Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation

• Published in: Latin American Journal of Solids and Structures Vol. 14; no. 6; pp. 1017 - 1039
• Main Authors: Hosseini, Samira, Malekan, Mohammad, Pitangueira, Roque L. S., Silva, Ramon P.
• Format: Journal Article
• Language: English
• Published: Latin American Journal of Solids and Structures 01.06.2017; Associação Brasileira de Ciências Mecânicas; Marcílio Alves
• Subjects: Boundary value problems; EFG-FE Coupling; Element Free Galerkin method; Engineering research; ENGINEERING, CIVIL; ENGINEERING, MECHANICAL; Finite element method; Lagrange Multipliers; MECHANICS; Object-Oriented Programming; Penalty Method; Penalty Method; EFG-FE Coupling; Object-Oriented Programming; Element Free Galerkin method; Lagrange Multipliers
• ISSN: 1679-7825; 1679-7817; 1679-7825
• DOI: 10.1590/1679-78253607

One of the main drawbacks of Element Free Galerkin (EFG) method is its dependence on moving least square shape functions which don't satisfy the Kronecker Delta property, so in this method it's not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.