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 a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose ...

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 impac...

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 i...

In [4] we put in relation graphs with Dilworth number at most two and the two classes LPG and mLPG. In order to prove this relation, we have heavily exploited a result we deduced from [1]. We have now realized that this result is not always true, so in this corrigendum we correctly restate the result concerning the relation between graphs with Dilworth number at most two and the two classes of ...

This paper reviews the developments and applications of meshfree method based on MLPG (Meshless Local Petrov Galerkin) in ocean engineering, primarily from work carried out at IIT Madras City, University London, UK. Apart discussing various stages model development, this will also reports its to small amplitude waves, wave overtopping breaking, porous layers, long run-up, vegetation, floating b...

The spread of different material processing technologies has led to the novel methods developed for reinforcing structural members. One these approaches is add carbon nanotubes (CNTs) with distributions through matrix phase composite materials improve its properties. Due superior properties such as lightweight and high values elastic modulus, strain, failure CNTs can be used reinforce structure...

Large deformations of rubber-like materials are analyzed by the meshless local Petrov–Galerkin (MLPG) method. The method does not require shadow elements or a background mesh and therefore avoids mesh distortion difficulties in large deformation problems. Basis functions for approximating the trial solution and test functions are generated by the moving least-squares (MLS) method. A local mixed...

A graph G is called a pairwise compatibility graph (PCG) if there exists an edge weighted tree T and two non-negative real numbers dmin and dmax such that each leaf lu of T corresponds to a vertex u ∈ V and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (lu, lv) ≤ dmax where dT (lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T . In this paper we analyze...

Abstract The complicated behavior of groundwater system in an arid aquifer is generally studied by solving the governing equations using either analytical or numerical methods. In this regard, methods are just for some aquifers with regular boundaries. Numerical used aim finite difference (FDM) and element (FEM) which engaged simple aquifers. Using them complex cases irregular boundaries has sh...

The two dimensional steady state Stokes equations are solved by using a novel MLPG-Mixed Finite Volume method, that is based on the independent meshless interpolations of the deviatoric velocity strain tensor, the volumetric velocity strain tensor, the velocity vector and the pressure. The pressure field directly obtained from this method does not suffer from the malady of checker-board pattern...