Stress Analysis of beams and plates using the Element Free Galerkin Method

Abstract

The project has dealt with the study of beams and thin plates under plane stress using the mesh-less technique, ELEMENT FREE GALERKIN METHOD. This involves a detailed study of the Element Free Galerkin Method consisting of its formulation, mode of application, its advantages and disadvantages along with a brief study of the analysis of thin plates. A MATLAB code was written for the analysis of a Timoshenko Beam Problem using EFGM, so that the logic and modus operandi of the method may be fully understood. Several cases of plane stress were considered in the project such as cantilever beams subjected to point loads and uniformly distributed loads, and plates with varying geometries and boundary conditions using MFree2D simulation package. The major aims of this project were twofold. Firstly, to check the accuracy of the Element Free Galerkin Method by means of comparison with the exact theoretical values and secondly to solve certain typical problems related to plates by the Element Free Galerkin Method.