Finite element analysis (FEA) has become the method of choice for the stress analysis of many of the complex configurations encountered in practice. Such configurations can contain stress singularities. Then, it is critical for the necessarily finite estimates from finite elements to be rejected as valid results for the infinite stresses present. There is an extensive literature devoted to the asymptotic identification of stress singularities that can often, but not always, provide a means for such rejection. The present study seeks to offer a further means of rejection: mesh refinement with divergence checks. These divergence checks are a natural counterpart to the convergence checks of ASME. The two are used together on 265 finite element stresses at 32 different singularities: all of these finite element stresses are thus rejected.

References

1.
Williams
,
M. L.
,
1952
, “
Stress Singularities Resulting From Various Boundary Conditions of Plates in Extension
,”
ASME J. Appl. Mech.
,
19
(
4
), pp.
526
528
.
2.
Sinclair
,
G. B.
,
2004
, “
Stress Singularities in Classical Elasticity—II: Asymptotic Identification
,”
ASME Appl. Mech. Rev.
,
57
(
5
), pp.
385
439
.
3.
Mittelstedt
,
C.
, and
Becker
,
W.
,
2007
, “
Free-Edge Effects in Composite Laminates
,”
ASME Appl. Mech. Rev.
,
60
(
5
), pp.
217
245
.
4.
Paggi
,
M.
, and
Carpinteri
,
A.
,
2008
, “
On the Stress Singularities at Multimaterial Interfaces and Related Analogies With Fluid Dynamics and Diffusion
,”
ASME Appl. Mech. Rev.
,
61
(
2
), p.
020801
.
5.
Erdogan
,
F.
, and
Ozturk
,
M.
,
2008
, “
On the Singularities in Fracture and Contact Mechanics
,”
ASME J. Appl. Mech.
,
75
(
5
), p.
051111
.
6.
Carpinteri
,
A.
, and
Paggi
,
M.
,
2009
, “
Asymptotic Analysis in Linear Elasticity: From the Pioneering Studies by Wieghardt and Irwin Until Today
,”
Eng. Fract. Mech.
,
76
(
12
), pp.
1771
1784
.
7.
Pook
,
L. P.
,
2013
, “
A 50-Year Retrospective Review of Three-Dimensional Effects at Cracks and Sharp Notches
,”
Fatigue Fract. Eng. Mater. Struct.
,
36
(
8
), pp.
699
723
.
8.
Bui
,
H. D.
, and
Queslati
,
A.
,
2005
, “
The Sliding Interface Crack With Friction Between Elastic and Rigid Bodies
,”
J. Mech. Phys. Solids
,
53
(
6
), pp.
1397
1421
.
9.
Kotousov
,
A.
,
2005
, “
On the Stress Singularities at Angular Corners of Plates of Arbitrary Thickness Under Tension
,”
Int. J. Fract.
,
132
(
3
), pp.
29
36
.
10.
Carpinteri
,
A.
, and
Paggi
,
M.
,
2005
, “
On the Asymptotic Stress Field in Angularly Nonhomogeneous Materials
,”
Int. J. Fract.
,
135
(
1–4
), pp.
267
283
.
11.
Mittelstedt
,
C.
, and
Becker
,
W.
,
2005
, “
Asymptotic Analysis of Stress Singularities in Composite Laminates by the Boundary Finite Element Method
,”
Comp. Struct.
,
71
(
2
), pp.
210
219
.
12.
Prukvilailert
,
M.
, and
Koguchi
,
H.
,
2005
, “
Stress Singularity Analysis Around the Singular Point on the Stress Singularity Line in Three-Dimensional Joints
,”
Int. J. Solids Struct.
,
42
(
11–12
), pp.
3059
3074
.
13.
Shahani
,
A. R.
,
2005
, “
Some Problems in the Antiplane Shear Deformation of Bi- Material Wedges
,”
Int. J. Solids Struct.
,
42
(
11–12
), pp.
3093
3113
.
14.
Carpinteri
,
A.
, and
Paggi
,
M.
,
2006
, “
Influence of the Intermediate Material on the Singular Stress Field in Trimaterial Junctions
,”
Mater. Sci.
,
42
(
1
), pp.
95
101
.
15.
Huang
,
C. S.
,
2006
, “
Analysis of Stress Singularities at Bi-Material Corners in Reddy's Theory of Plate Bending
,”
J. Mech.
,
22
(
1
), pp.
67
75
.
16.
Mittelstedt
,
C.
, and
Becker
,
W.
,
2006
, “
Efficient Computation of Order and Mode of Three-Dimensional Stress Singularities in Linear Elasticity by the Boundary Finite Element Method
,”
Int. J. Solids Struct.
,
43
(
10
), pp.
2868
2903
.
17.
Kotousov
,
A.
, and
Lew
,
Y. T.
,
2006
, “
Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates of Arbitrary Thickness in Extension
,”
Int. J. Solids Struct.
,
43
(
17
), pp.
5100
5109
.
18.
Linkov
,
A. M.
, and
Koshelev
,
V. F.
,
2006
, “
Multi-Wedge Points and Multi-Wedge Elements in Computational Mechanics: Evaluation of Exponent and Angular Distribution
,”
Int. J. Solids Struct.
,
43
(
18–19
), pp.
5909
5930
.
19.
Carpinteri
,
A.
, and
Paggi
,
M.
,
2007
, “
Analytical Study of the Singularities Arising at Multi-Material Interfaces in 2D Linear Elastic Problems
,”
Eng. Fract. Mech.
,
74
(
1–2
), pp.
59
74
.
20.
Fu
,
G.
,
2007
, “
An Extension to Hertz's Theory in Contact Mechanics
,”
ASME J. Appl. Mech.
,
74
(
2
), pp.
373
374
.
21.
Huang
,
C. S.
, and
Leissa
,
A. W.
,
2008
, “
Stress Singularities of Bimaterial Bodies of Revolution
,”
Comp. Struct.
,
82
(
4
), pp.
488
498
.
22.
Loveikin
,
A. V.
, and
Ulitko
,
A. F.
,
2009
, “
On the Stress Field Singularity in an Incompressible Half-Space Weakened by Two Near-Surface Wedge-Like Cracks
,”
Mech. Solids
,
44
(
4
), pp.
585
595
.
23.
Andreev
,
A. V.
,
2009
, “
Method for Determining Power-Type Complex Singularities in Solutions of Singular Integral Equations With Generalized Kernels and Complex Conjugate Unknowns
,”
Mech. Solids
,
44
(
5
), pp.
691
704
.
24.
Sinclair
,
G. B.
,
2009
, “
A Note on the Influence of Cohesive Stress-Separation Laws on Elastic Stress Singularities in Antiplane Shear
,”
J. Elasticity
,
94
(
1
), pp.
87
93
.
25.
Karihaloo
,
B. L.
, and
Xiao
,
Q. Z.
,
2010
, “
Asymptotic Fields Ahead of Mixed Mode Frictional Cohesive Cracks
,”
Z. Angew. Math. Mech.
,
90
(
9
), pp.
710
720
.
26.
Koguchi
,
H.
, and
da Costa
,
J. A.
,
2010
, “
Analysis of the Stress Singularity at a Vertex in 3D-Bonded Structures Having a Slanted Side Surface
,”
Int. J. Solids Struct.
,
47
(
22–23
), pp.
3131
3140
.
27.
Li
,
Z. L.
, and
Wang
,
C.
,
2010
, “
Particular Solutions of a Two-Dimensional Infinite Wedge for Various Boundary Conditions With Weak Singularity
,”
ASME J. Appl. Mech.
,
77
(
1
), p.
011004
.
28.
Paggi
,
M.
,
Carpinteri
,
A.
, and
Orta
,
R.
,
2010
, “
A Mathematical Analogy and a Unified Asymptotic Formulation for Singular Elastic and Electromagnetic Fields in Multimaterial Wedges
,”
J. Elast.
,
99
(
2
), pp.
131
146
.
29.
Andrianov
,
I. V.
,
Starushenko
,
G. A.
, and
Weichert
,
D.
,
2011
, “
Asymptotic Analysis of Thin Interface in Composite Materials With Coated Boundary
,”
Tech. Mech.
,
31
(
1
), pp.
33
41
.
30.
Sator
,
C.
, and
Becker
,
W.
,
2011
, “
On Stress Singularities at Plane Bi- and Tri- Material Junctions—A Way to Derive Some Closed-Form Analytical Solutions
,”
Procedia Eng.
,
10
(
1
), pp.
141
146
.
31.
Carpinteri
,
A.
, and
Paggi
,
M.
,
2011
, “
Singular Harmonic Problems at a Wedge Vertex: Mathematical Analogies Between Elasticity, Diffusion, Electromagnetism and Fluid Dynamics
,”
J. Mech. Mater. Struct.
,
6
(
1–4
), pp.
113
125
.
32.
Linkov
,
A.
, and
Rybarska-Rusinek
,
L.
,
2011
, “
Interface Conditions Simulating Influence of a Thin Elastic Wedge With Smooth Contacts
,”
Arch. Appl. Mech.
,
81
(
9
), pp.
1203
1214
.
33.
Reedy
,
E. D.
,
2011
, “
Singular Stress Fields of the Intersection of a Grain Boundary and a Stress-Free Edge in a Columnar Polycrystal
,”
ASME J. Appl. Mech.
,
78
(
1
), p.
014502
.
34.
Rössle
,
A.
, and
Sändig
,
A.-M.
,
2011
, “
Corner Singularities and Regularity Results for the Reissner/Mindlin Plate Model
,”
J. Elasticity
,
103
(
2
), pp.
113
135
.
35.
Lu
,
N.
,
Zhang
,
Z.
,
Yoon
,
J.
, and
Suo
,
Z.
,
2012
, “
Singular Stress Fields at Corners in Flip-Chip Packages
,”
Eng. Fract. Mech.
,
86
(
1
), pp.
38
47
.
36.
Sator
,
C.
, and
Becker
,
W.
,
2012
, “
Closed-Form Solutions for Stress Singularities at Plane Bi- and Trimaterial Junctions
,”
Arch. Appl. Mech.
,
82
(
5
), pp.
643
658
.
37.
Vasil'ev
,
T. A.
, and
Shaldyrvan
,
V. A.
,
2012
, “
Local Stress Singularities in Mixed Axisymmetric Problems of the Bending of Circular Cylinders
,”
Int. Appl. Mech.
,
48
(
2
), pp.
176
187
.
38.
Loveikin
,
A. V.
,
2013
, “
Specific Features of the Stress Behavior in an Incompressible Half-Space With Internal V-Shaped Crack Lying in a Plane Perpendicular to the Surface of the Half-Space With a Tip Reaching the Surface
,”
J. Math. Sci.
,
192
(
5
), pp.
593
607
.
39.
Luangarpa
,
C.
, and
Koguchi
,
H.
,
2013
, “
Intensity of Singularity in Three-Material Joints Under Shear Loading: Two Real Singularities and Power-Logarithmic Singularities
,”
Eur. J. Mech.—A/Solids
,
40
(
4
), pp.
60
68
.
40.
Sinclair
,
G. B.
, and
Kardak
,
A. A.
,
2013
, “
On the Stress Singularities at Clamped Butt Joints
,”
ASME J. Appl. Mech.
,
80
(
1
), p.
014501
.
41.
Yang
,
Y. Y.
,
2013
, “
Solutions of Dissimilar Material Contact Problems
,”
Eng. Fract. Mech.
,
100
(
3
), pp.
92
107
.
42.
Luangarpa
,
C.
, and
Koguchi
,
H.
,
2014
, “
Analysis of a Three-Dimensional Dissimilar Material Joint With One Real Singularity
,”
Int. J. Solids Struct.
,
51
(
15–16
), pp.
2908
2919
.
43.
Korepanova
,
T. O.
,
Matveenko
,
V. P.
, and
Shardakov
,
I. N.
,
2014
, “
Analytical Constructions of Eigensolutions for Isotropic Conical Bodies and Their Applications for Estimating Stress Singularity
,”
Dok. Phys.
,
59
(
7
), pp.
335
340
.
44.
Cheng
,
C. Z.
,
Han
,
Z. L.
,
Wang
,
D. P.
,
Niu
,
Z. R.
, and
Recho
,
N.
,
2015
, “
Singularity Analysis Near the Vertex of the V-Notch in Reissner's Plate by Coupling the Asymptotic Expansion Technique With the Interpolating Matrix Method
,”
Fatigue Fract. Eng. Mater. Struct.
,
38
(
3
), pp.
300
314
.
45.
He
,
Z.
,
Kotousov
,
A.
, and
Berto
,
F.
,
2015
, “
Effect of Vertex Singularities on Stress Intensities Near Plate Free Surfaces
,”
Fatigue Fract. Eng. Mater. Struct.
,
38
(
7
), pp.
860
869
.
46.
Dieringer
,
R.
, and
Becker
,
W.
,
2015
, “
A New Scaled Boundary Finite Element Formulation for the Computation of Singularity Orders at Cracks and Notches in Arbitrarily Laminated Composites
,”
Comp. Struct.
,
123
(
5
), pp.
263
270
.
47.
Sinclair
,
G. B.
,
2015
, “
On the Influence of Adhesive Stress-Separation Laws on Elastic Stress Singularities
,”
J. Elasticity
,
118
(
2
), pp.
187
206
.
48.
Tikhomirov
,
V. V.
,
2015
, “
Stress Singularity in a Top of Composite Wedge With Internal Functionally Graded Material
,”
St. Petersburg Poly. Univ. J.: Phys. Math
,
1
(
3
), pp.
278
286
.
49.
Zhou
,
M.
, and
Sun
,
L.
,
2015
, “
On the Corner Singularities in the Classical and Reissner-Mindllin Plate Theories
,”
IMA J. Appl. Math.
,
80
(
5
), pp.
1322
1335
.
50.
Felger
,
J.
, and
Becker
,
W.
,
2017
, “
A Complex Potential Method for the Asymptotic Solution of Wedge Problems Using First-Order Shear Deformation Plate Theory
,”
Eur. J. Mech.—A/Solids
,
61
(
1
), pp.
383
392
.
51.
Martin
,
P. A.
,
2017
, “
On Mixed Boundary-Value Problems in a Wedge
,”
Q. J. Mech. Appl. Math.
,
70
(
4
), pp.
373
386
.
52.
Zhou
,
Z.
,
Xu
,
W.
,
Leung
,
A. Y. T.
,
Rong
,
D.
, and
Xu
,
X.
,
2017
, “
A Study of Stress Singularities Arising at the Multi-Material Interface in a V-Notched Bending Plate
,”
Eng. Fract. Mech.
,
180
(
1
), pp.
179
194
.
53.
Fedorov
,
A. Y.
, and
Matveenko
,
V. P.
,
2018
, “
Investigation of Stress Behaviour in the Vicinity of Singular Points of Elastic Bodies Made of Functionally Graded Materials
,”
ASME J. Appl. Mech.
,
85
(
6
), p.
061008
.
54.
Juenger
,
J. A.
,
Peterson
,
S. C.
, and
Herzner
,
F. C.
,
1992
, “
Stress-Relieved Rotor Blade Attachment Slot
,” U.S. Patent No. 5,141,401.
55.
Dempsey
,
J. P.
, and
Sinclair
,
G. B.
,
1981
, “
On the Singular Behavior at the Vertex of a Bi-Material Wedge
,”
J. Elasticity
,
11
(
3
), pp.
317
327
.
56.
Dempsey
,
J. P.
,
1995
, “
Power-Logarithmic Stress Singularities at Bi-Material Corners and Interface Cracks
,”
J. Adhes. Sci. Technol.
,
9
(
2
), pp.
253
265
.
57.
Sinclair
,
G. B.
,
2004
, “
Stress Singularities in Classical Elasticity—I: Removal, Interpretation, and Analysis
,”
ASME Appl. Mech. Rev.
,
57
(
4
), pp.
251
297
.
58.
Sinclair
,
G. B.
,
Beisheim
,
J. R.
, and
Sezer
,
S.
,
2006
, “
Practical Convergence- Divergence Checks for Stresses From FEA
,”
International ANSYS Users Conference and Exhibition
, Pittsburgh, PA.https://www.ansys.com/-/media/ansys/corporate/resourcelibrary/conference-paper/2006-int-ansys-conf-28.pdf
59.
ASME,
2006
, “
Guide for Verification and Validation in Computational Solid Mechanics
,” American Society of Mechanical Engineers, New York, Standard No. ASME V&V 10.
60.
ASME
2012
, “
An Illustration of the Concepts of Verification and Validation in Computational Solid Mechanics
,” American Society of Mechanical Engineers, New York, Standard No. ASME V&V 10.1.
61.
Sinclair
,
G. B.
,
Beisheim
,
J. R.
, and
Roache
,
P. J.
,
2016
, “
Effective Convergence Checks for Verifying Finite Element Stresses at Two-Dimensional Stress Concentrations
,”
ASME J. Verif. Valid. Uncert. Quant
,
1
(
4
), p.
041003
.
62.
ANSYS
,
2016
, “
ANSYS Mechanical APDL Element Reference Guide Rev. 16.0
,” ANSYS, Canonsburg, PA.
63.
Sinclair
,
G. B.
,
Cormier
,
N. G.
,
Griffin
,
J. H.
, and
Meda
,
G.
,
2002
, “
Contact Stresses in Dovetail Attachments: Finite Element Modeling
,”
ASME J. Eng. Gas Turbines Power
,
124
(
1
), pp.
182
189
.
64.
Moaveni
,
S.
,
2015
,
Finite Element Analysis—Theory and Application With ANSYS
, 4th ed.,
Pearson Education
,
Essex, UK
.
65.
Aksentian
,
O. K.
,
1967
, “
Singularities of the Stress-Strain State of a Plate in the Neighborhood of an Edge
,”
J. Appl. Math. Mech.
,
31
(
1
), pp.
193
202
.
66.
Morrison
,
J. A.
, and
Lewis
,
J. A.
,
1976
, “
Charge Singularity at the Corner of a Flat Plate
,”
SIAM J. Appl. Math.
,
31
(
2
), pp.
233
250
.
67.
Sneddon
,
I. N.
,
1951
,
Fourier Transforms
,
McGraw-Hill
,
New York
.
68.
Love
,
A. E. H.
,
1939
, “
Boussinesq's Problem for a Rigid Cone
,”
Q. J. Math.
,
10
(
1
), pp.
161
175
.
69.
Kolossoff
,
G. V.
,
1914
, “
On Some Properties of the Plane Problem of Elasticity Theory
,”
Z. Math. Phys.
,
62
(
2
), pp.
384
409
.
70.
Inglis
,
C. E.
,
1913
, “
Stresses in a Plate Due to the Presence of Cracks and Sharp Corners
,”
Trans. Inst. Nav. Arch.
,
55
(
2
), pp.
219
241
.
71.
Neuber
,
H.
,
1946
,
Theory of Notch Stresses
,
J. W. Edwards
,
Ann Arbor, MI
.
72.
Kardak
,
A. A.
,
2015
, “
On an Effective Submodeling Procedure for Stresses Determined with Finite Element Analysis
,”
Ph.D. dissertation
, LSU, Baton Rouge, LA.https://digitalcommons.lsu.edu/gradschool_dissertations/306/
73.
Pilkey
,
W. D.
, and
Pilkey
,
D. F.
,
2008
,
Peterson's Stress Concentration Factors
, 3rd ed.,
Wiley
,
Hoboken, NJ
.
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