Overview and applications of the reproducing Kernel Particle methods

Archives of Computational Methods in Engineering - Tập 3 Số 1 - Trang 3-80 - 1996
W. K. Liu1, Y. Chen1, Sukky Jun1, J. S. Chen1, Ted Belytschko1, Chunhui Pan1, R. A. Uras1, C. T. Chang1
1Professor of Mechanical and Civil Engineering, Post-doctoral Fellow, Graduate Student, Assistant Professor, Walter P. Murphy Professor of Computational Mechanics, Granduate Student, Engineer, Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, 60208, Evanston, Illinois

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Amsden, A.A. and Harlow, F.H. (1970), “The SMAC Method, A Numerical Technique for Calculating Incompressible Fluid Flow”, Tech. Report LA-4370, Los Alamos Scientific Laboratory.

Babuska, I. and Melenk, J.M. (1995), “The Partition of Unity Finite Element Method”, Univ. of Maryland, Technical Note BN-1185.

Babuška, I. (1973), “The Finite Element Method with Lagrangian Multiplies,”Num. Math.,20, pp. 179–192.

Beklkin, G.R., Coifman, I., Daubechies, S., Mallat, Y., Meyer, L., Raphael, and Ruskai, B. (eds) (1992), “Wavelets and Their Applications”, Cambridge, MA.

Belytschko, T. (1994), “Are Finite Elements Passé?”,USACM Bulletin,7, 3, pp. 4–7.

Belytschko, T., Gu, L. and Lu, Y.Y. (1994a), “Fracture and Crack Growth by EFG Methods,”Modelling Simul. Mater. Sci. Eng.,2, pp. 519–534.

Belytschko, T., Lu, Y.Y. and Gu, L. (1994b), “Element Free Galerkin Methods”,International Journal for Numerical Methods in Engineering,37, pp. 229–256

Belytschko, T., Lu, Y.Y. and Gu, L. (1994c), “A New Implementation of the Element Free Galerkin Method”,Computer Methods in Applied Mechanics and Engineering 113, pp. 397–414.

Belytschko, T. (1983), “An Overview of Semidiscretization and Time Integration Procedures”, eds. Belytschko, T. and Hughes, T.J.R.,Computational Methods for Transient Analysis, North-Holland, Amsterdam, pp. 1–63.

Belytschko, T. and Kennedy, J.M. (1978), “Computer Methods for Subassembly Simulation,”Nuclear Engrg. Des.,49, pp. 17–38.

Brezzi, F. (1974), “On the Existance, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrange Multipliers”,R. A. I. R. O.,8-R2, pp. 129–151.

Chen, J.S. and Pan, C. (1995), “A Pressure Projection Method for Nearly Incompressible Rubber Hyperelasticity, Part I: Theory”, accepted byJournal of Applied Mechanics.

Chen, J.S., Pan, C. and Chang, T.Y.P. (1995b), “On The Control of Pressure Oscillation in Bilinear-Displacement Constant-Pressure Element”,Comput. Meth. Appl. Mech. Engng., in press.

Chen, J.S., Wu, C.T. and Pan, C. (1995c), “A Pressure Projection Method for Nearly Incompressible Rubber Hyperlasticity, Part II: Applications”, accepted by Journal of Applied Mechanics.

Chen, J.S., Han, H., Wu, C.T. and Duan, W. (1995d), “On the Perturbed Lagrangian Formulation for Nearly Compressible and Incompressible Hyperelasticity”, submitted toComputer Methods in Applied Mechanics and Engineering.

Chen, J.S., Satyamurthy, K.S. and Hirschfelt, L.R. (1994), “Consistent Finite Element Procedures for Nonlinear Rubber Elasticity with a Higher Order Strain Energy Function”,Comput. & Struct.,50, pp.715–727.

Chui, C.K. (1992), “An Introduction to Wavelets”, Academic Press.

Daubechies (1992), “Ten Lectures on Wavelets”,CBMS/NSF Series in Applied Mathematics,61, SIAM Publication.

Duarte, C.A. and Oden, J.T. (1995), “Hp Clouds— A Meshless Method to Solve Boundary-Value Problems”,TICAM Report 95-05.

Dym, C.L. and Shames, I.H. (1973), “Solid Mechanics: A Variational Approach”, McGraw-Hill, Inc.

Gent, A.N. and Lindley, P.B. (1959), “The Compression of Bonded Rubber Blocks”,Proc. Inst. Mech. Engrs.,173, pp. 11–122.

Glowinski, R., Lawton, W.M., Ravachol, M. and Tenenbaum, E. (1990), “Wavelets solution of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension”. Glowinski, R. and Lichnewsky, A. eds.,Computing Methods in Applied Sciences and Engineering, SIAM, Philadelphia, pp. 55–120.

Gingold, R.A. and Monaghan, J.J. (1982), “Kernel Estimates as a Basis for General Particle Methods in Hydrodynamics”,J. Comp. Phys.,46, pp. 429–453.

Gingold, R.A. and Monaghan, J.J. (1977), “Smoothed Particle Bydrodynamics: Theory and Application to Non-Spherical Stars”,Mon. Not. Roy. Astron. Soc.,181, pp. 375–389.

Grossmann, A. and Morlet, J. (1984), “Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape”,SIAM J. Math.,15, pp. 723–736.

Haar, A. (1910), “Zur Theorie dr orthogonalen Funktionsysteme”,Math. Ann.,69, pp. 331–371.

Harlow, F.H., Amsden, A.A. and Nix, J.R. (1976), “Relativistic Fluid Dynamics Calculation with Particle-in-Cell Technique”,J. Comput. Phys.,20.

Harlow, F.H., and Welch, J.E. (1965), “Numberical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface”,The Physics of Fluids,8, pp. 2182–2189.

Hirt, C.W. (1983), “Flow Analysis for Non-Experts”,Engineering Foundation Conference Proceedings, Modeling and Control of Casting and Welding Processes II.

Hirt, C.W. (1975), “SOLA-A Numerical Solution Algorithm for Transient Fluid Flows”, Los Alamos Scientific Laboratory Report LA-5852.

Huerta, A. and Liu, W.K. (1988), “Viscous Flow with Large Free Surface Motion”,Computer Methods in Applied Mechanics and Engineering,69, pp. 277–324.

Hughes, T.J.R., Liu, W.K. and Zimmerman, T.K. (1981), “Lagrangian-Eulerian Finite Element Formulations for Incompressible Viscous Flows”,Computer Methods in Applied Mechanics and Engineering,29, pp. 329–349.

Hughes, T.J.R. (1987), “The Finite Element Method”, Prentice-Hall.

Hughes, T.J.R. (1980), “Generalization of Selective Integration Procedures to Anisotropic and Nonlinear Medium”,Int. J. Numer. Mech. Engng.,15, pp. 141–1418.

Johnson, G.R., Peterson, E.H. and Stryrk, R.A. (1993), “Incorporation of an SPH Option into the EPIC code for a Wide Range of High Velocity Impact Computations”, preprint.

Lancaster, P. and Salkauskas, K. (1981), “Surfaces Generated by Moving Least Squares Methods.”Mathematics of Computation,37, pp. 141–158.

Libersky, L. and Petchek, A.G. (1990), “Smooth Particle Hydrodynamics with Strength of Materials”,Proceedings of The next Free-Lagrange Conference, Jackson Lake Lodge, Moran, Wyoming, June 3–7.

Liu, W.K. (1995), “An Introduction to Wavelet Reproducing Kernel Particle Methods”,USACM Bulletin,8, 1, pp. 3–16.

Liu, W.K. and Chen, Y. (1995), “Wavelet and Multiple Scale Reproducing Kernel Methods”,International Journal for Numerical Methods in Fluids, Vol.21, pp. 901–932.

Liu, W.K., Jun, S., Li, S., Adee, J. and Belytschko, T. (1995a), “Reproducing Kernel Particle Methods for Structural Dynamics”,International Journal of Numerical Methods for Engineering,38, pp. 1655–1679.

Liu, W.K., Jun, S. and Zhang, Y.F. (1995b), “Reproducing Kernel Particle Methods”,International Journal of Numerical Methods in Fluids,20, pp. 1081–1106.

Liu, W.K., Li, Shaofan and Belytschko, T. (1995c), “Moving Least Square Kernel Galerkin Method (I) Methodology and Convergence”, submitted toComputer Methods in Applied Mechanics and Engieering.

Liu, W.K., Chen, Y. and Uras, R.A. (1995d), “Enrichment of the Finite Element Method with Reproducing Kernel Particle Method”,Current Topics in Computational Mechanics, eds. Cory, J.F. Jr. and Gordon, J.L., ASME PVP,305, pp. 253–258.

Liu, W.K. and Hu, Y.K. (1994), “Finite Element Hydrodynamic Friction Model for Metal Forming,”International Journal of Numerical Methods for Engineering,37, pp. 4015–4037.

Liu, W.K., Hu, Y.K. and Belytschko, T. (1994), “Multiple Quadrature Underintegrated Finite Elements”,Int. J. Numer. Mech. Engng. 37, pp. 3262–3289.

Liu, W.K. and Hu, Y.K. (1993), “An ALE Hydrodynamic Lubricated Finite Element Method with Application to Strip Rolling”,International Journal of Numerical Methods for Engineering,36, pp. 855–880.

Liu, W.K. and Oberste-Brandenburg, C. (1993), “Reproducing Kernel and Wavelet Particle Methods”,Aerospace Structures: Nonlinear Dynamics and System Response, eds. Cusumano, J.P., Pierre, C., and Wu, S.T., AD 33, ASME, pp. 39–56.

Liu, W.K., Adee, J. and Jun, S. (1993), “Reproducing Kernel Particle Methods for Elastic and Plastic Problems”,Advanced Computational Methods for Material Modeling, eds. Beson, D.J. and Asaro, R.A., AMD 180 and PVP 268, ASME, pp. 175–190.

Liu, W.K. (1992), “Arbitrary Lagrangian-Eulerian Finite Elements for Fluid-Shell Interaction Problems”,J. of the Braz. Soc. of Mech. Sc.,XIV-4, pp. 347–368.

Liu, W.K. and Haeussermann, U. (1992), “Multiple Temporal and Spatial Scale Methods,”New Methods in Transient Analysis, P. Smolinski, W. K. Liu, G. Hulbert and K. Tamma, eds., PVP 246/AMD 143, ASME, pp. 51–64.

Liu, W.K. and Hu, Y.K. (1992), “ALE Finite Element Formulation for Ring Rolling Analysis,”International Journal of Numerical Methods for Engineering,33, pp. 1217–1236.

Liu, W.K., Hu, Y.K. and Belytschko, T. (1992a), “ALE Finite Elements with Hydrodynamic Lubricated for Metal Forming”,Nuclear Engineering and Design,138, pp. 1–10.

Liu, W.K., Zhang, Y.F. and Ramirez, M.R. (1991a), “Multiple Scale Finite Element Methods”,International Journal for Numerical Methods in Engineering,32, pp. 969–990.

Liu, W.K., Zhang, Y.F., Belytschko, T. and Chen, J.S. (1991b), “Adaptive ALE Finite Elements with Particular Reference to External Work Rate on Frictional Interface”,Computer Methods in Applied Mechanics and Engineering,93, pp. 189–216.

Liu, W.K., Belytschko, T. and Chen, J.S. (1988a), “Nonlinear Versions of Flexurally Superconvergent Elements”,Comput. Meth. Appl. Mech. Engng.,71, pp. 24–256.

Liu, W.K., Chang, H. and Belytschko, T. (1988b), “Arbitrary Lagrangian and Eulerian Petrov-Galerkin Finite Elements for Nonlinear Continua”,Computer Methods in Applied Mechanics and Engineering,68, pp. 259–310.

Liu, W.K., Belytschko, T. and Chang, H. (1986), “An Arbitrary Lagrangian Eulerian Finite Element Method for Path-Dependent Materials”,Computer Methods in Applied Mechanics and Engineering,58, pp. 227–246.

Liu, W.K., Belytschko, T., Ong, J.S.J. and Law, E. (1985a), “Use of Stabilization Matrices in Nonlinear Finite Element Analysis”,Engineering Computations,2, pp. 47–55.

Liu, W.K., Ong, J.S.J. and Uras, R.A. (1985b), “Finite Element Stabilization Matrices—A Unification Approach,”Comput. Meth. Appl. Mech. Engng.,53, pp. 13–46.

Liu, W.K. and Belytschko, T. (1984), “Efficient Linear and Nonlinear Heat Conduction with a Quadrilateral Element”,International Journal for Numerical Methods in Engineering,20, pp. 931–948.

Liu, W.K. (1981), “Finite Element Procedures for Fluid-Structure Interactions and Applications to Liquid Storage Tanks”,Nuclear Engineering and Design,64, 2, pp. 221–238.

Lucy, L. (1977), “A Numerical Approach to Testing the Fission Hypothesis”,A.J.,82, pp. 1013–1024.

Lu, Y.Y., Belytschko, T. and Gu, L. (1994), “A New Implementation of the Element Free Galerkin Method”,Comput. Meth. Appl. Mech. Engng.,113, pp. 397–414.

Mallat, S. (1989), “Multi-resolution Approximations and Wavelet Orthogonal Bases of L2(R)”,Trans. Amer. Math. Soc.,315, pp. 69–87.

Monaghan, J.J. (1982), “Why Particle Methods Work”,SIAM J. Sci. Stat. Comput.,3, pp. 422–433.

Monaghan, J.J. and Gingold, R.A. (1983), “Shock Simulation by the Particle Method SPH”,J. Comp. Phys.,52, pp. 374–389.

Monaghan, J.J. (1988), “An Introduction to SPH”,Comp. Phys. Comm.,48, pp. 89–96.

Mooney, M. (1940), “A Theory of Large Elastic Deformation”,J. Appl. Phys.,11, pp. 582–592.

Nayroles, B., Touzot, G. and Villon, P. (1992), “Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements”,Computational Mechanics,10, pp.307–318.

Nichols, B.D. and Hirt, C.W. (1971), “Improved Free Surface Boundary Conditions for Numerical Incompressible Flow Calculations”,J. Comp. Phys.,8.

Oñate, E., Idelsohn, S. and Zienkiewicz, O.C. (1995), “Finite Point Methods in Computational Mechanics”,International Center for Numerical Methods in Engineering, July.

Penn, R. W. (1970), “Volume Changes Accompanying the Extension of Rubber”,Trans. Soc. Rheo.,14, 4, pp. 50–517.

Poularikas, A.D. and Seely, S., “Signals and Systems”, PWS-KENT Publishing Company, 2nd edition.

Rivlin, R.S. (1956), “Rheology Theory and Applications”, ed. Eirich, F.R. 1, Chap. 10, pp. 351–385, Academic Press, New York.

Shodja, H.M., Mura, T. and Liu, W.K. (1995), “Multiresolution analysis of a Micromechanical Model”,Computational Methods in Micromechanics, ASME AMD 212/MD 62, eds. S. Ghosh and M. Ostoja-Starzewski, pp. 33–54.

Stellingwerf, R.F. and Wingate, C.A. (1993), “Impact Modeling with Smooth Particle Hydrodynamics”,Int. J. Impact Engng.,14, pp. 707–718.

Strang, G. (1989), “Wavelets and Dilation Equations: a Brief Introduction”,SIAM Rev.,31, 4, pp. 614–627.

Subbiah, S.,et al.(1989), “Non-isothermal Flow of Polymers into Two-dimensional, Thin Cavity Molds: A Numerical Grid Generation Approach”,Int. J. Heat Mass Transfer,32, 3, pp. 415–434.

Sulsky, D., Chen, Z. and Schreyer, H.L. (1992), “The Application of a Material-Spatial Numerical Method to Penetration”,New Methods in Transient Analysis, eds. Smolinski, P., Liu, W.K., Hulbert, G. and Tamma, K., ASME, PVP, Vol. 246/AMD143, pp 91–102.

Sussman, T.S. and Bathe, K.J. (1987), “A Finite Element Formulation for Incompressible Elastic and Inelastic Analysis”,Comput. & Struct.,26, pp. 357–409.

Williams, J.R. and Amaratunga, K. (1994), “Introduction to Wavelets in Engineering”,International Journal for Numerical Methods in Engineering,37, pp. 2365–2388.

Yagawa, G., Yamada, T. and Kawai (1995), “Some Remarks on Free Mesh Method: A kind of Meshless Finite Element Methods”, To be presented at ICES-95.

Yeoh, O.H., “Characterization of Elastic Properties of Carbon Black Filled Rubber Vulcanizates”,Rubb. Chem. Technol.,63, pp. 79–805.

Yeoh, O.H. (1993), “Some Forms of the Strain Energy Function for Rubber”,Rubb. Chem. Technol.,66, pp. 754–771.