Conjunction of Displacement Fields of the Element Free Galerkin Method and Finite Element Method

A principle weakness of the element free Galerkin method, a method widely discussed over the past decade, has been its computation efficiency. This paper describes a new simple and efficient method that overcomes this weakness by combining together the finite element and element free Galerkin methods. No transmission zones are required in this new method. The new method introduced differs from methods such as Lagrange multipliers or the penalty method in that so-called "virtual particles" are defined to approach the compatibility between two displacement fields. Virtual particles are derived from the finite element formulation and used as the particles in the element free Galerkin formulation.