V. Minutolo¹, E. Ruocco¹, S. Ciaramella¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 27-48, 2009, DOI:10.3970/cmes.2009.041.027

Abstract A Field Boundary Element Method (FBEM) for Functionally Graded Materials (FGM) is presented and compared with Isoparametric Finite Element Method. The presented formulation, using the Kelvin's fundamental solution, is able to analyse structures although no fundamental solution is actually known. Isoparametric FGM Finite Element Method is a well established tool for FGM structural analysis. The comparison shows that both FBEM and FEM give accurate results. In the paper, the solution of some examples for 2D plates are reported both using FEM and FBEM. Some comparisons with analytical results are discussed and accuracy of the solutions is highlighted. The comparison between… More >

Wen-Hwa Chen¹, Cheng-Te Chi, Ming-Hsiao Lee

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 175-200, 2009, DOI:10.3970/cmes.2009.040.175

Abstract Based on an incremental formulation of element-free Galerkin method (EFGM), a highly efficient three-dimensional EFGM analysis procedure is proposed to deal with the structure with extremely large deformation. By this procedure, a fixed and uniform background grid, part of which coincides with the background cells employed in the conventional EFGM for numerical integration, is devised. The background grid is connected by uniformly distributed fictitious nodes which do not move during loading process even if extremely large deformation occurs. A deformable analysis domain, which is discretized by moving boundary nodes and interior nodes, is established for describing the deformation of the… More >

J. Sladek¹, V. Sladek¹, P. Solek², P.H. Wen³, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 77-98, 2008, DOI:10.3970/cmes.2008.030.077

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory is transformed into local integral equations on local subdomains in the base plane of the shell by using a unit test function. Nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which… More >

Vladimir Sladek¹, Jan Sladek¹, Chuanzeng Zhang²

CMC-Computers, Materials & Continua, Vol.4, No.3, pp. 177-188, 2006, DOI:10.3970/cmc.2006.004.177

Abstract This paper concerns the stability, convergence of accuracy and cost efficiency of four various formulations for solution of boundary value problems in non-homogeneous elastic solids with functionally graded Young's modulus. The meshless point interpolation method is employed with using various basis functions. The interaction among the elastic continuum constituents is considered in the discretized formulation either by collocation of the governing equations or by integral satisfaction of the force equilibrium on local sub-domains. The exact benchmark solutions are used in numerical tests. More >

T. D. Tran¹, Chien H. Thai^2,3,*, H. Nguyen-Xuan^4,5,*

CMC-Computers, Materials & Continua, Vol.57, No.3, pp. 447-483, 2018, DOI:10.32604/cmc.2018.01738

Abstract A size-dependent computational approach for bending, free vibration and buckling analyses of isotropic and sandwich functionally graded (FG) microplates is in this study presented. We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory (MCST). The present model only retains a single material length scale parameter for capturing properly size effects. A rule of mixture is used to model material properties varying through the thickness of plates. The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation (MKI)… More >

Haolong Chen^1,2, Bo Yu¹, Huanlin Zhou^1*, Zeng Meng¹

CMC-Computers, Materials & Continua, Vol.53, No.4, pp. 271-290, 2017, DOI:10.3970/cmc.2017.053.271

Abstract The cuckoo search algorithm (CS) is improved by using the conjugate gradient method(CGM), and the CS-CGM is proposed. The unknown inner boundary shapes are generated randomly and evolved by Lévy flights and elimination mechanism in the CS and CS-CGM. The CS, CGM and CS-CGM are examined for the prediction of a pipe’s inner surface. The direct problem is two-dimensional transient heat conduction in functionally graded materials (FGMs). Firstly, the radial integration boundary element method (RIBEM) is applied to solve the direct problem. Then the three methods are compared to identify the pipe’s inner surfacewith the information of measured temperatures. Finally,… More >

K. Khanna^1,2, V.K. Gupta³, S.P. Nigam¹

CMC-Computers, Materials & Continua, Vol.48, No.3, pp. 147-161, 2015, DOI:10.3970/cmc.2015.048.147

Abstract A mathematical model is developed to describe the steady state creep in a rotating Al-SiC_p disc having a non-linear thickness profile and distribution of SiC particles along the radial direction. The model is used to investigate the effect of imposing three different kinds of radial temperature profiles viz. linear, parabolic and exponential with fixed values of inner and outer surface temperatures, on the creep stresses and strain rates. It is noticed that by increasing the temperature exponent (n_T), the radial stress (over the entire radius) and tangential stress (near the inner radius) increase in the disc. However, the tangential stress… More >

Chih-Ping Wu, Ruei-Yong Jiang

CMC-Computers, Materials & Continua, Vol.46, No.1, pp. 17-56, 2015, DOI:10.3970/cmc.2015.046.017

Abstract An asymptotic meshless method using the differential reproducing kernel (DRK) interpolation and multiple time scale methods is developed for the three-dimensional (3D) free vibration analysis of sandwich functionally graded material (FGM) circular hollow cylinders with combinations of simply-supported and clamped edge conditions. In the formulation, we perform the mathematical processes of nondimensionalization, asymptotic expansion and successive integration to obtain recurrent sets of motion equations for various order problems. Classical shell theory (CST) is derived as a first-order approximation of the 3D elasticity theory, and the motion equations for higher-order problems retain the same differential operators as those of CST, although… More >

Chih-Ping Wu^1,2, Hao-Yuan Li¹

CMC-Computers, Materials & Continua, Vol.34, No.1, pp. 27-62, 2013, DOI:10.3970/cmc.2013.034.027

Abstract A Reissner's mixed variational theorem (RMVT)-based finite rectangular prism method (FRPM) is developed for the three-dimensional (3D) analysis of sandwich functionally graded material (FGM) plates subjected to mechanical loads, in which the edge conditions of the plates are such that one pair of opposite edges is simply supported and the other pair may be combinations of free, clamped or simply supported edges. The sandwich FGM plate considered consists of two thin and stiff homogeneous material face sheets combined with an embedded thick and soft FGM core, the material properties of which are assumed to obey the powerlaw distributions of the… More >

Chih-Ping Wu^1,2, Hao-Yuan Li²

CMC-Computers, Materials & Continua, Vol.19, No.2, pp. 155-198, 2010, DOI:10.3970/cmc.2010.019.155

Abstract The Reissner mixed variational theorem (RMVT)- and principle of virtual displacements (PVD)-based finite layer methods (FLMs) are developed for the quasi-three-dimensional (3D) free vibration analysis of simply-supported, multilayered composite and functionally graded material (FGM) plates. The material properties of the FGM layers are assumed to obey either an exponent-law exponentially varied with the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In these formulations, the plate is divided into a number of finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of… More >