H.-K. Ching, R. C. Batra¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 273-290, 2001, DOI:10.3970/cmes.2001.002.273

Abstract It is shown that the MLPG method augmented with the enriched basis functions and either the visibility criterion or the diffraction criterion successfully predicts the singular stress fields near a crack tip. Results are presented for a single edge-cracked plate and a double edge-cracked plate with plate edges parallel to the crack axis loaded in tension, the single edge-cracked plate with one plate edge parallel to the crack axis clamped and the other loaded by tangential tractions, and for a double edge-notched plate with the side between the notches loaded in compression. For the first three problems, the stress intensity… More >

H. Lin, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 117-142, 2001, DOI:10.3970/cmes.2001.002.117

Abstract The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus^~ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. More >

H.-G. Kim, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 11-32, 2000, DOI:10.3970/cmes.2000.001.313

Abstract The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are… More >

H. Lin, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 45-60, 2000, DOI:10.3970/cmes.2000.001.205

Abstract Due to the very general nature of the Meshless Local Petrov-Galerkin (MLPG) method, it is very easy and natural to introduce the upwinding concept (even in multi-dimensional cases) in the MLPG method, in order to deal with convection-dominated flows. In this paper, several upwinding schemes are proposed, and applied to solve steady convection-diffusion problems, in one and two dimensions. Even for very high Peclet number flows, the MLPG method, with upwinding, gives very good results. It shows that the MLPG method is very promising to solve the convection-dominated flow problems, and fluid mechanics problems. More >

K.Y. Liu^1,2,3, S.Y. Long^1,2,4, G.Y. Li¹

CMC-Computers, Materials & Continua, Vol.7, No.1, pp. 43-58, 2008, DOI:10.3970/cmc.2008.007.043

Abstract A meshless local Petrov-Galerkin method (MLPG) [[Atluri and Zhu (1998)] for the analysis of cracks in isotropic functionally graded materials is presented. The meshless method uses the moving least squares (MLS) to approximate the field unknowns. The shape function has not the Kronecker Delta properties for the trial-function-interpolation, and a direct interpolation method is adopted to impose essential boundary conditions. The MLPG method does not involve any domain and singular integrals to generate the global effective stiffness matrix if body force is ignored; it only involves a regular boundary integral. The material properties are smooth functions of spatial coordinates and… More >

V. Vavourakis, D. Polyzos¹

CMC-Computers, Materials & Continua, Vol.5, No.3, pp. 185-196, 2007, DOI:10.3970/cmc.2007.005.185

Abstract Very recently, Vavourakis, Sellountos and Polyzos (2006) ({CMES: Computer Modeling in Engineering {\&} Sciences, vol. 13, pp. 171--184}) presented a comparison study on the accuracy provided by five different elastostatic Meshless Local Petrov-Galerkin (MLPG) type formulations, which are based on Local Boundary Integral Equation (LBIE) considerations. One of the main conclusions addressed in this paper is that the use of derivatives of the Moving Least Squares (MLS) shape functions decreases the solution accuracy of any MLPG(LBIE) formulation. In the present work a new, free of MLS-derivatives and non-singular MLPG(LBIE) method for solving elastic problems is demonstrated. This is accomplished by… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², F. Garcia-Sanche³, M. Wünsche²

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 109-118, 2006, DOI:10.3970/cmc.2006.004.109

Abstract Piezoelectric materials have wide range engineering applications in smart structures and devices. They have usually anisotropic properties. Except this complication electric and mechanical fields are coupled each other and the governing equations are much more complex than that in the classical elasticity. Thus, efficient computational methods to solve the boundary or the initial-boundary value problems for piezoelectric solids are required. In this paper, the Meshless local Petrov-Galerkin (MLPG) method with a Heaviside step function as the test functions is applied to solve two-dimensional (2-D) piezoelectric problems. The mechanical fields are described by the equations of motion with an inertial term.… More >

H. T. Liu¹, Z. D. Han¹, A. M. Rajendran², S. N. Atluri³

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 43-54, 2006, DOI:10.3970/cmc.2006.004.043

Abstract The Rajendran-Grove (RG) ceramic damage model is a three-dimensional internal variable based constitutive model for ceramic materials, with the considerations of micro-crack extension and void collapse. In the present paper, the RG ceramic model is implemented into the newly developed computational framework based on the Meshless Local Petrov-Galerkin (MLPG) method, for solving high-speed impact and penetration problems. The ability of the RG model to describe the internal damage evolution and the effective material response is investigated. Several numerical examples are presented, including the rod-on-rod impact, plate-on-plate impact, and ballistic penetration. The computational results are compared with available experiments, as well… More >

Somayeh Hessam¹, Shaghayegh Vahdat¹, Irvan Masoudi Asl^2,*, Mahnaz Kazemipoor³, Atefeh Aghaei⁴, Shahaboddin Shamshirband,^5,6,*, Timon Rabczuk⁷

CMC-Computers, Materials & Continua, Vol.61, No.1, pp. 11-26, 2019, DOI:10.32604/cmc.2019.06472

Abstract In recent years, Parkinson's Disease (PD) as a progressive syndrome of the nervous system has become highly prevalent worldwide. In this study, a novel hybrid technique established by integrating a Multi-layer Perceptron Neural Network (MLP) with the Biogeography-based Optimization (BBO) to classify PD based on a series of biomedical voice measurements. BBO is employed to determine the optimal MLP parameters and boost prediction accuracy. The inputs comprised of 22 biomedical voice measurements. The proposed approach detects two PD statuses: 0-disease status and 1- good control status. The performance of proposed methods compared with PSO, GA, ACO and ES method. The… More >

Qiubao Ouyang¹, Di Zhang^1,2, Xinhai Zhu³, Zhidong Han³

CMC-Computers, Materials & Continua, Vol.41, No.1, pp. 37-54, 2014, DOI:10.3970/cmc.2014.041.037

Abstract The present work is to investigate the failure mechanisms in the deformation of silicon carbide (SiC) particle reinforced aluminum Metal Matrix Composites (MMCs). To better deal with crack growth, a new numerical approach: the MLPG-Eshelby Method is used. This approach is based on the meshless local weak-forms of the Noether/Eshelby Energy Conservation Laws and it achieves a faster convergent rate and is of good accuracy. In addition, it is much easier for this method to allow material to separate in the material fracture processes, comparing to the conventional popular FEM based method. Based on a statistical method and physical observations,… More >