A new method for essential boundary conditions imposition in explicit meshless methods. (July 2017)

• Record Type: Journal Article
• Authors: Joldes, Grand Roman; Chowdhury, Habib; Wittek, Adam; Miller, Karol
• Is Part Of: Engineering analysis with boundary elements. Volume 80(2017)
• Page Start: 94
• Page End: 104
• Publication Date: 2017-07
• Subjects: Essential boundary conditions -- Meshless methods -- Explicit time integration -- Element free galerkin -- Non-interpolating shape functions; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2017.03.011
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper we present a new technique of enforcing Essential Boundary Conditions (EBC) in Meshless Methods (MMs) based on the Element Free Galerkin (EFG) principles. Imposing EBC is a fundamental issue in MMs. The imposition of prescribed displacement values on the boundary in MMs based on approximating shape functions is not as straightforward as in the Finite Element Method (FEM) because the meshless shape functions are generally not interpolating at nodes. Furthermore, many techniques of enforcing EBC are not compatible with explicit time integration schemes. This paper describes a new method of imposing EBC in EFG based MMs suitable for explicit time integration, named Essential Boundary Conditions Imposition in Explicit Meshless (EBCIEM). The effectiveness of the proposed method is demonstrated using both 2D and 3D numerical examples.