We analyze transient heat conduction in a thick functionally graded plate by using a higher-order plate theory and a meshless local Petrov-Galerkin (MLPG) method. The temperature field is expanded in the thickness direction by using Legendre polynomials as basis functions. For temperature prescribed on one or both major surfaces of the plate, modified Lagrange polynomials are used as basis and ...

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 ...

Discussed is here the multipoint meshless finite difference method (MMFDM) following the original Collatz [2] multipoint concept, and the essential ideas of the meshless FDM [3]. The Collatz approach was based on interpolation, regular meshes and the local formulation of b.v. problems. On the other hand in the MFDM we deal with the moving weighted least squares (MWLS) approximation, arbitrarily...

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 Meshless Local Petrov Galerkin (MLPG) method is used to solve the non-steady two dimensional Navier-Stokes equations. Transient laminar flow field calculations have been carried out in domains wherein certain surfaces have: (i) a sliding motion, (ii) a harmonic motion, (iii) an undulatory movement, and (iv) a contraction-expansion movement. The weak form of the governing equations has been ...

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...

In this paper, the conventional moving least squares interpolation scheme is generalized, to incorporate the information concerning the derivative of the ®eld variable into the interpolation scheme. By using this generalized moving least squares interpolation, along with the MLPG (Meshless Local Petrov±Galerkin) paradigm, a new numerical approach is proposed to deal with 4th order problems of t...

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...

In this paper the meshless local Petrov-Galerkin (MLPG) method is implemented to study the buckling of isotropic cylindrical shells under axial load. Displacement field equations, based on Donnell and first order shear deformation theory, are taken into consideration. The set of governing equations of motion are numerically solved by the MLPG method in which according to a semi-inverse method, ...