Meshless methods: An overview and recent developments

Lucy, 1977, A numerical approach to the testing of the fission hypothesis, The Astron. J., 8, 1013, 10.1086/112164

Monaghan, 1982, Why particle methods work, SIAM J. Sci. Stat. Comput., 3, 422, 10.1137/0903027

Monaghan, 1988, An introducion to SPH, Comput. Phys. Comm., 48, 89, 10.1016/0010-4655(88)90026-4

Swegle, 1995, Smoothed particle hydrodynamics stability analysis, J. Comput. Phys., 116, 123, 10.1006/jcph.1995.1010

Dyka, 1994, Addressing tension instability in SPH methods

Johnson, 1996, Normalized smoothing funtions for SPH impact computations, Int. J. Numer. Methods Engrg., 10.1002/(SICI)1097-0207(19960830)39:16<2725::AID-NME973>3.0.CO;2-9

Liu, 1995, Reproducing kernel particle methods, Int. J. Numer. Methods Engrg., 20, 1081, 10.1002/fld.1650200824

Nayroles, 1992, Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. Mech., 10, 307, 10.1007/BF00364252

Belytschko, 1994, Fracture and crack growth by element-free Galerkin methods, Model. Simul. Mater. Sci. Engrg., 2, 519, 10.1088/0965-0393/2/3A/007

Duarte, 1995, Hp clouds—a meshless method to solve boundary-value problems

I. Babuška and J.M. Melenk, The partition of unity finite element method, in preparation.

Liu, 1996, Reproducing least-square kernel Galerkin method. (i) Methodology and convergence, Comput. Methods Appl. Mech. Engrg., 10.1016/S0045-7825(96)01082-1

Perrone, 1975, A general finite difference method for arbitrary meshes, Comput. Struct., 5, 45, 10.1016/0045-7949(75)90018-8

Liszka, 1980, The finite difference method at arbitrary irregular grids and its application in applied mechanics, Comput. Struct., 11, 83, 10.1016/0045-7949(80)90149-2

Monaghan, 1992, Smooth particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 543, 10.1146/annurev.aa.30.090192.002551

Lancaster, 1981, Surfaces generated by moving least-squares methods, Math. Comput., 37, 141, 10.1090/S0025-5718-1981-0616367-1

Cleveland, 1993

Shepard, 1968, A two-dimensional interpolation function for irregularly spaced points, 517

Y. Krongauz and T. Belytschko, Enforcement of essential boundary conditions in meshless approximations using finite elements, Comput. Methods Appl. Mech. Engrg., to appear.

T. Belytschko, Y. Krongauz, M. Fleming, D. Organ and W.K. Liu, Smoothing and accelerated computations in the element-free Galerkin method, J. Comput. Appl. Math., to appear.

M. Fleming, Y.A. Chu, B. Moran and T. Belytschko, Enriched element-free Galerkin methods for singular fields, Int. J. Numer. Methods Engrg., submitted.

Belytschko, 1994, Element-free Galerkin methods, Int. J. Numer. Methods Engrg., 37, 229, 10.1002/nme.1620370205

Liu, 1995, Reproducing kernel particle methods for structural dynamics, Int. J. Numer. Methods Engrg., 38, 1655, 10.1002/nme.1620381005

Liu, 1995, Wavelet and multiple scale reproducing kernel methods, Int. J. Numer. Methods Fluids, 21, 901, 10.1002/fld.1650211010

Liu, 1996, Advances in multiple scale kernel particle methods, Comput. Mech., An International Journal, 10.1007/BF00350529

P. Krysl and T. Belytschko, Nonconforming element-free Galerkin method, Comput. Methods Appl. Mech. Engrg., submitted.

D. Organ, M. Fleming, T. Terry and T. Belytschko, Continuous meshless approximations for nonconvex bodies by diffraction and transparency, Comput. Mech., to appear.

C.A. Duarte, Personal communication, 1996.

L.W. Cordes and B. Moran, Treatment of material discontinuity in the element-free Galerkin method, Comput. Methods Appl. Mech. Engrg., in press.

Y. Krongauz and T. Belytschko, Meshless approximations for discontinuous derivatives., submitted.

E. Oñate, S. Idelsohn, O.C. Zienkiewicz, R.L. Taylor and C. Sacco, A stabalized finite point method for analysis of fluid mechanics problems, submitted.

Yagawa, 1995, Some remarks on free mesh method: A kind of meshless finite element method

Lu, 1994, A new implementation of the element free Galerkin method, Comput. Methods Appl. Mech. Engrg., 113, 397, 10.1016/0045-7825(94)90056-6

Chu, 1995, A computational model for nucleation of solid-solid phase transformations, Model. Simul. Mater. Sci. Engrg., 3, 455, 10.1088/0965-0393/3/4/003

J. Gosz, Personal communication, 1996.

Johnson, 1994, Linking Lagrangian particle methods to standard finite element methods for high velocity impact computations, Nucl. Engrg. Des., 150, 265, 10.1016/0029-5493(94)90143-0

Attaway, 1994, Coupling of smooth particle hydrodynamics with the finite element method, Nucl. Engrg Des., 150, 199, 10.1016/0029-5493(94)90136-8

Hegen, 1994, Numerical techniques for the simulation of crack growth, Technical report, Eindhoven University of Technology. Final report of the postgraduate programme Mathematics for Industry

Belytschko, 1995, A coupled finite element-element-free Galerkin method, Comput. Mech., 17, 186, 10.1007/BF00364080

Liu, 1995, Enrichment of the finite element method with the reproducing kernel particle method, Vol. 305, 253

Liu, 1996, Overview and applications of the reproducing kernel particle methods, Archives of Computational Methods in Engineering: State of the art reviews, 3, 3, 10.1007/BF02736130

Y. Krongauz and T. Belytschko, Fast consistent derivatives in meshless methods, in preparation.

Hein, 1993, Diffuse element method applied to Kirchhoff plates

Lu, 1996, Internal report

Krysl, 1996, Analysis of thin plates by the element-free Galerkin method, Comput. Mech., 17, 26, 10.1007/BF00356476

P. Krysl and T. Belytschko, Analysis of thin shells by the element-free Galerkin method, Int. J. Solids Struct., to appear.

Belytschko, 1985, Stress projection for membrane and shear locking in shell finite elements, Comput. Methods Appl. Mech. Engrg., 51, 221, 10.1016/0045-7825(85)90035-0

Stummel, 1979, The generalized patch test, SIAM J. Numer. Anal., 3, 449, 10.1137/0716037

Strang, 1973

Ciarlet, 1991, Basic error estimates for elliptic problems, Vol. II

Timoshenko, 1970

Sumi, 1985, On crack path stability in a finite body, Engrg. Fracture Mech., 22, 759, 10.1016/0013-7944(85)90106-7

Sumi, 1985, Computational crack path prediction, Theoret. Appl. Fracture Mech., 4, 149, 10.1016/0167-8442(85)90019-9

Y. Sumi, C. Yang and Z.N. Wang, Morphological aspects of fatigue crack propagation Part II — effects of stress biaxiality and welding residual stress., submitted.

Kalthoff, 1987, Failure mode transition at high rates of shear loading, Vol. 1, 185

Organ, 1996, Numerical solutions to dynamic fracture problems using the element-free Galerkin method

John, 1990, Mixed mode fracture of concrete subjected to impact loading, ASCE J. Struct. Engrg., 116, 585, 10.1061/(ASCE)0733-9445(1990)116:3(585)

John, 1988, Mixed mode fracture of concrete subjected to impact loading

Li, 1985, A comparison of methods for calculating energy release rates, Engrg. Fracture Mech., 21, 405, 10.1016/0013-7944(85)90029-3

Moran, 1987, Crack tip and associated domain integral from momentum and energy balance, Engrg. Fracture Mech., 22, 615, 10.1016/0013-7944(87)90155-X

Hallquist, 1980

Liu, 1988, Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua, Comput. Methods Appl. Mech. Engrg., 68, 259, 10.1016/0045-7825(88)90011-4

Belytschko, 1996, Dynamic fracture using element-free Galerkin methods, Int. J. Numer. Methods Engrg., 39, 10.1002/(SICI)1097-0207(19960330)39:6<923::AID-NME887>3.0.CO;2-W