Meshfree and particle methods and their applications

2002/01/01 by Shaofan Li, Wing Kam Liu · 836 citations
Engineering · Mathematics · #Boundary value problem #Classical mechanics #Collocation (remote sensing) #Compressibility #Computer science #Engineering #Finite element method #Fluid Dynamics Simulations and Interactions #Galerkin method #Geology #Geotechnical Engineering and Underground Structures #Kernel (algebra) #Mathematical analysis #Mathematics #Mechanics #Meshfree methods #Numerical methods in engineering #Particle (ecology) #Particle method #Physics #Smoothed-particle hydrodynamics #Structural engineering

paper · doi:10.1115/1.1431547

published in Applied Mechanics Reviews 55(1), 1-34 (American Society of Mechanical Engineers)

openalex publication_date 2002/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics (SPH) is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics (MD) in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references.

Citations

• Zur Quantentheorie der Molekeln

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