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ASTM Selected Technical Papers
Fracture Mechanics: Nineteenth Symposium
By
TA Cruse
TA Cruse
1
Southwest Research Institute
,
San Antonio, TX 78284
;
symposium chairman and editor
.
Search for other works by this author on:
ISBN-10:
0-8031-0972-5
ISBN:
978-0-8031-0972-8
No. of Pages:
952
Publisher:
ASTM International
Publication date:
1988

The theoretical basis and performance characteristics of two new methods for the computation of the coefficients of the terms of asymptotic expansions at reentrant corners from finite-element solutions are presented. The methods, called the contour integral method (CIM) and the cutoff function method (CFM), are very efficient: the coefficients converge to their true values as fast as the strain energy, or faster.

In order to make the presentation as simple as possible, we assume that the elastic body is homogeneous and isotropic, is loaded by boundary tractions only, and, in the neighborhood of the reentrant corner, has stress-free boundaries. The methods described herein can be adapted to cases without such restrictions.

1.
Babuška
,
I.
and
Szabó
,
B.
, “
On the Rates of Convergence of the Finite Element Method
,”
International Journal for Numerical Methods in Engineering
 0029-5981, Vol.
18
,
1982
, pp. 323-341.
2.
Babuška
,
I.
,
Gui
,
W.
, and
Szabó
,
B. A.
, “
Performance of the h, p, and h-p Versions of the Finite Element Method
,”
Research in Structures and Dynamics
,
Hayduk
R. J.
and
Noor
A. K.
, Eds. NASA Conference Publication
2335
,
National Aeronautics and Space Administration
,
Washington, DC
,
1984
, pp. 73-93.
3.
Gui
,
W.
, “
The h-p Version of the Finite Element Method for the One-Dimensional Problem
,” doctoral dissertation,
University of Maryland
, College Park, MD,
1985
.
4.
Guo
,
B.
and
Babuška
,
I.
, “
The h-p Version of the Finite Element Method: Part I—Basic Approximation Results. Part II—General Results and Applications
,”
Computational Mechanics
,
Springer-Verlag
,
New York
,
1986
.
5.
Szabó
,
B.
, “
Estimation and Control of Error Based on P-Convergence
,”
Accuracy Estimates and Adaptive Refinements in Finite Element Computations
,
Babuška
I.
,
Gago
J.
,
Oliveira
E. R. de A.
, and
Zienkiewicz
O. C.
, Eds.,
Wiley
,
New York
,
1986
, pp. 61-78.
6.
Szabó
,
B. A.
, “
Implementation of a Finite Element Software System with H- and P-Extension Capabilities
,”
Finite Elements in Analysis and Design
, Vol.
2
,
1986
, pp. 177-194.
7.
Szabó
,
B. A.
, “
Mesh Design for the p-Version of the Finite Element Method
,”
Computer Methods in Applied Mechanics and Engineering
 0045-7825, Vol.
55
,
1986
, pp. 181-197.
8.
Babuška
,
I.
and
Suri
,
M.
, “
The Optimal Convergence Rate of the p-Version of the Finite Element Method
,” Technical Note BN-1045,
Laboratory for Numerical Analysis, Institute for Physical Science and Technology, University of Maryland
,
College Park, MD
,
10
1985
.
9.
Babuška
,
I.
and
Miller
,
A.
, “
The Post-Processing Approach in the Finite Element Method: Part 1—Calculation of Displacements, Stresses, and Other Higher Derivatives of the Displacements
,”
International Journal for Numerical Methods in Engineering
 0029-5981, Vol.
20
,
1984
, pp. 1085-1109.
10.
Babuška
,
I.
and
Miller
,
A.
, “
The Post-Processing Approach in the Finite Element Method: Part 2—The Calculation of Stress Intensity Factors
,”
International Journal for Numerical Methods in Engineering
 0029-5981, Vol.
20
,
1984
, pp. 1111-1129.
11.
Babuška
,
I.
and
Miller
,
A.
, “
The Post-Processing Approach in the Finite Element Method: Part 3—A-Posteriori Error Estimates and Adaptive Mesh Selection
,”
International Journal for Numerical Methods in Engineering
 0029-5981, Vol.
20
,
1984
, pp. 2311-2324.
12.
Karp
,
S. N.
and
Karal
,
F. C.
, “
The Elastic-Field Behavior in the Neighborhood of a Crack of Arbitrary Angle
,”
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,
1962
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Kondratev
,
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, “
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,”
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,
1967
, pp. 227-313.
14.
Melzer
,
H.
and
Rannacher
,
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, “
Spannungskonzentrationen in Eckpunkten der Kirchhoffschen Platte
,”
Bauingenieur
 0005-6650, Vol.
55
,
1980
, pp. 181-184.
15.
Muskhelishvili
,
N. I.
, “
Some Basic Problems of the Mathematical Theory of Elasticity
,”
P. Noordhoff Ltd.
,
Groningen, Holland
,
1953
.
16.
Williams
,
M. L.
, “
Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension
,”
Journal of Applied Mechanics
 0021-8936,
1952
, pp. 526-528.
17.
Szabó
,
B. A.
,
PROBE: Theoretical Manual
,
Noetic Technologies Corp.
,
St. Louis, MO
,
1985
.
18.
Izadpanah
,
K.
, “
Computation of the Stress Components in the P-Version of the Finite Element Method
,” doctoral dissertation,
Washington University
, St. Louis, MO,
1984
.
19.
Vasilopoulos
,
D.
, “
Treatment of Geometric Singularities with the P-Version of the Finite Element Method
,” doctoral dissertation,
Washington University
, St. Louis, MO,
1984
.
20.
Paris
,
P. C.
and
Sih
,
G. C.
, “
Stress Analysis of Cracks
,”
Fracture Toughness Testing and Its Application
, ASTM STP 381,
American Society for Testing and Materials
,
Philadelphia
,
1970
, pp. 30-81.
21.
Sha
,
G. T.
and
Yang
,
C-T.
, “
Weight Function Calculations for Mixed-Mode Fracture Problems with the Virtual Crack Extension Technique
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
21
,
1985
, pp. 1119-1149.
22.
Andersson
,
B.
,
Memorandum
 FFAP-H-736,
The Aeronautical Research Institute of Sweden
,
Bromma, Sweden
, 19 March, 1985.
23.
Rybicki
,
E. F.
and
Kanninen
,
M. F.
, “
A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
9
,
1977
, pp. 931-938.
24.
Dempsey
,
J. P.
and
Sinclair
,
G. B.
, “
On the Singular Behavior at the Vertex of a Bi-Material Wedge
,”
Journal of Elasticity
, Vol.
11
,
1981
, pp. 317-327.
25.
Babuška
,
I.
and
Rank
,
M.
, “
An Expert System-like Feedback Approach in the h-p Version of the Finite Element Method
,” Technical Note,
Laboratory for Numerical Analysis, Institute for Physical Science and Technology, University of Maryland
,
College Park, MD
,
04
1986
.
26.
Whitney
,
J. M.
and
Nuismer
,
R. J.
, “
Stress Fracture Criteria for Laminated Composities Containing Stress Concentrations
,”
Journal of Composite Materials
 0021-9983, Vol.
8
,
1974
, pp. 253-265.
27.
Nuismer
,
R. J.
and
Whitney
,
J. M.
, “
Uniaxial Failure of Composite Laminates Containing Stress Concentrations
,” in
Fracture Mechanics of Composites
, ASTM STP 593,
American Society for Testing Materials
,
Philadelphia
,
1975
, p. 117.
28.
Potter
,
R. T.
, “
On the Mechanism of Tensile Fracture in Notched Fibre Reinforced Plastics
,”
Proceedings of the Royal Society
,
A361
,
1978
, pp. 325-341.
29.
Nuismer
,
R. J.
and
Labor
J. D.
, “
Applications of Average Stress Failure Criterion: Part I—Tension
,”
Journal of Composite Materials
 0021-9983, Vol.
12
,
1978
, p. 238.
30.
Nuismer
,
R. J.
, “
Applications of Average Stress Failure Criterion: Part II—Compression
,”
Journal of Composite Materials
 0021-9983, Vol.
13
,
1979
, pp. 49-60.
31.
Mikulas
,
M. M.
, “
Failure Prediction Techniques for Compression Loaded Laminates with Holes
,” NASA Conference Publication
2142
,
National Aeronautics and Space Administration
,
Washington, DC
,
1980
.
32.
Szabó
,
B. A.
, “
Computation of Stress Field Parameters in Areas of Steep Stress Gradients
,”
Communications in Applied Numerical Methods
 0748-8025, Vol.
2
,
1986
, pp. 133-137.
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