The Meshless Local Petrov–Galerkin method (MLPG) is one of the popular meshless methods that has been used very successfully to solve several types of boundary value problems since the late nineties. In this paper, using a generalized moving least squares (GMLS) approximation, a new direct MLPG technique, called DMLPG, is presented. Following the principle of meshless methods to express everyth...

The MLPG method is the general basis for several variations of meshless methods presented in recent literature. The interrelation of the various meshless approaches is presented in this paper. Several variations of the meshless interpolation schemes are reviewed also. Recent developments and applications of the MLPG methods are surveyed.

A truly meshless Galerkin method is formulated in the present study, as a special case of the general Meshless Local Petrov-Galerkin (MLPG) “Mixed” approach. The Galerkin method is implemented as a truly meshless method, for solving elasto-static problems. In the present Galerkin method, the test function is chosen to be the same as the trial function, as a special case of the MLPG approach. Ho...

a truly meshless local petrov-galerkin (mlpg) method is developed for solving 3d elasto-static problems. using the general mlpg concept, this method is derived through the local weak forms of the equilibrium equations, by using test functions, namely, the heaviside function. the moving least squares (mls) are chosen to construct the shape functions, for the mlpg method. the penalty approximatio...

The Meshless Finite Volume Method (MFVM) is developed for solving elasto-static problems, through a new Meshless Local Petrov-Galerkin (MLPG) “Mixed” approach. In this MLPG mixed approach, both the strains as well as displacements are interpolated, at randomly distributed points in the domain, through local meshless interpolation schemes such as the moving least squares(MLS) or radial basis fun...

The Finite Difference Method (FDM), within the framework of the Meshless Local PetrovGalerkin (MLPG) approach, is proposed in this paper for solving solid mechanics problems. A “mixed” interpolation scheme is adopted in the present implementation: the displacements, displacement gradients, and stresses are interpolated independently using identical MLS shape functions. The system of algebraic e...

A Meshless Local Petrov-Galerkin (MLPG) method has been developed for solving 3D elastodynamic problems. It is derived from the local weak form of the equilibrium equations by using the general MLPG concept. By incorporating the moving least squares (MLS) approximations for trial and test functions, the local weak form is discretized, and is integrated over the local sub-domain for the transien...

We analyze plane strain static thermoelastic deformations of a simply supported functionally graded (FG) plate by a meshless local Petrov–Galerkin (MLPG) method. Material moduli are assumed to vary only in the thickness direction. The plate material is made of two isotropic randomly distributed constituents and the macroscopic response is also modeled as isotropic. Displacements and stresses co...

The essential features of the Meshless Local Petrov-Galerkin (MLPG) method, and of the Local Boundary Integral Equation (LBIE) method, are critically examined from the points of view of a non-element interpolation of the ®eld variables, and of the meshless numerical integration of the weak form to generate the stiffness matrix. As truly meshless methods, the MLPG and the LBIE methods hold a gre...