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 >

H. K. Ching^1,2, J. K. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 199-218, 2006, DOI:10.3970/cmes.2006.013.199

Abstract The Meshless Local Petrov-Galerkin (MLPG) method is a novel numerical approach similar to finite element methods, but it allows the construction of the shape function and domain discretization without defining elements. In this study, the MLPG analysis for transient thermomechanical response of a functionally graded composite heated by Gaussian laser beams is presented. The composite is modeled as a 2-D strip which consists of metal and ceramic phases with the volume fraction varying over the thickness. Two sets of the micromechanical models are employed for evaluating the effective material properties, respectively. Numerical results are presented for the thermomechanical responses in… More >

S.M. Moussavinezhad¹, Farzad Shahabian¹, Seyed Mahmoud Hosseini^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.3, pp. 177-204, 2013, DOI:10.3970/cmes.2013.091.177

Abstract In this article, the propagation of elastic wave is studied in two dimensional functionally graded thick hollow cylinder with finite length subjected to mechanical shock loading, considering two dimensional variations for mechanical properties. The meshless local Petrov-Galerkin (MLPG) method is developed to solve the boundary value problem. The Newmark finite difference method is used to treat the time dependence of the variables for transient problems. The FG cylinder is considered to be under axisymmetric conditions. The mechanical properties of FG cylinder are assumed to vary across thickness and length of FG cylinder in terms of two dimensional volume fractions as… More >

P. L. Bishay¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 41-98, 2012, DOI:10.3970/cmes.2012.084.041

Abstract Higher-order two-dimensional as well as low and higher-order three-dimensional new Hybrid/Mixed (H/M) finite elements based on independently assumed displacement, and judiciously chosen strain fields, denoted by HMFEM-2, are developed here for applications in macro-mechanics. The idea of these new H/M finite elements is based on collocating the components of the independent strain field, with those derived from the independently assumed displacement fields at judiciously and cleverly chosen collocation points inside the element. This is unlike the other techniques used in older H/M finite elements where a two-field variational principle was used in order to enforce both equilibrium and compatibility conditions… More >

Marco Dondero¹, Adrián P. Cisilino^1,2, J. Pablo Tomba¹

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 225-246, 2011, DOI:10.3970/cmes.2011.078.225

Abstract This paper introduces a numerical methodology for the design of random micro-heterogeneous materials with functionally graded effective thermal conductivities (ETC). The optimization is carried out using representative volume elements (RVEs), a parallel Genetic Algorithm (GA) as optimization method, and a Fast Multipole Boundary Element Method (FMBEM) for the evaluation of the cost function. The methodology is applied for the design of foam-like microstructures consisting of random distributions of circular insulated holes. The temperature field along a material sample is used as objective function, while the spatial distribution of the holes is the design variable. There are presented details of the… 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 >

Seyed Mahmoud Hosseini¹, Farzad Shahabian²,Jan Sladek³, Vladimir Sladek³

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.1, pp. 39-66, 2011, DOI:10.3970/cmes.2011.071.039

Abstract The thermo-elastic wave propagation based on Green-Naghdi (GN) coupled thermo-elasticity (without energy dissipation) is studied in a functionally graded thick hollow cylinder considering uncertainty in constitutive mechanical properties under thermal shock loading. The meshless local Petrov-Galerkin method accompanied with Monte-Carlo simulation is developed to solve the stochastic boundary value problem. In the presented method, the mechanical properties of FGM are considered to be as random variables with Gaussian distribution and mean values equal to deterministic values reported in previous works, which are generated using Monte-Carlo simulation with various coefficients of variations (COVs). The time evolution for transient problems is treated… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², M. Wünsche²

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.068.185

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed to solve initial-boundary value crack problems of piezoelectric solids with nonlinear electrical boundary conditions on crack faces. Homogeneous and continuously varying material properties of the piezoelectric solid are considered. Stationary governing equations for electrical fields and the elastodynamic equations with an inertial term for mechanical 2-D fields are considered. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements and electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations,… More >