Reproducing kernel particle methods for structural dynamics

Keywords

Kernel (algebra), Smoothed-particle hydrodynamics, Interpolation (computer graphics), Instability, Range (aeronautics)

References

• An Introduction to WaveletsLee Barford, R. Shane Fazzio, David R. Smith — 1992
• High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material responseLarry D. Libersky, A. G. Petschek, Theodore C. Carney — 1993
• Wavelet and multiple scale reproducing kernel methodsWing Kam Liu, Yi-Jung Chen — 1995
• Surfaces generated by moving least squares methodsPeter Lancaster, K. Šalkauskas — 1981
• Implicit-Explicit Finite Elements in Transient Analysis: Stability TheoryThomas J.R. Hughes, W. K. Liu — 1978
• Fracture and crack growth by element free Galerkin methodsTed Belytschko, Linxia Gu, Ye Lu — 1994
• An introduction to SPHJ. J. Monaghan — 1987
• Generalizing the finite element method: Diffuse approximation and diffuse elementsBernard Nayroles, Gilbert Touzot, Pierre Villon — 1992
• Physical stabilization of the 4-node shell element with one point quadratureTed Belytschko, Itai Leviathan — 1994
• Why Particle Methods WorkJoe J. Monaghan — 1982
• A new implementation of the element free Galerkin methodYe Lu, Ted Belytschko, Linxia Gu — 1994
• Element‐free Galerkin methodsTed Belytschko, Ye Lu, Linxia Gu — 1994
• Multiple scale finite element methodsWing Kam Liu, Yan Zhang, Martin R. Ramirez — 1991
• Smoothed particle hydrodynamics: Theory and application to non-spherical starsR. A. Gingold, J. J. Monaghan — 1977
• Reproducing kernel and wavelet particle methodsWing Kam Liu, Claus Oberste‐Brandenburg — 1993
• Ten lectures on wavelets Contains lectures delivered at the CBMS conference organized in June 1990 by the Mathematics Dept. at the University of Lowell, MassIngrid Daubechies — 1992
• IMPLICIT-EXPLICIT FINITE ELEMENTS IN TRANSIENT ANALYSIST. Hughes, Wing Kam Liu — 1978
• Smooth particle hydrodynamics with strength of materialsL. Libersky, A. Petschek — 1991

Cited by

• Simulation du soudage par friction et malaxage à l'aide de méthodes sans maillageAbdelaziz Timesli — 2013
• Filters, reproducing kernel, and adaptive meshfree methodYang You, J.-S. Chen, Hongjing Lu — 2003
• The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid MechanicsN. Sunilkumar, Debasish Roy — 2010
• A Metal Forming Analysis by Using the Hybrid PCM/FEMYongming Guo — 2009
• ANALYSIS OF A MESHFREE METHOD FOR THE COMPRESSIBLE EULER EQUATIONSYongsik Kim, Dae-Hyeon Pahk — 2006
• Application of the Generalized Finite Difference Method to improve the approximated solution of pdesJuan José Benito, Francisco Ureña, L. Gavete — 2008
• The development of a generalized meshfree approximation for solid and fracture analysisChung-Kyu Park — 2009
• A NURBS-based Parametric Method Bridging Mesh-free and Finite Element FormulationsAmit Shaw, B. Banerjee, Debasish Roy — 2008
• Approximation with harmonic and generalized harmonic polynomials in the partition of unity methodJens Markus Melenk, Ivo Babuška — 1997
• Solution of Nonlinear Transient Heat Transfer ProblemsDonovan O Buckley — 2010
• Point Set Surfaces with Sharp FeaturesPatrick Reuter, Pierre Joyot, Jean Trunzler — 2005
• A Modified Method of Fundamental Solutions with Source on the Boundary for Solving Laplace Equations with Circular and Arbitrary DomainsD.L. Young, K. H. Chen, Jeng‐Tzong Chen — 2007
• Least squares moving particle semi-implicit methodT. Tamai, Seiichi Koshizuka — 2014
• Simulations of Blood Drop Spreading and Impact forBloodstain Pattern AnalysisChu Wang, Lucy T. Zhang — 2014
• Classification and Overview of Meshfree MethodsThomas‐Peter Fries, Hermann G. Matthies — 2004
• SPH in a Total Lagrangian FormalismRade Vignjević, Juan Reveles, J. Campbell — 2006
• Regularized Meshless Method for Solving Acoustic Eigenproblem with Multiply-Connected DomainK.H. Chen, Jeng‐Tzong Chen, Jui-Hsiang Kao — 2006
• The Finite Point Method for Reaction-Diffusion Systems in Developmental BiologyMehdi Tatari, Maryam Kamranian, Mehdi Dehghan — 2011
• On Interpolation in SPHRade Vignjević, Tom De Vuyst, Mustapha Gourma — 2001
• Meshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds NumberGeorge C. Bourantas, Eugene D. Skouras, Vasilios Loukopoulos — 2010

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