A new method employing the fitting of a least squares plane to stress distribution obtained from a finite element analysis for evaluating categorized values is presented. The property of a least squares fit, i.e., the preservation of volume under stress distribution and the plane of consideration, is used in evaluating various numerical integrals. The procedure is demonstrated through application to a typical shell nozzle junction.

Issue Section:
Design and Analysis
Keywords:
finite element analysis, least squares approximations, nozzles, shells (structures), yield stress, stress category, least squares fit, membrane and bending stresses
Topics:
Stress, Finite element analysis, Membranes, Stress concentration, Bending (Stress)
1.
Kroenke
,
W. C.
, 1973, “
Classification of Finite Element Stresses According to ASME Section. III Stress Categories
,”
ASME Winter Annual Meeting
, Detroit, MI, November, pp.
107
–
140
.
2.
Hsu
,
K. H.
, and
McKinley
,
D. A.
, 1990, “
SOAP—A Computer Program for Classification of Three Dimensional Finite Element Stresses on a Plane
,”
ASME Pressure Vessel and Piping Conference and Exhibition
, Tennessee, PVP 185, pp.
11
–
19
.
3.
Hechmer
,
J. L.
, and
Hollinger
,
G. L.
, 1989, “
Code Evaluation of 3-D Stresses on a Plane
,”
PVP (Am. Soc. Mech. Eng.)
,
161
, pp.
33
–
46
.
4.
Hechmer
,
J. L.
, and
Hollinger
,
G. L.
, 1987, “
Three-Dimensional Stress Criteria-Application of Code Rules
,”
PVP (Am. Soc. Mech. Eng.)
,
120
, pp.
189
–
195
.
5.
Hechmer
,
J. L.
, and
Hollinger
,
G. L.
, 1991, “
The ASME Code and 3-D Stress Evaluation
,”
ASME J. Pressure Vessel Technol.
,
113
, pp.
481
–
487
.
Crossref
Search ADS
 
6.
Hollinger
,
G. L.
, and
Hechmer
,
J. L.
, 1986, “
Three Dimensional Stress Criteria—A Weak Link in Vessel Design and Analysis
,”
PVP (Am. Soc. Mech. Eng.)
,
109
, pp.
9
–
14
.
7.
Hechmer
,
J. L.
, and
Hollinger
,
G. L.
, 1988, “
Considerations in the Calculations of the Primary Plus Secondary Stress Intensity Range for Code Stress Classification
,”
PVP (Am. Soc. Mech. Eng.)
,
136
, pp.
17
–
33
.
8.
Maekawa
,
O.
,
Aoki
,
M.
,
Nishimura
,
Y.
, and
Nishiguchi
,
I.
, 1995, “
JPVRC Activities to Establish Stress Classification for 3-D FEA Results
,”
PVP (Am. Soc. Mech. Eng.)
,
313-1
, pp.
377
–
392
.
9.
ASME Boiler and Pressure Vessel Code, Section VIII, 2007, “
Linearization of Stress Results for Stress Classification
,” Annex 5.A, Division 2—Alternative Rules, The American Society of Mechanical Engineers, New York, NY.
10.
Godbole
,
P. B.
, 1989, “
A Method of Quadrature Using Least Square Straight Line Fit
,”
Adv. Eng. Software
,
11
(
3
), pp.
156
–
158
.
Crossref
Search ADS
 
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