A new method for essential boundary conditions imposition in explicit meshless methods

被引：14

作者：

Joldes, Grand Roman ^{[1
,2
]}

Chowdhury, Habib ^{[1
]}

Wittek, Adam ^{[1
]}

Miller, Karol ^{[1
,3
]}

机构：

[1] Univ Western Australia, Sch Mech & Chem Engn, Intelligent Syst Med Lab, 35 Stirling Highway, Perth, WA 6009, Australia

[2] Murdoch Univ, Sch Engn & Informat Technol, 90 South St, Perth, WA 6150, Australia

[3] Cardiff Univ, Sch Engn, Cardiff CF24 3AA, S Glam, Wales

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2017年 / 80卷

基金：

澳大利亚研究理事会;

关键词：

Essential boundary conditions; Meshless methods; Explicit time integration; Element free galerkin; Non-interpolating shape functions; MOVING LEAST-SQUARES; FREE GALERKIN METHOD; DYNAMIC RELAXATION; FINITE-ELEMENTS; SIMULATION;

D O I：

10.1016/j.enganabound.2017.03.011

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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.

引用

页码：94 / 104

页数：11

共 50 条

[1] Imposition of essential boundary conditions by displacement constraint equations in meshless methods
Zhang, X
Liu, X
Lu, MW
Chen, Y
[J]. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2001, 17 (03): : 165 - 178
[2] Modified equilibrium on line method for imposition of Neumann boundary conditions in meshless collocation methods
Sadeghirad, A.
Kani, I. Mahmoudzadeh
[J]. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2009, 25 (02): : 147 - 171
[3] Imposition of boundary conditions for elliptic equations in the context of non boundary fitted meshless methods
Fougeron, Gabriel
Aubry, Denis
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2019, 343 : 506 - 529
[4] Implementation of essential boundary conditions in a meshless method
Gavete, L
Benito, JJ
Falcón, S
Ruiz, A
[J]. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2000, 16 (06): : 409 - 421
[5] Imposition of essential boundary conditions in the material point method
Cortis, Michael
Coombs, William
Augarde, Charles
Brown, Michael
Brennan, Andrew
Robinson, Scott
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2018, 113 (01) : 130 - 152
[6] On the imposition of essential boundary conditions in natural neighbour Galerkin methods
Cueto, E
Cegoñino, J
Calvo, B
Doblaré, M
[J]. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2003, 19 (05): : 361 - 376
[7] An augmented Lagrangian approach to essential boundary conditions in meshless methods
Ventura, G
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2002, 53 (04) : 825 - 842
[8] Exact imposition of essential boundary condition and material interface continuity in Galerkin-based meshless methods
Zheng, Hong
Li, Wei
Du, Xiuli
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2017, 110 (07) : 637 - 660
[9] Essential boundary condition enforcement in meshless methods: boundary flux collocation method
Wu, CKC
Plesha, ME
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2002, 53 (03) : 499 - 514
[10] Approximate imposition of boundary conditions in immersed boundary methods
Codina, Ramon
Baiges, Joan
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2009, 80 (11) : 1379 - 1405

← 1 2 3 4 5 →