References

Abbassian, F., Dawswell, D. J., and Knowles, N. C.,

Free Vibration Benchmarks

, Atkins Engineering

Sciences, Glasgow, 1987.

Anderson, T. L.,

Fracture Mechanics: Fundamentals and Applications

, CRC Press, Boca Raton, FL, 1991.

Armando, D. C. and Oden, J. T., Hp Clouds—A Meshless Method to Solve Boundary Value Problems,

TICAM Report 95-05, University of Texas, Austin, 1995.

Atluri, S. N. and Zhu, T., A new meshless local Petrov–Galerkin (MLPG) approach in computational

mechanics,

Comput. Mech.

, 22, 117–127, 1998.

Atluri, S. N., Cho, J. Y., and Kim, H. G., Analysis of thin beams, using the meshless local Petrov–Galerkin

method, with generalized moving least squares interpolations,

Comput. Mech.

, 24, 334–347, 1999a.

Atluri, S. N., Kim, H. G., and Cho, J. Y., A critical assessment of the truly meshless local Petrov–Galerkin

(MLPG), and local boundary integral equation (LBIE) methods,

Comput. Mech.

, 24, 348–372,

1999b.

Babu ka, I. and Melenk, J. M., The partition of unity finite element method, Technical report technical

note BN-1185, Institute for Physical Science and Technology, University of Maryland, April
1995.

Barnhill, R. E., Representation and approximation of surfaces, in

Mathematical Software III

, Academic

Press, New York, 1977, 69–120.

Bathe, K. J., Wilson, E. L., and Paterson, F. E., SAP IV, a structural analysis program for static and

dynamic response of linear systems. University of California, Berkeley. Rep. EERC 73–11, 1973.

Beissel, S. and Belytschko, T., Nodal integration of the element-free Galerkin method,

Comput.

Methods Appl. Mech. Eng.

, 139, 49–74, 1996.

Belytschko, T., Gu, L., and Lu, Y. Y., Fracture and crack growth by element free Galerkin methods,

Modeling Simulations Mater. Sci. Eng.

, 2, 519–534, 1994a.

Belytschko, T., Guo, Y., Liu, W. K., and Xiao, S. P., A unified stability of meshless particle methods,

Int. J. Numer. Methods Engng.,

48, 1359–1400, 2000.

Belytschko, T., Lu, Y. Y., and Gu, L., Element-free Galerkin methods,

Int. J. Numer. Methods Eng.

, 37,

229–256, 1994b.

Belytschko, T. et al., Stress projection for membrane and shear locking in shell finite elements,

Comput. Methods Appl. Mech. Eng.

, 51, 221–258, 1985.

Belytschko, T. et al., Smoothing and accelerated computations in the element free Galerkin method,

J. Comput. Appl. Math.

, 74, 111–126, 1996a.

Belytschko, T. et al., Meshless method: an overview and recent developments,

Comput. Methods Appl.

Mech. Eng.

, 139, 3–47, 1996b.

Benz, W. and Asphaug, E., Explicit 3D continuum fracture modeling with smoothed particle hydro-

dynamics, in

Proceedings of Twenty-fourth Lunar and Planetary Science Conference

, Lunar and

Planetary Institute, 1993, 99–100.

Benz, W. and Asphaug, E., Impact simulations with fracture. I. Methods and tests,

Icarus

, 107, 98–116,

1994.

Benz, W. and Asphaug, E., Simulations of brittle solids using smoothed particle hydrodynamics,

Comput. Phys. Commun.

, 87, 253–265, 1995.

Beskos, D. E., Dynamic analysis of plates and shallow shells by the D/BEM, in

Advances in the Theory

of Plates and Shells

, Elsevier, Oxford, 1990, 177–196.

Biot, M. A., General theory of three-dimensional consolidation,

J. Appl. Phys.

, 12, 155, 1941.

Bonet, J. and Kulasegaram, S., Correction and stabilization of smoothed particle hydrodynamics

methods with applications in metal forming simulations,

Int. J. Numer. Methods Eng.

, 47,

1189–1214, 2000.

sˇ

1238_frame_REF Page 675 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

Brebbia, C. A.,

The Boundary Element Method for Engineers

, Pentech Press, London, Halstead Press,

New York, 1978.

Brebbia, C. A. and Georgiou, P., Combination of boundary and finite elements in elastostatics,

Appl.

Math. Modeling

, 3, 212–219, 1979.

Brebbia, C. A., Telles, J. C., and Wrobel, L. C.,

Boundary Element Techniques,

Springer Verlag, Berlin,

1984.

Breitkopf, P., Touzot, G., and Villon, P., Consistency approach and diffuse derivation in element free

methods based on moving least squares approximation,

Comput. Assisted Mech. Eng. Sci.

, 5,

479–501, 1998.

Campbell, J., Vignjevic, R., and Libersky, L., A contact algorithm for smoothed particle hydrody-

namics,

Comput. Methods Appl. Mech. Eng.

, 184, 49–65, 2000.

Campbell, P. M., Some new algorithms for boundary value problems in smoothed particle hydro-

dynamics, DNA Report, DNA-88-286, 1989.

Carlson, R. E. and Foley, T. A., The parameter

R

2

in multiquadric interpolation,

Comput. Math. Appl.

,

21, 29–42, 1991.

Carter, R. L., Robinson, A. R., and Schnobrich, W. C., 1. Free vibrations of hyperboloidal shells of

revolution,

J. Eng. Mech.

, 93, 1033–1053, 1969.

Chati, M. K. and Mukherjee, S., The boundary node method for three-dimensional problems in

potential theory,

Int. J. Numer. Methods Eng.

, 47, 1523–1547, 2000.

Chati, M. K., Mukherjee, S., and Mukherjee, Y. X., The boundary node method for three-dimensional

linear elasticity,

Int. J. Numer. Methods Eng.

, 46, 1163–1184, 1999.

Chen, J. K., Beraun, J. E., and Carney, T. C., A corrective smoothed particle method for boundary

value problems in heat conduction,

Int. J. Numer. Methods Eng.

, 46, 231–252, 1999a.

Chen, J. K., Beraun, J. E., and Jih, C. J., An improvement for tensile instability in smoothed particle

hydrodynamics,

Comput. Mech.

, 23, 279–287, 1999b.

Chen, J. S. et al., Reproducing kernel particle methods for large deformation analysis of nonlinear

structures,

Comput. Methods Appl. Mech. Eng.

, 139, 195–228, 1996.

Chen, X. L., Liu, G. R., and Lim, S. P., Deflection analyses of laminates using EFG method, in

International Conference on Scientific and Engineering Computing

, March 19–23, Beijing, P.R.

China, 2001, 67.

Chen, X. L., Liu, G. R., and Lim, S. P., A mesh-free method for free vibration and stability analyses

of shear deformable plates,

J. Sound Vib

. (in press), 2002a.

Chen, X. L., Liu, G. R., and Lim, S. P., An element free Galerkin method for free vibration analysis

of composite laminates of complicated shape,

Composite Structures

(in press), 2002b.

Chen, Y. Z., Evaluation of fundamental vibration frequency of an orthotropic bending plate by using

an iterative approach,

Comput. Methods Appl. Mech. Eng.

, 161, 289–296, 1998.

Cheng, M. and Liu, G. R., A finite point method for analysis of fluid flow, in

Proceedings of 4th

International Asia-Pacific Conference on Computational Mechanics

, December, Singapore, 1999,

1015–1020.

Cho, J. Y., Kim, H. G., and Atluri, S. N., Analysis of shear flexible beams, using the meshless local

Petrov–Galerkin method based on locking-free formulation, in

Proceedings of Advances in

Computational Engineering and Science

, Los Angeles, 2000, 1404–1409.

Chow, S. T., Liew, K. M., and Lam, K. Y., Transverse vibration of symmetrically laminated rectangular

composite plates,

Compos. Struct.

, 20, 213–226, 1992.

Chung, H. J. and Belytschko, T., An error estimate in the EFG method,

Comput. Mech.

, 21, 91–100, 1998.

Cleary, P. W., Modeling confined multi-material heat and mass flows using SPH,

Appl. Math. Modeling

,

22, 981–993, 1998.

Cleveland, W. S.,

Visualizing Data,

AT&T Bell Laboratories, Murray Hill, NJ, 1993.

Coleman, C. J., On the use of radial basis functions in the solution of elliptic boundary value

problems,

Comput. Mech.

, 17, 418–422, 1996.

Combe, U. H. and Korn, C., An adaptive approach with the element-free-Galerkin method,

Comput.

Methods Appl. Mech. Eng.

, 162, 203–222, 1998.

Cordes, L. W. and Moran, B., Treatment of material discontinuity in the element-free Galerkin

method,

Comput. Methods Appl. Mech. Eng.

, 139, 75–89, 1996.

Davis, G. de Vahl, Natural convection of air in a square cavity: a benchmark numerical solution,

Int. J. Numer. Methods Fluids,

3, 249–264, 1983.

1238_frame_REF Page 676 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

DeFigueiredo, T. G. B.,

New Boundary Element Formulation in Engineering

, Springer-Verlag, Berlin,

1991.

DeFigueiredo, T. G. B. and Brebbia, C. A., A new hybrid displacement variational formulation of

BEM for elastostatics, in

Advances in Boundary Elements

, Vol. 1, Brebbia, C. A., Ed., Springer-

Verlag, Berlin, 1989, 33–42.

Delaunay, B., Sur la sphere vide,

Bul. Acad. Sci. URSS Class. Sci. Nat.,

793–800, 1934.

Dolbow, J. and Belytschko, T., Numerical integration of the Galerkin weak form in mesh free

methods,

Comput. Mech.

, 23, 219–230, 1999.

Donning, B. M. and Liu, W. K., Meshless methods for shear-deformable beams and plates,

Comput.

Methods Appl. Mech. Eng.

, 152, 47–71, 1998.

Duarte, C. A. and Oden, J. T., An

hp

adaptive method using clouds,

Comput. Methods Appl. Mech.

Eng.

, 139, 237–262, 1996.

Dumont, N. A., The hybrid boundary element method, in

Boundary Elements

, IX, Vol. 1, Brebbia,

C. A., Ed., Springer-Verlag, Berlin, 1988, 117–130.

Duncan, J. M. and Chang, C. Y., Nonlinear analysis of stress and strain in soils,

Proc. ASCE J. Soil

Mech. Foundation Division

, 96(SM5), 1970.

Duncan, J. M. et al., Strength, Stress Strain and Bulk Modulus Parameters for Finite Element Analyses

of Stress and Movements in Soil Masses, Rep. VCB/GT/78-02, University of California,
Berkeley, 1978.

Fasshauer, G. E., Solving partial differential equations by collocation with radial basis functions, in

Surface Fitting and Multiresolution Methods

, Mehaute, A. L., Rabut, C., and Schumaker, L. L.,

Eds., 1997, 131–138.

Flebbe, O. S. et al., Smoothed particle hydrodynamics—physical viscosity and the simulation of

accretion disks,

Astron. J

., 431, 754–760, 1994.

Fleming, M. et al., Enriched element-free Galerkin methods for crack tip fields,

Int. J. Numer. Methods

Eng

., 40, 1483–1504, 1997.

Franke, C. and Schaback, R., Solving partial differential equations by collocation using radial basis

functions,

Appl. Math. Comput

., 93, 73–82, 1997.

Franke, R., Scattered data interpolation: tests of some method,

Math. Comput

., 38(157), 181–200, 1982.

Gingold, R. A. and Monaghan, J. J., Smooth particle hydrodynamics: theory and applications to non-

spherical stars,

Mon. Not. R. Astron. Soc

., 181, 375–389, 1977.

Gingold, R. A. and Monaghan, J. J., Kernel estimates as a basis for general particle methods in

hydrodynamics,

J. Comput. Phys

., 46, 429–453, 1982.

Golberg, M. A., Chen, C. S., and Bowman, H., Some recent results and proposals for the use of radial

basis functions in the BEM,

Eng. Anal. Boundary Elements

, 23, 285–296, 1999.

Golberg, M. A., Chen, C. S., and Karur, S. R., Improved multiquadric approximation for partial

differential equations,

Eng. Anal. Boundary Elements

, 18, 9–17, 1996.

Gontkewitz, V. C., Natural vibration of plates and shells,

Nayka Dymka

(Kiev), 1964 [in Russian].

Griffel, D. H.,

Linear Algebra and Its Applications

, Ellis Horwood Limited, New York, 1989.

Gu, Y. T. and Liu, G. R., A boundary point interpolation method (BPIM) using radial function basis,

in

First MIT Conference on Computational Fluid and Solid Mechanics

, June 2001, MIT, 2001a,

1590–1592.

Gu, Y. T. and Liu, G. R., A coupled element free Galerkin/boundary element method for stress

analysis of two-dimensional solids,

Comput. Methods Appl. Mech. Eng

., 190, 4405–4419, 2001b.

Gu, Y. T. and Liu, G. R., A meshless local Petrov–Galerkin (MLPG) method for free and forced

vibration analyses for solids,

Comput. Mech

., 27(3), 188–198, 2001c.

Gu, Y. T. and Liu, G. R., A local point interpolation method for static and dynamic analysis of thin

beams,

Comput. Methods Appl. Mech. Eng

., 190, 5515–5528, 2001d.

Gu, Y. T. and Liu, G. R., A boundary point interpolation method for stress analysis of solids,

Comput.

Mech

., 28(1), 47–54, 2002.

Gu, Y. T. and Liu, G. R., A meshless local Petrov–Galerkin (MLPG) formulation for static and free

vibration analyses of thin plates,

Comput. Modeling Eng. Sci.

, 2(4), 463–476, 2001f.

Haggblad, B. and Bathe, K. J., Specifications of boundary conditions for Reissner/Mindlin plate

bending finite elements,

Int. J. Numer. Methods Eng

., 30, 981–1011, 1990.

Hardy, R. L., Theory and applications of the multiquadrics—biharmonic method (20 years of dis-

covery 1968–1988),

Comput. Math. Appl.

, 19, 163–208, 1990.

1238_frame_REF Page 677 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

Hernquist, L. and Katz, N., TreeSPH—a unification of SPH with the hierarchical tree method,

Astrophys. J. Suppl. Ser

., 70, 419–446, 1989.

Huang, W. X.,

The Engineering Property of Soil

, Hydraulic & Electric Press, Beijing 1983 [Chinese

version].

Hughes, T. J. R.,

The Finite Element Method

, Prentice-Hall, Englewood Cliffs, NJ, 1987.

Jensen, P. S., Finite difference techniques for variable grids,

Comput. Struct.

, 2, 17–29, 1980.

Jin, Z. L., Gu, Y. T., and Zheng, Y. L., Hybrid boundary elements for potential and elastic problem,

in

Proceedings of the 7th Japan-China Symposium on Boundary Element Methods

, Japan, 1996,

143–152.

Johnson, G. R. and Beissel, S. R., Normalized smoothing functions for SPH impact computations,

Int. J. Numer. Methods Eng

., 39(16), 2725–2741, 1996.

Johnson, G. R., Stryk, R. A., and Beissel, S. R., SPH for high velocity impact computations,

Comput.

Methods Appl. Mech. Eng

., 139, 347–373, 1996.

Kanok-Nukulchai, W., Barry, W., Saran-Yasoontorn, K., and Bouillard, P. H., On elimination of shear

locking in the element-free Galerkin method,

Int. J. Numer. Methods Engng.,

52, 705–725, 2001.

Kansa, E. J., A scattered data approximation scheme with application to computational fluid-

dynamics—I & II,

Comput. Math. Appl.

, 19, 127–161, 1990a.

Kansa, E. J., Multiquadrics—a scattered data approximation scheme with applications to computa-

tional fluid dynamics,

Comput. Math. Appl

., 19(8/9), 127–145, 1990b.

Kothnur, V. S., Mukherjee, S., and Mukherjee, Y. X., Two-dimensional linear elasticity by the bound-

ary node method,

Int. J. Solids Struct.

, 36, 1129–1147, 1999.

Krongauz, Y. and Belytschko, T., Enforcement of essential boundary conditions in meshless approx-

imations using finite elements,

Comput. Methods Appl. Mech. Eng

., 131(1–2), 133–145, 1996.

Krongauz, Y. and Belytschko, T., EFG approximation with discontinuous derivatives,

Int. J. Numer.

Methods Eng

., 41(7), 1215–1233, 1998.

Krysl, P. and Belytschko, T., Analysis of thin plates by the element-free Galerkin method,

Comput.

Mech

., 17, 26–35, 1996a.

Krysl, P. and Belytschko, T., Analysis of thin shells by the element-free Galerkin method,

Int. J. Solids

Struct

., 33, 3057–3080, 1996b.

Kuehn, T. H. and Goldstein, R. J., An experimental and theoretical study of natural convection in

the annulus between horizontal concentric cylinders,

J. Fluid Mech

., 74, 695–716, 1976.

Lam, K. Y. et al., Smoothed particle hydrodynamics for fluid dynamic problems, presented at

Int.

Symp. Supercomputing and Fluid Science

, August, Institute of Fluid Science, Tohoku University,

Sendai, Japan (Plenary Lecture), 2000.

Lancaster, P. and Salkauskas, K., Surfaces generated by moving least squares methods,

Math. Comput

.,

37, 141–158, 1981.

Leissa, A. W. and Narita, Y., Vibration studies for simply supported symmetrically laminated regular

plates,

Compos. Struct

., 12, 113–132, 1989.

Li, H. B. and Han, G. M., A new method for the coupling of finite element and boundary element

discretized subdomains of elastic bodies,

Comput. Methods Appl. Mech. Eng

., 54, 161–185, 1986.

Li, S., Hao, W., and Liu, W. K., Numerical simulations of large deformation of thin shell structures

using meshfree methods,

Comput. Mech.

, 25, 102–116, 2000.

Libersky, L. D. and Petscheck, A. G., Smoothed particle hydrodynamics with strength of materials,

in

Proceedings of the Next Free Lagrange Conference

, Vol. 395, Trease, H., Fritts, J., and Crowley, W.,

Eds., Springer-Verlag, New York, 1991, 248–257.

Libersky, L. D. and Petscheck, A. G., High strain Lagrangian hydrodynamics—a three-dimensional

SPH code for dynamic material response,

J. Comput. Phys

., 109, 67–75, 1993.

Liszka, T. and Orkisz, J., The finite difference method at arbitrary irregular grids and its application

in applied mechanics,

Comput. Struct.

, 11, 83–95, 1980.

Lin, H., and Atluri, S. N., The meshless local Petrov–Galerkin (MLPG) method for solving incom-

pressive Navier-Stokers equations,

Comput. Model. Engrg. Sci.,

2, 117–142, 2001.

Liu, G. R., A point assembly method for stress analysis for solid, in

Impact Response of Materials &

Structures

, Shim, V. P. W. et al., Eds., Oxford University Press, Oxford, 1999, 475–480.

Liu, G. R. and Chen, X. L., Static buckling of composite laminates using EFG method, in

Proc. 1st

Int. Conf. on Structural Stability and Dynamics

, December 7–9, Taipei, Taiwan, 2000, 321–326.

1238_frame_REF Page 678 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

Liu, G. R., and Chen, X. L., A mesh-free method for static and free vibration analyses of thin plates

of complicated shape,

J. Sound Vib

., 241(5), 839–855, 2001.

Liu, G. R. and Gu, Y. T., A point interpolation method, in

Proc. 4th Asia-Pacific Conference on Compu-

tational Mechanics

, December, Singapore, 1999, 1009–1014.

Liu, G. R. and Gu, Y. T., Meshless local Petrov–Galerkin (MLPG) method in combination with finite

element and boundary element approaches,

Comput. Mech.

, 26, 536–546, 2000a.

Liu, G. R. and Gu, Y. T., Vibration analyses of 2-D solids by the local point interpolation method

(LPIM), in

Proc. 1st International Conference on Structural Stability and Dynamics

, December 7–9,

Taiwan, 2000b, 411–416.

Liu, G. R. and Gu, Y. T., Coupling of element free Galerkin and hybrid boundary element methods

using modified variational formulation,

Comput. Mech

., 26(2), 166–173, 2000c.

Liu, G. R. and Gu, Y. T., Coupling of element free Galerkin method with boundary point interpolation

method, in

Advances in Computational Engineering & Science

, Atluri, S. N. and Brust, F. W., Eds.,

ICES’2K, Los Angeles, August, 2000d, 1427–1432.

Liu, G. R. and Gu, Y. T., A local point interpolation method for stress analysis of two-dimensional

solids,

Struct. Eng. Mech

., 11(2), 221–236, 2001a.

Liu, G. R. and Gu, Y. T., A local radial point interpolation method (LR-PIM) for free vibration analyses

of 2-D solids,

J. Sound Vib

., 246(1), 29–46, 2001b.

Liu, G. R. and Gu, Y. T., A point interpolation method for two-dimensional solids,

Int. J. Numer.

Methods Eng

., 50, 937–951, 2001c.

Liu, G. R. and Gu, Y. T., A matrix triangularization algorithm for point interpolation method, in

Proc.

Asia-Pacific Vibration Conference

, Bangchun, W., Ed., November, Hangzhou, China, 2001d,

1151–1154.

Liu, G. R. and Gu, Y. T., On formulation and application of local point interpolation methods for

computational mechanics, in

Proc. First Asia-Pacific Congress on Computational Mechanics

, 20–23

November, Sydney, Australia, 2001e, 97–106 [Invited paper].

Liu, G. R. and Gu, Y. T., Truly meshless methods based on the local concept and its applications,

presented at

International Congress on Computational Engineering Science (ICES’01)

, 19–25 August,

Puerto Vallarta, Mexico, 2001f [Keynote lecture].

Liu, G. R. and Gu, Y. T., Comparisons of two meshfree local point interpolation methods for

structured analyses,

Comput. Mech

. (in press).

Liu, G. R. and Quek, S. S.,

Finite Element Methods for Readers of All Backgrounds,

Academic Press, San

Diego, 2002 (in press).

Liu, G. R. and Tu, Z. H., MFree2D

©

: an adaptive stress analysis package based on mesh-free

technology, in

First MIT Conference on Computational Fluid and Solid Mechanics

, June, MIT, 2001,

327–329.

Liu, G. R. and Tu, Z. H., An adaptive procedure based on background cells for meshless methods,

Comput. Methods Appl. Mech. Eng

., 191, 1923–1943, 2002.

Liu, G. R., Wu, Y. L., and Gu, Y. T., Application of meshless local Petrov–Galerkin (MLPG) approach

to fluid flow problem. In

Computational Mechanics—New Frontiers for New Millennium,

Valliappan,

S. and Khalili, N., Eds., Elsevier, Amsterdam, 2001.

Liu, G. R. and Wu, Y. L., Application of local radial point interpolation method (LRPIM) to impress-

ible flow simulation,

Int. J. Numer. Methods Fluids

(submitted), 2002.

Liu, G. R. and Xi, Z. C.,

Elastic Waves in Anisotropic Laminates

, CRC Press, Boca Raton, FL, 2001.

Liu, G. R. and Yan, L., A study on numerical integrations in element free methods, in

Proc. APCOM ’99

,

Singapore, 1999, 979–984.

Liu, G. R. and Yan, L., A modified meshless local Petrov–Galerkin method for solid mechanics, in

Advances in Computational Engineering and Sciences

, Atluri, N. K. and Brust, F. W., Eds., Tech

Science Press, Palmdale, CA, 2000, 1374–1379.

Liu, G. R. and Yan, L., A modified MLPG method for solid mechanics,

Comput. Methods Appl. Mech.

Eng

., 2001 (in press).

Liu, G. R. and Yang, K. Y., A penalty method for enforce essential boundary conditions in element

free Galerkin method, in

Proc. 3rd HPC Asia’98

, Singapore, 1998, 715–721.

Liu, G. R. and Yang, K. Y., A new meshless method for stress analysis for solids and structure, in

Proc. Fourth Asia-Pacific Conference on Computational Mechanics, 15–17 December, Singapore, 1999.

1238_frame_REF Page 679 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

Liu, G. R., Yang, K. Y., and Cheng, M., Some recent developments in element free methods in

computational mechanics, in Proc. Fourth Asia-Pacific Conference on Computational Mechanics,
15–17 December, Singapore, 1999.

Liu, G. R., Tu, Z. H., and Wu, Y. G., MFree2D

©

: an adaptive stress analysis package based on mesh

free technology, presented at 3rd South Africa Conference on Applied Mechanics, 11–13 January,
Durban, South Africa, 2000.

Liu, G. R., Liu, M. B., and Lam, K. Y., Smoothed particle hydrodynamics for numerical simulation

of high explosive explosions, presented at First International Symposium on Advanced Fluid
Information (AFI-2001), Institute of Fluid Science, Tohoku University, Sendai, Japan, 2001a.

Liu, G. R. Simulation of the high explosive detonation process using SPH methodology, presented

at First MIT Conference on Computational Solid and Fluid Mechanics, June, MIT, Cambridge,
MA, 2001b.

Liu, G. R., Wu, Y. L., and Gu, Y. T., Application of meshless local Petrov–Galerkin (MLPG) approach

to fluid flow problem, in Proc. First Asian-Pacific Congress on Computational Mechanics, 20–23
November, Sydney, Australia, 2001c.

Liu, G. R., Liu, M. B., and Lam, K. Y., A general approach for constructing smoothing functions for

meshfree methods, presented at Ninth International Conference on Computing in Civil and Building
Engineering, April 3–5, Taipei, Taiwan, 431–436, 2002a.

Liu, G. R. Numerical simulation of the high explosive detonation process using SPH methodology,

Shock Vib., 2002b (in press).

Liu, G. R., Liu, L., Tan, V. B. C., and Gu, Y. T., A Conforming Point Interpolation Method for Analyzing

Spatial Thick Shell Structures, 2nd Int. Conf. on Structural Stability and Dynamics, December
16–18, (accepted), 2002c.

Liu, G. R., Liu, M. B., and Lam, K. Y., Computer simulation of shaped charge detonation using

meshless particle method, (submitted).

Liu, G. R., and Tu, Z. H., An adaptive procedure based on background cells for meshless methods,

Comput. Method Appl. Mech. Engrg., 191, 1923–1942, 2002.

Liu, G. R., Yan, L., and Wang, J. G., Point interpolation method based on local residual formulation

using radial basis functions, Struct. Eng. Mech., 2001 (submitted).

Liu, L., Liu, G. R., and Tan, V. B. C., Element free analyses for static and free vibration of thin shells,

in Proc. Asia-Pacific Vibration Conference, Bangchun, W., Ed., November, Hangzhou, China, 2001.

Liu, G. R. et al., A combined finite element method/boundary element method for V(z) curves of

anisotropic-layer/substrate configurations, J. Acoust. Soc. Am. U.S.A., 92(5), 2734–2740, 1992.

Liu, M. B. et al., Numerical simulation of underwater explosion by SPH, in Advances in Computational

Engineering & Science, Atluri, S. N. and Brust, F. W., Eds., Tech Science Press, Palmdale, CA,
2000a, 1475–1480.

Liu, M. B. et al., Numerical simulation of underwater shock using SPH methodology, presented at

Computational Mechanics and Simulation of Underwater Explosion Effects—US/Singapore
Workshop, November, Washington, D.C., 2000b.

Liu, M. B. et al., A new technique to treat material interfaces for smoothed particle hydrodynamics,

in Proc. First Asia-Pacific Congress on Computational Mechanics, 20–23 November, Sydney, Australia,
2001a, 997–982.

Liu, M. B. et al., Numerical simulation of incompressible flows by SPH, Presented at International

Conference on Scientific & Engineering Computing, March, Beijing, China, 2001b.

Liu, M. B. et al., Computer simulation of the high explosive explosion using SPH methodology,

Comput. Fluids, 2002 (in press).

Liu, M. B., Liu, G. R., and Lam, K. Y., An SPH formulation for simulating discontinuous phenomena,

Comput. Fluid (submitted).

Liu, M. B., Liu, G. R., and Lam, K. Y., Investigations on water mitigations by using meshless particle

method, Shock Waves (in press).

Liu, M. B. et al., Smoothed particle hydrodynamics for numerical simulation of underwater explo-

sions (revised).

Liu, W. K., Adee, J., and Jun, S., Reproducing kernel and wavelet particle methods for elastic and

plastic problems, in Advanced Computational Methods for Material Modeling, Benson, D. J., Ed.,
180/PVP 268 ASME, 1993, 175–190.

1238_frame_REF Page 680 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

Liu, W. K., Jun, S., and Zhang, Y., Reproducing kernel particle methods, Int. J. Numer. Methods Fluids,

20, 1081–1106, 1995.

Liu, W. K. et al., Advances in multiple scale kernel particle methods, Comput. Mech., 18, 73–111, 1996.
Liu, W. K. et al., Multiresolution reproducing kernel particle method for computational fluid dynamics,

Int. J. Numer. Methods Fluids, 24, 1–25, 1997a.

Liu, W. K. et al., Multiresolution reproducing kernel particle method for computational fluid dynamics,

Int. J. Numer. Methods Fluids, 24, 1391–1415, 1997b.

Liu, W. K., Li, S. F., and Belytschko, T., Moving least-square reproducing kernel methods. I. Meth-

odology and convergence, Comput. Methods Appl. Mech. Eng., 143, 113–154, 1997c.

Lu, Y. Y., Belytschko, T., and Gu, L., A new implementation of the element free Galerkin method,

Comput. Methods Appl. Mech. Eng., 113, 397–414, 1994.

Lucy, L., A numerical approach to testing the fission hypothesis, Astron. J., 82, 1013–1024, 1977.
Melenk, J. M. and Babu ka, I., The Partition of Unity Finite Element Method: Basic Theory and

Applications, TICAM Report 96-01, University of Texas, Austin, 1996.

Monaghan, J. J., Why particle methods work, Siam J. Sci. Sat. Comput., 3(4), 423–433, 1982.
Monaghan, J. J., SPH Meets the Shocks of Noh, Monash University Paper, Melbourne, Australia, 1987.
Monaghan, J. J., An introduction to SPH, Comput. Phys. Commun., 48, 89–96, 1988.
Monaghan, J. J., On the problem of penetration in particle methods, J. Comput. Phys., 82, 1–15, 1989.
Monaghan, J. J., Smoothed particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 543–574, 1992.
Monaghan, J. J., Simulating free surface flows with SPH, J. Comput. Phys., 110, 399–406, 1994.
Monaghan, J. J., Heat Conduction with Discontinuous Conductivity, Applied Mathematics Reports

and Preprints 95/18, Monash University, Melbourne, Australia, 1995.

Monaghan, J. J., An introduction to SPH, Comput. Phys. Commun., 48, 89–96, 1998.
Monaghan, J. J. and Gingold, R. A., Shock simulation by the particle method SPH, J. Comput. Phys.,

52, 374–389, 1993.

Monaghan, J. J. and Kocharyan, A., SPH simulation of multi-phase flow, Comput. Phys. Commun.,

87, 225–235, 1995.

Monaghan, J. J. and Poinracic, J., Artificial viscosity for particle methods, Appl. Numer. Math., 1,

187–194, 1985.

Morris, J. P. and Monaghan, J. J., A switch to reduce SPH viscosity, J. Comput. Phys., 136, 41–50, 1997.
Morris, J. P., Patrick, J. F., and Zhu, Y., Modeling lower Reynolds number incompressible flows using

SPH, J. Comput. Phys., 136, 214–226, 1997.

MSC/Dytran User’s Manual, version 4, The MacNeal-Schwindler Corporation, 1997.
Mukherjee, Y. X. and Mukherjee, S., Boundary node method for potential problems, Int. J. Numer.

Methods Eng., 40, 797–815, 1997a.

Mukherjee, Y. X. and Mukherjee, S., On boundary conditions in the element-free Galerkin method,

Comput. Mech., 19, 264–270, 1997b.

Nagashima, T., Node-by-node meshless approach and its application to structural analyses, Int. J.

Numer. Methods Eng., 46, 341–385, 1999.

Nayroles, B., Touzot, G., and Villon, P., Generalizing the finite element method: diffuse approxima-

tion and diffuse elements, Comput. Mech., 10, 307–318, 1992.

Nelson, R. P. and Papaloizou, J. C. B., Variable smoothing lengths and energy conservation in

smoothed particle hydrodynamics, Mon. Not. R. Astron. Soc., 270, 1–20, 1994.

Noguchi, H., Kawashima, T., and Miyamura, T., Element free analyses of shell and spatial structures,

Int. J. Numer. Methods Eng., 47, 1215–1240, 2000.

Oden, J. T. and Abani, P., A Parallel Adaptive Strategy for hp Finite Element Computations, TICAM

Rep. 94-06, University of Texas, Austin, 1994.

Onate, E. et al., A finite point method in computational mechanics applications to convective

transport and fluid flow, Int. J. Numer. Methods Eng., 39, 3839–3866, 1996.

Organ, D. et al., Continuous meshless approximations for nonconvex bodies by diffraction and

transparency, Comput. Mech., 18(3), 225–235, 1996.

Orkisz, J., Finite difference method, in Handbook of Computational Solid Mechanics, Kleiber, M., Ed.,

Springer-Verlag, Berlin, 1998.

Ouatouati, A. E. and Johnson, D. A., A new approach for numerical modal analysis using the element

free method, Int. J. Numer. Methods Eng., 46, 1–27, 1999.

sˇ

1238_frame_REF Page 681 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

Ozakca, M. and Hinton, E., Free vibration analysis and optimization of axisymmetrical plates and

shells—I. Finite element formulation, Comput. Struct., 52, 1181–1197, 1994.

Petyt, M., Vibration of curved plates, J. Sound Vib., 15, 381–395, 1971.
Petyt, M., Introduction to Finite Element Vibration Analysis, Cambridge University Press, Cambridge,

1990.

Poulos, H. G. and Davis, E. H., Elastic Solution for Soil and Rock Mechanics, Wiley, London, 1974.
Powell, M. J. D., The theory of radial basis function approximation in 1990, in Advances in Numerical

Analysis, Light, F. W., Ed., Oxford University Press, Oxford, 1992, 303–322.

Radovitzky, R. M. O., Error estimation and adaptive meshing in strongly nonlinear dynamic prob-

lems, Comput. Methods Appl. Mech. Eng., 172, 203–240, 1999.

Randles, P. W. et al., Calculation of oblique impact and fracture of tungsten cubes using smoothed

particle hydrodynamics, Int. J. Impact Eng., 17, 1995.

Randles, P. W. and Libersky, L. D., Smoothed particle hydrodynamics—some recent improvements

and applications, Comput. Methods Appl. Mech. Eng., 138, 375–408, 1996.

Reddy, J. N., A simple higher-order theory for laminated composite plates, J. Appl. Mech., 51, 745–752,

1984.

Reddy, J. N., Finite Element Method, John Wiley & Sons, New York, 1993.
Reddy, J. N., Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton,

FL, 1997.

Reddy, J. N., Theory and Analysis of Elastic Plates, Taylor & Francis, Philadelphia, PA, 1999.
Rippa, S., An algorithm for selecting a good value for the parameter c in radial basis function

interpolation, Adv. Comput. Math., 1, 193–210, 1999.

Robert, D. B., Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold, New York, 1979.
Schaback, R., Approximation of polynomials by radial basis functions, in Wavelets, Images and Surface

Fitting, Laurent, P. J., Mehaute, L., and Schumaker, L. L., Eds., A. K. Peters Ltd. Wellesley, MA,
1994, 459–466.

Schiffman, R. L. and Gibson, R. E., Consolidation of non-homogeneous clay layers, Proc. ASCE,

JSMFD, 90(SM5), 1964.

Schinzinger, R. and Laura, P. A. A., Conformal Mapping Methods and Applications, Elsevier Science,

New York, 1991.

Senthilnathan, N. R., A Simple Higher-Order Shear Deformation Plate Theory, Ph.D. thesis, National

University of Singapore, Singapore, 1989.

Sharan, M., Kansa, E. J., and Gupta, S., Application of the multiquadric method for numerical

solution of elliptic partial differential equations, Appl. Math. Comput., 84, 275–302, 1997.

Shin, Y. S. and Chisum, J. E., Modeling and simulation of underwater shock problems using a

coupled Lagrangian–Eulerian analysis approach, Shock Vib., 4, 1–10, 1997.

Shu, C., Application of differential quadrature method to simulate natural convection in a concentric

annulus, Int. J. Numer. Methods Fluids, 30, 977–993, 1999.

Simo, J. and Fox, D. D., On a stress resultant geometrically exact shell model, Part I: formulation

and optimal parameterization, Comput. Methods Appl. Mech. Eng., 72, 267–304, 1989.

Simo, J., Fox, D. D., and Rifai, M. S., On a stress resultant geometrically exact shell model, Part II:

The linear theory; computational aspects, Comput. Methods Appl. Mech. Eng., 73, 53–92, 1989.

Sneddon, I. N., The symmetrical vibrations of a thin elastic plate, Proc. Cambridge Philos. Soc., 41,

27–43, 1945.

Song, B. et al., Application of finite point method to fluid flow and heat transfer, in Proc. 4th Asia-

Pacific Conference on Computational Mechanics, December, Singapore, 1999, 1091–1096.

Srinivas, S., Kameswara Rao, A. K., and Joga Rao, C. V., Flexure of simply-supported thick homo-

geneous and laminated rectangular plates, ZAMM, 49, 449–458, 1969.

Steinmetz, M. and Muller, E., On the capabilities and limits of smoothed particle hydrodynamics,

Astron. Astrophys., 268, 391–410, 1993.

Strang, G., Linear Algebra and Its Application, Academic Press, New York, 1976.
Subir, K. S. and Gould, P. L., Free vibration of shells of revolution using FEM, J. Eng. Mech. Div.

ASCE EM2, 100, 283–303, 1974.

Swegle, J. W. and Attaway, S. W., On the feasibility of using smoothed particle hydrodynamics for

underwater explosion calculations, Comput. Mech., 17, 151–168, 1995.

1238_frame_REF Page 682 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC

Takeda, H., Miyama, S. M., and Sekiya, M., Numerical simulation of viscous flow by smoothed

particle hydrodynamics, Prog. Theor. Phys., 92(5), 939–959, 1994.

Terzaghi, K. and Peck, R. B., Soil Mechanics in Engineering Practice, 2nd ed., John Wiley & Sons,

New York, 1976.

Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 1970.
Timoshenko, S. P. and James, M. G., Theory of Elastic Stability, McGraw-Hill, Singapore, 1985.
Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd ed., McGraw-Hill,

New York, 1995.

Tou, S. K. and Wong, K. K., High-precision finite element analysis of cylindrical shells, Comput.

Struct., 26, 847–854, 1987.

Tu, Z. H. and Liu, G. R., An error estimate based on background cells for meshless methods, in

Advances in Computational Engineering and Sciences, Atluri, S. N. and Brust, F. W., Eds., Tech
Science Press, Palmdale, CA, 2000, 1487–1492.

Uras, R. A. et al., Multiresolution reproducing kernel particle methods in acoustics, J. Comput. Acoust.,

5(1), 71–94, 1997.

Wang, C. M. et al., Buckling of rectangular Mindlin plates with internal line supports, Int. J. Solids

Struct., 30, 1–17, 1993.

Wang, C. M., Reddy, J. N., and Lee, K. H., Shear Deformable Beams and Plates (Relationships with

Classical Solutions), Elsevier, Singapore, 2000.

Wang, J. G. and Liu, G. R., Radial point interpolation method for elastoplastic problems, in Proc. 1st

Int. Conf. on Structural Stability and Dynamics, December 7–9, Taipei, Taiwan, 2000, 703–708.

Wang, J. G. and Liu, G. R., Radial point interpolation method for no-yielding surface models, in

Proc. First MIT Conference on Computational Fluid and Solid Mechanics, 12–14 June, 2001a,
538–540.

Wang, J. G. and Liu, G. R., A point interpolation meshless method based on radial basis functions,

Int. J. Numer. Methods Eng., 2001b (in press).

Wang, J. G. and Liu, G. R., On the optimal shape parameters of radial basis functions used for 2D

meshless methods, Comput. Method Appl. Mech. Engrg., 191, 2611–2630, 2002.

Wang, J. G., Liu, G. R., and Wu, Y. G., A point interpolation method for simulating dissipation

process of consolidation, Comput. Methods Appl. Mech. Eng., 190, 5907–5922, 2001.

Wendland, H., Error estimates for interpolation by compactly supported radial basis functions of

minimal degree, J. Approx. Theor., 93, 258–396, 1998.

Whitworth, A. P. et al., Estimating density in smoothed particle hydrodynamics, Astron. Astrophys.,

301, 929–932, 1995.

Xu, X. G. and Liu, G. R., A local-function approximation method for simulating two-dimensional

incompressible flow, in Proc. 4th International Asia-Pacific Conference on Computational Mechanics,
December, Singapore, 1999, 1021–1026.

Yagawa, G. and Yamada, T., Free mesh method, a kind of meshless finite element method, Comput.

Mech., 18, 383–386, 1996.

Yagawa, G., Yamada, T., and Furukawa, T., Parallel computing with free mesh method: Virtually

meshless FEM, in IUTAM Symp., Solid Mechanics and Its Applications, Mang, H. A. and
Rammerstorfer, F. G. Eds., Kluwer, Dordrecht, 1997, 165–172.

Yang, H. T. Y., Saigal, S., and Liaw, D. G., Advances of thin shell finite elements and some applications—

version I, Comput. Struct., 35, 481–504, 1990.

Zhang, S. Z. et al., Detonation and Its Applications, Press of National Defense Industry, Beijing, 1976.
Zhu, T. and Atluri, S. N., A modified collocation and a penalty formulation for enforcing the essential

boundary conditions in the element free Galerkin method, Comput. Mech., 21, 211–222, 1998.

Zienkiewicz, O. C., The Finite Element Method, 4th ed., McGraw-Hill, London, 1989.

1238_frame_REF Page 683 Wednesday, June 12, 2002 5:46 PM

© 2003 by CRC Press LLC