<abstract xmlns="http://www.w3.org/1999/xhtml"><p> A numerical analysis based on the meshless local Petrov- Galerkin (MLPG) method is proposed for a functionally graded material FGM (FGMfunctionally graded material) beam. The planar bending of the beam is considered with a transversal gradation of Young's modulus and a variable depth of the beam. The collocation formulation is constructed from the equilibrium equations for the mechanical fields. Dirac's delta function is employed as a test function in the derivation of a strong formulation. The Moving Least Squares (MLS) approximation technique is applied for an approximation of the spatial variations of all the physical quantities. An investigation of the accuracy, the convergence of the accuracy, the computational efficiency and the effect of the level of the gradation of Young's modulus on the behaviour of coupled mechanical fields is presented in various boundary value problems for a rectangular beam with a functionally graded Young's modulus.</p></abstract>

A numerical analysis based on the meshless local Petrov- Galerkin (MLPG) method is proposed for a functionally graded material FGM (FGMfunctionally graded material) beam. The planar bending of the beam is considered with a transversal gradation of Young's modulus and a variable depth of the beam. The collocation formulation is constructed from the equilibrium equations for the mechanical fields. Dirac's delta function is employed as a test function in the derivation of a strong formulation. The Moving Least Squares (MLS) approximation technique is applied for an approximation of the spatial variations of all the physical quantities. An investigation of the accuracy, the convergence of the accuracy, the computational efficiency and the effect of the level of the gradation of Young's modulus on the behaviour of coupled mechanical fields is presented in various boundary value problems for a rectangular beam with a functionally graded Young's modulus.

Analysis of Beams with Transversal Gradations of the Young's Modulus and Variable Depths by the Meshless Method

Department of Mechanics, Institute of Constrution and Architecture, Slovak Academy of Sciences, Dúbravská cesta 9, 845 03 Bratislava 45, Slovakia

Slovak Journal of Civil Engineering

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

A numerical analysis based on the meshless local Petrov- Galerkin (MLPG) method is proposed for a functionally graded material FGM (FGMfunctionally graded...

Analysis of Beams with Transversal Gradations of the Young's Modulus and Variable Depths by the Meshless Method

Published Online: Apr 12, 2014

Page range: 23 - 36

DOI: https://doi.org/10.2478/sjce-2014-0004

Keywords
Planar bending, FGM beam, Moving Least Squares approximation scheme, meshless local Petrov -Galerkin (MLPG) method, collocation formulation

© Faculty of Civil Engineering, Slovak University of Technology

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Analysis of Beams with Transversal Gradations of the Young's Modulus and Variable Depths by the Meshless Method

Published Online: Apr 12, 2014

Page range: 23 - 36

DOI: https://doi.org/10.2478/sjce-2014-0004

KeywordsPlanar bending, FGM beam, Moving Least Squares approximation scheme, meshless local Petrov -Galerkin (MLPG) method, collocation formulation

© Faculty of Civil Engineering, Slovak University of Technology

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords
Planar bending, FGM beam, Moving Least Squares approximation scheme, meshless local Petrov -Galerkin (MLPG) method, collocation formulation