Meshless methods: A review and computer implementation aspects
By Vinh Phu Nguyen, Timon Rabczuk, Stéphane P.A. Bordas, Marc Duflot. Mathematics and Computers in Simulation, 2008
1,275 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/72dd7e711b555e2fcb3d933c5596d873d655f474
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Stéphane P.A. Bordas
- Hung Nguyen-Xuan
- Timon Rabczuk
- Trung Nguyen-Thoi
- Xiaoying Zhuang
- Guirong Liu
- E. Ooi
- Charles E. Augarde
In Mechanics of Materials
- Timon Rabczuk
- Stéphane P.A. Bordas
- Trung Nguyen-Thoi
- Hung Nguyen-Xuan
- Guirong Liu
- Xiaoying Zhuang
- Sundararajan Natarajan
- E. Ooi
Citations in the corpus
- Orthotropic enriched element free Galerkin method for fracture analysis of composites (2011, background): “One drawback of the intrinsic enrichment is that it usually used in the entire domain; otherwise, undesired discontinuities may be introduced at the interface of enriched and regular domains [19].”
- Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “Since the inception of smoothed particle hydrodynamics [1], a wide variety of meshless (or meshfree) methods [2, 3] have been proposed, as outlined in recent surveys [4, 5].”
- Particle dynamics modeling methods for colloid suspensions (2014, methodology): “We also exclude particle-based continuum treatments of the solvent (sometimes referred to as “meshless methods” [13,161]), such as smoothed particle hydrodynamics (SPH) [82,159], the element-free Galerkin method (EFGM) [12,73], the reproducing kernel particle method (RKPM) [137,138] or the finite po”