Review: Meshless methods: A review and computer implementation aspects

Authors:
Vinh Phu Nguyen;Timon Rabczuk;Stéphane Bordas;Marc Duflot
Affiliations:
Ecole Nationale d'Ingénieur de Saint Etienne (ENISE), Laboratoire de Tribologie et Dynamique des Systèmes (LTDS), France;University of Canterbury, Department of Mechanical Engineering, 4800 Private Bag, Christchurch, New Zealand;University of Glasgow, Civil Engineering, Rankine Building, Glasgow G12 8LT, UK;CENAERO, Rue des Frères Wright 29, 6041 Gosselies, BELGIUM
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our discourse. The source code is available for download on our website and should help students and researchers get started with some of the basic meshless methods; it includes intrinsic and extrinsic enrichment, point collocation methods, several boundary condition enforcement schemes and corresponding test cases. Several one and two-dimensional examples in elastostatics are given including weak and strong discontinuities and testing different ways of enforcing essential boundary conditions.