Introduction of Meshfree Methods and Implementation of Element Free Galerkin (EFG) Method to Beam Problem

Numerical simulation using computers has increasingly become a very important approach for solving problems in engineering and science. It plays a valuable role in providing tests and examinations for theories, offering insights to complex physics, and assisting in the interpretation and even the discovery of new phenomena. Grid or mesh based numerical methods such as FDM, CFD, FEM despite of great success, suffer from difficulties in some aspects, which limit their applications in many complex problems. The major difficulties are inherited from the use of grid or mesh. A recent strong interest is focused on the next generation computational methods — meshfree methods, which are expected to be superior to conventional grid-based FDM and FEM in many applications. The Element Free Galerkin (EFG) method is a meshless method because only a set of nodes and a description of model’s boundary are required to generate the discrete equations. In this paper the EFG method is applied to 2-D beam problem and results are compared with the analytical solution by using Timoshenko Beam Theory. The step by step algorithm for EFG MATLAB program is also provided inside.