Moving particle finite element method

This paper presents the fundamental concepts behind the moving particle finite element method, which combines salient features of finite element and meshfree methods. The proposed method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the method in benchmark problems. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[2]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[3]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

[4]  Gregory J. Wagner,et al.  Hierarchical enrichment for bridging scales and mesh-free boundary conditions , 2001 .

[5]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[6]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[7]  T. Belytschko,et al.  THE NATURAL ELEMENT METHOD IN SOLID MECHANICS , 1998 .

[8]  Wing Kam Liu,et al.  Numerical simulations of strain localization in inelastic solids using mesh‐free methods , 2000 .

[9]  Pedro Díez,et al.  Convergence of finite elements enriched with mesh-less methods , 2003, Numerische Mathematik.

[10]  Hui-Ping Wang,et al.  A Lagrangian reproducing kernel particle method for metal forming analysis , 1998 .

[11]  I. Babuska,et al.  The design and analysis of the Generalized Finite Element Method , 2000 .

[12]  B.,et al.  Natural Neighbor Galerkin Methods , 2001 .

[13]  L. Libersky,et al.  Smoothed Particle Hydrodynamics: Some recent improvements and applications , 1996 .

[14]  J. C. Simo,et al.  On the Variational Foundations of Assumed Strain Methods , 1986 .

[15]  Gregory J. Wagner,et al.  Application of essential boundary conditions in mesh-free methods: a corrected collocation method , 2000 .

[16]  Jaromír Slavík,et al.  COMPUTATIONAL MECHANICS I , 2004 .

[17]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[18]  S. Attaway,et al.  Smoothed particle hydrodynamics stability analysis , 1995 .

[19]  Wing Kam Liu,et al.  Wavelet and multiple scale reproducing kernel methods , 1995 .

[20]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[21]  Satya N. Atluri,et al.  The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics , 2000 .

[22]  Antonio Huerta,et al.  Enrichment and coupling of the finite element and meshless methods , 2000 .

[23]  B. Moran,et al.  Natural neighbour Galerkin methods , 2001 .

[24]  Mark A Fleming,et al.  Smoothing and accelerated computations in the element free Galerkin method , 1996 .

[25]  John H. Argyris,et al.  Computer Methods in Applied Mechanics and Engineering , 1990 .

[26]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[27]  Wing Kam Liu,et al.  Reproducing kernel particle methods for structural dynamics , 1995 .

[28]  Genki Yagawa,et al.  Recent developments of free mesh method , 2000 .

[29]  Shaofan Li,et al.  Reproducing kernel hierarchical partition of unity, Part II—applications , 1999 .

[30]  O. C. Zienkiewicz,et al.  A new cloud-based hp finite element method , 1998 .

[31]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[32]  Eugenio Oñate,et al.  Announcement ?Meshfree Methods? , 2000 .

[33]  T. Belytschko,et al.  Nodal integration of the element-free Galerkin method , 1996 .

[34]  Wing Kam Liu,et al.  Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures , 1996 .

[35]  Genki Yagawa,et al.  Quadrilateral approaches for accurate free mesh method , 2000 .

[36]  Sivakumar Kulasegaram,et al.  Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations , 2000 .

[37]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .