The reproducing kernel particle method (RKPM) has attractive properties in handling high gradients, concentrated forces, and large deformations where other widely implemented methodologies fail. In the present work, a multiple field computational procedure is devised to enrich the finite element method with RKPM, and RKPM with analytical functions. The formulation includes an interaction term that accounts for any overlap between the fields, and increases the accuracy of the computational solutions in a coarse mesh or particle grid. By replacing finite element method shape Junctions at selected nodes with higher-order RKPM window functions, RKPM p-enrichment is obtained. Similarly, by adding RKPM window functions into a finite element method mesh, RKPM hp-enrichment is achieved analogous to adaptive refinement. The fundamental concepts of the multiresolution analysis are used to devise an adaptivity procedure.

Issue Section:
Technical Papers
Topics:
Finite element methods, Particulate matter, Deformation, Junctions, Shapes
1.
Belytschko
T.
,
Lu
Y. Y.
, and
Gu
L.
,
1994
a, “
Element Free Galerkin Methods
,”
International Journal for Numerical Methods in Engineering
, Vol.
37
, pp.
229
–
256
.
2.
Belytschko
T.
,
Lu
Y. Y.
, and
Gu
L.
,
1994
b, “
A New Implementation of the Element Free Galerkin Method
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
113
, pp.
397
–
414
.
3.
Belytschko
T.
,
Gu
L.
, and
Lu
Y. Y.
,
1994
c, “
Fracture and Crack Growth by EFG Methods
,”
Modeling Simul. Mater. Sci. Eng.
, Vol.
2
, pp.
519
–
534
.
4.
Gingold
R. A.
, and
Monaghan
J. J.
,
1977
, “
Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars
,”
Mort. Not. Roy. Astron. Soc.
, Vol.
181
, pp.
375
–
389
.
5.
Hughes, T. J. R., 1987, The Finite Element Method, Prentice-Hall Inc., Englewood Cliffs, NJ.
6.
Krongauz, Y., and Belytschko, T., 1996, “Enforcement of Essential Boundary Conditions in Meshless Approximation using Finite Element Method,” Computer Methods in Applied Mechanics and Engineering, accepted for publication.
7.
Liu, W. K., and Oberste-Brandenburg, C., 1993, “Reproducing Kernel and Wavelet Particle Methods,” Aerospace Structures: Nonlinear Dynamics and System Response, J. P. Cusumano, C. Pierre, and S. T. Wu, eds., ASME, New York, pp. 39–56.
8.
Liu, W. K., Adee, J., and Jun, S., 1993a, “Reproducing Kernel Particle Methods for Elastic and Plastic Problems,” Advanced Computational Methods for Material Modeling, D. J. Benson and R. A. Asaro, eds., ASME, New York, pp.175–190.
9.
Liu
W. K.
,
1995
, “
Feature Article on An Introduction to Wavelet Reproducing Kernel Particle Methods
,”
USACM Bulletin
, Vol.
8
, No.
1
, pp.
3
–
16
.
10.
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
.
11.
Liu
W. K.
,
Jun
S.
,
Li
S.
,
Adee
J.
, and
Belytschko
T.
,
1995
a, “
Reproducing Kernel Particle Methods for Structural Dynamics
,”
International Journal of Numerical Methods for Engineering
, Vol.
38
, pp.
1655
–
1679
.
12.
Liu
W. K.
,
Jun
S.
, and
Zhang
Y. F.
,
1995
b, “
Reproducing Kernel Particle Methods
.”
International Journal of Numerical Methods in Fluids
, Vol.
20
, pp.
1081
–
1106
.
13.
Liu, W. K., Belytschko, T., and Oden, J. T., eds, 1996, “Meshless Methods,” Computer Methods in Applied Mechanics and Engineering, Vol. 139.
14.
Liu
W. K.
,
Chen
Y.
,
Chang
C. T.
, and
Belytschko
T.
,
1996
a, “
Advances in Multiple Scale Kernel Particle Methods
,”
Computational Mechanics
(An International Journal, A Special Feature Article for the 10th Anniversary Volume of Computational Mechanics), Vol.
18
,
73
–
111
.
15.
Liu
W. K.
,
Chen
Y.
,
Jun
S.
,
Chen
J. S.
,
Belytschko
T.
,
Pan
C.
,
Uras
R. A.
, and
Chang
C. T.
,
1996
b “
Overview and Applications of the Reproducing Kernel Particle Methods
,”
Archives of Computational Methods in Engineering, State of the Art Reviews
, Vol.
3
, pp.
3
–
80
.
16.
Liu
W. K.
,
Chen
Y.
,
Uras
R. A.
, and
Chang
T. C.
,
1996
c, “
Generalized Multiple Scale Reproducing Kernel Particle Methods
,”
Computer Methods in Applied and Engineering
, Vol.
139
, pp.
91
–
157
.
17.
Liu
W. K.
,
Jun
S.
,
Sihling
D. T.
,
Chen
Y.
, and
Hao
W.
,
1997
a, “
Multiresolution Reproducing Kernel Particle Method for Computational Fluid Dynamics
,”
International Journal of Numerical Methods in Fluids
, Vol.
24
, pp.
1391
–
1415
.
18.
Liu
W. K.
,
Li
S.
, and
Belytschko
T.
,
1997
b, “
Moving Least Square Kernel Galerkin Method (I) Methodology and Convergence
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
143
, pp.
113
–
154
.
19.
Lucy
L.
,
1977
, “
A Numerical Approach to Testing the Fission Hypothesis
,”
Astronomical Journal
, Vol.
82
, pp.
1013
–
1024
.
20.
Sulsky
D.
, and
Schreyer
H. L.
,
1996
, “
Axisymmetric Form of the Material Point Method with Applications to Upsetting and Taylor Impact Problems
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
139
, pp.
409
–
430
.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.