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Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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TL;DR: In this article, an approach is introduced to handle the contact between Lagrangian SPH particles and rigid solid boundaries, where boundary contact forces are derived based on a variational formulation, thus directly ensuring the conservativeness of the governing equations.
Abstract: Smooth particle Hydrodynamics (SPH) is one of the most effective meshless techniques used in computational mechanics. SPH approximations are simple and allow greater flexibility in various engineering applications. However, modelling of particle-boundary interactions in SPH computations has always been considered an aspect that requires further research. A number of techniques have been developed to model particle-boundary interactions in SPH and allied methods. In this paper, an innovative approach is introduced to handle the contact between Lagrangian SPH particles and rigid solid boundaries. The formulation of boundary contact forces are derived based on a variational formulation, thus directly ensuring the conservativeness of the governing equations. In addition, the new elegant boundary contact force terms maintain the simplicity of the SPH governing equations.
149 citations
TL;DR: In this paper, a new variational formulation for boundary node method (BNM) using a hybrid displacement functional is presented, which does not require a "boundary element mesh" either for the purpose of interpolation of the solution variables, or for the integration of the energy.
Abstract: A new variational formulation for boundary node method (BNM) using a hybrid displacement functional is presented here. The formulation is expressed in terms of domain and boundary variables, and the domain variables are interpolated by classical fundamental solution; while the boundary variables are interpolated by moving least squares (MLS). The main idea is to retain the dimensionality advantages of the BNM, and get a truly meshless method, which does not require a ‘boundary element mesh’, either for the purpose of interpolation of the solution variables, or for the integration of the ‘energy’. All integrals can be easily evaluated over regular shaped domains (in general, semi-sphere in the 3-D problem) and their boundaries.
Numerical examples presented in this paper for the solution of Laplace's equation in 2-D show that high rates of convergence with mesh refinement are achievable, and the computational results for unknown variables are most accurate. No further integrations are required to compute the unknown variables inside the domain as in the conventional BEM and BNM. Copyright © 2001 John Wiley & Sons, Ltd.
148 citations
TL;DR: In this paper, a radial point interpolation method (radial PIM) is proposed to solve Biot's consolidation problem using meshless method called a radial PIM, which is advantageous over the meshless methods based on moving least-square (MLS) method in implementation of essential boundary condition and over the original PIM with polynomial basis in avoiding singularity when shape functions are constructed.
146 citations
TL;DR: In this article, a face-based smoothed finite element method (FS-FEM) using tetrahedral elements was proposed to improve the accuracy and convergence rate of the existing standard FEM for the solid mechanics problems.
142 citations
TL;DR: This work presents optimizations for both centralprocessing units (CPU) and graphics processing units (GPU) focused on a Lagrangian Smoothed Particle Hydrodynamics (SPH) method and a comparison between the most efficient implementations for CPU and GPU is shown.
140 citations