Soleiman Ghouhestani¹, Farzad Shahabian¹, Seyed Mahmoud Hosseini^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.4, pp. 295-321, 2014, DOI:10.3970/cmes.2014.100.295

Abstract In this paper, the meshless local Petrov-Galerkin (MLPG) method is exploited for dynamic analysis of functionally graded nanocomposite cylindrical layered structure reinforced by carbon nanotube subjected to mechanical shock loading. The carbon nanotubes (CNTs) are distributed across radial direction on thickness of cylinder, which can be simulated by linear and nonlinear volume fraction. Free vibration and elastic wave propagation are studied for various value of volume fraction exponent at various time intervals. The layered cylinder is assumed to be under axisymmetric and plane strain conditions. Four types of CNTs distributions including uniform and three kinds of functionally graded distributions along… More >

L. Godinho¹, D. Dias-da-Costa²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 293-316, 2013, DOI:10.3970/cmes.2013.096.293

Abstract Transient heat conduction problems can be dealt with using different numerical approaches. In some recent papers, a strategy to tackle these problems using a frequency domain formulation has been presented and successfully applied associated to methods such as the BEM. Here a formulation of the meshless local Petrov-Galerkin (MLPG) is developed and presented to allow the analysis of such problems. The proposed formulation makes use of the RBF-based version of the MLPG and employs the Heaviside step function as the test function, leading to the so-called MLPG(5). In addition, the method is associated with a visibility criterion to allow the… More >

L. Sun¹, G. Yang², Q. Zhang³

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 235-258, 2013, DOI:10.3970/cmes.2013.095.234

Abstract We propose numerical integration rules for meshless local Petrov- Galerkin methods (MLPG) employed to solve elliptic partial different equations (PDE) with Neumann boundary conditions. The integration rules are required to satisfy an integration constraint condition of Green’s formula type (GIC). GIC was first developed in [Babuska, Banerjee, Osborn, and Zhang (2009)] for Galerkin meshless method, and we will show in this paper that it has better features for MLPG due to flexibility of MLPG in choosing different trial and test function spaces. A general constructive algorithm is presented to design the integration rules satisfying GIC. We also present a useful… More >

Tao Zhang^1,2, Leiting Dong^2,3, Abdullah Alotaibi⁴, Satya N. Atluri^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 1-28, 2013, DOI:10.3970/cmes.2013.094.001

Abstract In this paper, a novel Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed for solving the inverse Cauchy problem of linear elasticity, wherein both the tractions as well as displacements are prescribed/measured at a small portion of the boundary of an elastic body. The elastic body may be isotropic/anisotropic and simply connected or multiply-connected. In the MLPG mixed collocation method, the same meshless basis function is used to interpolate both the displacement as well as the stress fields. The nodal stresses are expressed in terms of nodal displacements by enforcing the constitutive relation between stress and the displacement gradient… More >

A. Tadeu¹, P. Stanak², J. Sladek², V. Sladek², J. Prata¹, N. Simões¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.6, pp. 489-516, 2013, DOI:10.3970/cmes.2013.093.489

Abstract This paper presents a technique that couples the boundary element method (BEM) with the meshless local Petrov-Galerkin (MLPG) method, formulated in the frequency domain. It is then used to study the transient heat diffusion through a two-dimensional unbounded medium containing confined subdomains where the material properties vary from point to point. To exploit the advantages of each method, the BEM is used for the homogeneous unbounded domain and the MLPG method is used for the non-homogeneous confined subdomains. The nodal points placed at the interface between the confined subdomains and the unbounded homogenous medium are used to couple the BEM… More >

J. Sladek¹, P. Stanak¹, Z-D. Han², V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 423-475, 2013, DOI:10.3970/cmes.2013.092.423

Abstract A review is presented for analysis of problems in engineering & the sciences, with the use of the meshless local Petrov-Galerkin (MLPG) method. The success of the meshless methods lie in the local nature, as well as higher order continuity, of the trial function approximations, high adaptivity and a low cost to prepare input data for numerical analyses, since the creation of a finite element mesh is not required. There is a broad variety of meshless methods available today; however the focus is placed on the MLPG method, in this paper. The MLPG method is a fundamental base for the… More >

V. C. Loukopoulos¹, G. C. Bourantas²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 531-558, 2012, DOI:10.3970/cmes.2012.088.531

Abstract Meshless Local Petrov-Galerkin (MLPG) approach is used for the solution of the Navier-Stokes and energy equations. More specific as a special case we apply the MLPG6 approach. In the MLPG6 method, the test function is chosen to be the same as the trial function (Galerkin method). The MLPG local weak form is written over a local sub-domain which is completely independent from the trial or test functions. The sizes of nodal trial and test function domains, as well as the size of the local sub-domain over which the local weak-form is considered, can be arbitrary. This may lead to either… More >

Annamaria Mazzia¹, Giorgio Pini¹, Flavio Sartoretto²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.3, pp. 183-210, 2012, DOI:10.3970/cmes.2012.088.183

Abstract Pure meshless techniques are promising methods for solving Partial Differential Equations (PDE). They alleviate difficulties both in designing discretization meshes, and in refining/coarsening, a task which is demanded e.g. in adaptive strategies. Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques that receive increasing attention. Very recently, new methods, called Direct MLPG (DMLPG), have been proposed. They rely upon approximating PDE via the Generalized Moving Least Square method. DMLPG methods alleviate some difficulties of MLPG, e.g. numerical integration of tricky, non-polynomial factors, in weak forms. DMLPG techniques require lower computational costs respect to their MLPG counterparts. In this paper… More >

A. Arefmanesh¹, M. Najafi², M. Nikfar³

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.2, pp. 91-118, 2010, DOI:10.3970/cmes.2010.069.091

Abstract Procuring a numerical solution through an application of the meshless local Petrov-Galerkin method (MLPG) on the fluid flow and mixed convection in a complex geometry cavity filled with a nanofluid is the scope of the present study. The cavity considered is a square enclosure having a lower temperature sliding lid at the top, a differentially higher temperature wavy wall at the bottom, and two thermally insulated walls on the sides. The nanofluid medium used is a water-based nanofluid, Al₂O₃-water with various volume fractions of its solid. To carry out the numerical simulations, the developed governing equations are determined in terms… More >

Meiling Zhao¹, Yufeng Nie²

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 97-112, 2008, DOI:10.3970/cmes.2008.037.097

Abstract Meshless local Petrov-Galerkin (MLPG) method is successfully applied for electromagnetic field computations. The moving least square technique is used to interpolate the trial and test functions. More attention is paid to imposing the essential boundary conditions of electromagnetic equations. A new coupled meshless local Petrov-Galerkin and finite element (MLPG-FE) method is presented to enforce the essential boundary conditions. Unlike the conventional coupled technique, this approach can ensure the smooth blending of the potential variables as well as their derivatives in the transition region between the meshless and finite element domains. Then the boundary singular weight method is proposed to enforce… More >