduli and coefficients of thermal expansion on the solutions are studied. Two special cases, constant elastic modulus and constant coefficient of thermal expansion, are finally discussed. More >

Mohammad Hossein Ghadiri Rad¹, Farzad Shahabian^1,2, Seyed Mahmoud Hosseini³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.3, pp. 135-157, 2015, DOI:10.3970/cmes.2015.108.135

Abstract A meshless method based on the local Petrov-Galerkin approach is developed for elasto-dynamic analysis of geometrically nonlinear two dimensional (2D) problems in hyper-elastic functionally graded materials. The radial point interpolation method (RPIM) is utilized to build the shape functions and the Heaviside step function is used as the test function. The mechanical properties of functionally graded material are considered to continuously vary in a certain direction and are simulated using a nonlinear power function in volume fraction form. Considering the large deformations, it is assumed that the domain be made of large deformable neo-Hookean hyperelastic materials. Rayleigh damping is employed… More >

Da-Guang Zhang^1,2, Hao-Miao Zhou¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.3, pp. 201-222, 2014, DOI:10.3970/cmes.2014.100.201

Abstract A model of FGM beams resting on nonlinear elastic foundations is put forward by physical neutral surface and high-order shear deformation theory. Material properties are assumed to be temperature dependent and von Kármán strain-displacement relationships are adopted. Nonlinear bending and thermal postbuckling are given by multi-term Ritz method, and influences played by different supported boundaries, thermal environmental conditions, different elastic foundations, and volume fraction index are discussed in detail. It is worth noting that the effect of nonlinear elastic foundation increases with increasing deflection. More >

A.V. Ekhlakov^1,2, O.M. Khay^1,3, Ch. Zhang¹, X.W. Gao⁴, J. Sladek⁵, V. Sladek⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.6, pp. 595-614, 2013, DOI:10.3970/cmes.2013.092.595

Abstract A boundary-domain integral equation method is applied to the transient thermoelastic crack analysis in functionally graded materials. Fundamental solutions for homogeneous, isotropic and linear elastic materials are used to derive the boundary-domain integral equations. The radial integration method, the Cartesian transformation method and the cell-integration method are applied for the evaluation of the arising domain-integrals. Numerical results for dynamic stress intensity factors obtained by the three approaches are presented, compared and discussed to show the accuracy and the efficiency of the domain-integral evaluation techniques. More >

G. Mattei^1,2, A. Tirella^1,2, A. Ahluwalia^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.6, pp. 483-504, 2012, DOI:10.3970/cmes.2012.087.483

Abstract Biological function is intricately linked with structure. Many biological structures are characterised by functional spatially distributed gradients in which each layer has one or more specific functions to perform. Reproducing such structures is challenging, and usually an experimental trial-and-error approach is used. In this paper we investigate how the gravitational sedimentation of discrete solid particles (secondary phase) within a primary fluid phase with a time-varying dynamic viscosity can be used for the realisation of stable and reproducible continuous functionally graded materials (FGMs). Computational models were used to simulate the distribution of a particle phase in a fluid domain. Firstly a… More >

H. T. Xiao¹, Z. Q. Yue²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.2, pp. 159-180, 2009, DOI:10.3970/cmes.2009.052.159

Abstract This paper presents a three-dimensional boundary element method for contact problems of an elastic indenter on the surface of functionally graded materials (FGMs). The FGM elastic properties can have any irregular variations with depth. The indenter is subjected to the loading normal to the flat contact surface. The classical Kelvin solution is used for the mathematical formulation of the homogeneous elastic indenter. The generalized Kelvin solution is used for the mathematical formulation of the FGM base. The contact variables are defined with respect to each of the surfaces using local coordinate systems. The corresponding contact equations are used to couple… More >

F. Han¹, E. Pan¹, A.K. Roy², Z.Q. Yue³

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.1, pp. 15-30, 2006, DOI:10.3970/cmes.2006.014.015

Abstract In this paper, an analytical solution is presented to study the response of piezoelectric, transversely isotropic, functionally graded, and multilayered half spaces to uniform circular surface loadings (pressure or negative electric charge). The inhomogeneous material is exponentially graded in the vertical direction and can have multiple discrete layers. The propagator matrix method and cylindrical system of vector functions are used to first derive the solution in the transformed domain. In order to find the responses in the physical-domain, which are expressed in one-dimensional infinite integrals of the Bessel function products, we introduced and adopted an adaptive Gauss quadrature. Two piezoelectric… More >

D. Mirzaei¹, M. Dehghan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.3, pp. 185-210, 2011, DOI:10.3970/cmes.2011.072.185

Abstract The meshless local Petrov-Galerkin (MLPG) method with an efficient technique to deal with the time variable are used to solve the heat conduction problem in this paper. The MLPG is a meshless method which is (mostly) based on the moving least squares (MLS) scheme to approximate the trial space. In this paper the MLS is used for approximation in both time and space domains, and we avoid using the time difference discretization or Laplace transform method to overcome the time variable. The technique is applied for continuously nonhomogeneous functionally graded materials (FGM) in a finite strip and a hallow cylinder.… More >

Liviu Marin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.3, pp. 221-254, 2009, DOI:10.3970/cmes.2009.046.221

Abstract We investigate the stable numerical reconstruction of an unknown portion of the boundary of a two-dimensional domain occupied by a functionally graded material (FGM) from a given boundary condition on this part of the boundary and additional Cauchy data on the remaining known portion of the boundary. The aforementioned inverse geometric problem is approached using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. The optimal value of the regularization parameter is chosen according to Hansen's L-curve criterion. Various examples are considered in order to show that the proposed method is numerically stable with respect to… More >

Yueting Zhou¹, Xing Li², Dehao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 191-222, 2009, DOI:10.3970/cmes.2009.043.191

Abstract The transient response of an orthotropic functionally graded strip with a partially insulated crack under convective heat transfer supply is considered. It is modeled there exists thermal resistant in the heat conduction through the crack region. The mixed boundary value problems of the temperature field and displacement field are reduced to a system of singular integral equations in Laplace domain. The expressions with high order asymptotic terms for the singular integral kernel are considered to improve the accuracy and efficiency. The numerical results present the effect of the material nonhomogeneous parameters, the orthotropic parameters and dimensionless thermal resistant on the… More >