Journal ArticleDOI
A modified meshless local Petrov-Galerkin method to elasticity problems in computer modeling and simulation
TLDR
In this article, a modified meshless local Petrov-Galerkin (MLPG) method is presented for elasticity problems using the moving least squares (MLS) approximation, which does not need a mesh for the interpolation of the solution variables or for the integration of the energy.Abstract:
A modified meshless local Petrov–Galerkin (MLPG) method is presented for elasticity problems using the moving least squares (MLS) approximation. It is a truly meshless method because it does not need a mesh for the interpolation of the solution variables or for the integration of the energy. In this paper, a simple Heaviside test function is chosen to overcome the computationally expensive problems in the MLPG method. Essential boundary conditions are imposed by using a direct interpolation method based on the MLPG method establishes equations node by node. Numerical results in several examples show that the present method yielded very accurate solutions. And the sensitivity of the method to several parameters is also studied in this paper.read more
Citations
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Journal ArticleDOI
Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
Mehdi Dehghan,Arezou Ghesmati +1 more
TL;DR: The meshless local radial point interpolation method (LRPIM) is adopted to simulate the two-dimensional nonlinear sine-Gordon (S-G) equation and a simple predictor–corrector scheme is performed to eliminate the nonlinearity.
Journal ArticleDOI
Meshless Local Petrov--Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
Mehdi Dehghan,Davoud Mirzaei +1 more
TL;DR: In this paper, a meshless local Petrov-Galerkin (MLPG) method is given to obtain the numerical solution of the coupled equations in velocity and magnetic field for unsteady magnetohydrodynamic (MHD) flow through a pipe of rectangular section having arbitrary conducting walls.
Journal ArticleDOI
Combination of meshless local weak and strong (MLWS) forms to solve the two dimensional hyperbolic telegraph equation
Mehdi Dehghan,Arezou Ghesmati +1 more
TL;DR: In this article, a meshless local weak-strong (MLWS) method is proposed to solve the second-order two-space-dimensional telegraph equation, which combines the advantage of local weak and strong forms to avoid their shortcomings.
Journal ArticleDOI
Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping
TL;DR: The unconditional stability and convergence with order O ( ? 6 - 2 α ) are proved, where ? is time stepping and the MLRPI scheme based on Galerkin weak form is analyzed.
Journal ArticleDOI
The meshless local Petrov–Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrödinger equation
Mehdi Dehghan,Davoud Mirzaei +1 more
TL;DR: In this paper, the meshless local Petrov-Galerkin (MLPG) method is presented for numerical solution of the two-dimensional non-linear Schrodinger equation, which is based on the local weak form and the moving least squares (MLS) approximation.
References
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Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
Journal ArticleDOI
A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
Satya N. Atluri,T. Zhu +1 more
TL;DR: In this article, a local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy.
Journal ArticleDOI
Generalizing the finite element method: Diffuse approximation and diffuse elements
TL;DR: The diffuse element method (DEM) as discussed by the authors is a generalization of the finite element approximation (FEM) method, which is used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives.
Journal ArticleDOI
The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods
Satya N. Atluri,Shengping Shen +1 more
TL;DR: In this paper, a comparison study of the efficiency and ac- curacy of a variety of meshless trial and test functions is presented, based on the general concept of the meshless local Petrov-Galerkin (MLPG) method.
Book
Elasticity : theory and applications
TL;DR: In this paper, the concept of tensor and its associated notations is introduced for training in advanced elasticity, plasticity, fracture, elastic stability, plates and shells, with emphasis placed on geometry.
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