The accurate determination of stresses at two-dimensional (2D) stress risers is both an important and a challenging problem in engineering. Finite element analysis (FEA) has become the method of choice in making such determinations when new configurations with unknown stress concentrations are encountered in practice. For such FEA to be useful, discretization errors in peak stresses have to be sufficiently controlled. Convergence checks and companion error estimates offer a means of exerting such control. Here, we report some new convergence checks to this end. These checks are designed to promote conservative error estimation. They are applied to seven benchmark problems that have exact solutions for their peak stresses. Associated stress concentration factors span a range that is larger than that normally experienced in engineering. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 91 error assessments for the benchmark problems. For these 91, errors are assessed as being at the same level as true exact errors on 83 occasions and one level worse for the other 8. Thus, stress error estimation is largely accurate (91%) and otherwise modestly conservative (9%).

References

References
1.
Pilkey
,
W. D.
, and
Pilkey
,
D. F.
,
2008
,
Peterson's Stress Concentration Factors
,
Wiley
,
Hoboken, NJ
.
2.
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
.
3.
Cormier
,
N. G.
,
Smallwood
,
B. S.
,
Sinclair
,
G. B.
, and
Meda
,
G.
,
1999
, “
Aggressive Submodelling of Stress Concentrations
,”
Int. J. Numer. Methods Eng.
,
46
(
6
), pp.
889
909
.
4.
Richardson
,
L. F.
,
1910
, “
The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, With an Application to the Stresses in a Masonry Dam
,”
Philos. Trans. R. Soc. London, Ser. A
,
210
, pp.
307
357
.
5.
Richardson
,
L. F.
,
1927
, “
The Deferred Approach to the Limit—Part I: Single Lattice
,”
Philos. Trans. R. Soc. London, Ser. A
,
226
(636–646), pp.
299
349
.
6.
De Vahl Davis
,
G.
,
1983
, “
Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution
,”
Int. J. Numer. Methods Fluids
,
3
(
3
), pp.
249
264
.
7.
Roache
,
P. J.
,
1994
, “
Perspective: A Method for Uniform Reporting of Grid Refinement Studies
,”
ASME J. Fluids Eng.
,
116
(
3
), pp.
405
413
.
8.
Roache
,
P. J.
,
1998
, “
Verification of Codes and Calculations
,”
AIAA J.
,
36
(
5
), pp.
696
702
.
9.
Roache
,
P. J.
,
2009
,
Fundamentals of Verification and Validation
, Hermosa Publishing, Socorro, NM.
10.
ASME
,
2006
, “
Guide for Verification and Validation in Computational Solid Mechanics
,” American Society of Mechanical Engineers, New York, Standard No. ASME V&V10.
11.
ASME
,
2012
, “
An Illustration of the Concepts of Verification and Validation in Computational Solid Mechanics
,” American Society of Mechanical Engineers, New York, NY, Standard No. ASME V&V 10.1.
12.
Neuber
,
H.
,
1946
,
Theory of Notch Stresses
,
J. W. Edwards
,
Ann Arbor, MI
.
13.
ANSYS
,
2016
, “
ANSYS Modeling and Meshing Guide, Rev. 16.0
,” ANSYS Inc., Canonsburg, PA.
14.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
,
2002
,
Concepts and Applications of Finite Element Analysis
,
Wiley
,
New York, NY
.
15.
Shtaerman
,
I. Ya.
,
1949
,
Contact Problems of the Theory of Elasticity
,
Gostekhizdat
,
Moscow, Russia
.
16.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
17.
Sinclair
,
G. B.
,
2013
, “
Edge-of-Contact Stresses in Blade Attachments in Gas Turbines
,”
Surface Effects and Contact Mechanics
, Vol.
XI
,
Siena, Italy
,
WIT Press
, Wessex, UK, pp.
87
108
.
18.
ANSYS
,
2016
, “
ANSYS Element Reference Guide, Rev. 16.0
,” ANSYS Inc., Canonsburg, PA.
19.
Sinclair
,
G. B.
,
Beisheim
,
J. R.
, and
Sezer
,
S.
,
2006
, “
Practical Convergence-Divergence Checks for Stresses from FEA
,”
International ANSYS Users' Conference
, Pittsburgh, PA, May 2–4.
20.
Kolosov
,
G. V.
,
1914
, “
On Some Properties of the Plane Problem of Elasticity Theory
,”
Z. Math. Phys.
,
62
, pp.
383
409
.
You do not currently have access to this content.