Using a computational weld mechanics (CWM) frame-work for exploring a design space, a recent direct-search algorithm from Kolda, Lewis and Torczon is modified to use a least-square approximation to improve the method of following a path to the minimum in the algorithm. To compare the original and modified algorithms, a CWM optimization problem on a 152 × 1220 × 12.5 mm bar of Aluminum 5052-H32 to minimize the weld distortion mitigated by a side heating technique is solved. The CWM optimization problem is to find the best point in the space of side heater design parameters: power, heated area, longitudinal and transverse distance from the weld such that the final distortion is as low as possible (minimized). This CWM optimization problem is constrained to keep the stress level generated by the side heaters, in the elastic region to avoid adding an additional permanent plastic strain to the bar. The number of iterations, size of design of experiments (DOE) matrix required and CPU time to find the minimum for the two algorithms are compared.

References

References
1.
Lindgren
,
L.
,
2001
, “
Finite Element Modeling and Simulation of Welding. Part 1: Increased Complexity
,”
J. Therm. Stresses
,
24
, pp.
141
192
.10.1080/01495730150500442
2.
Lindgren
,
L.
,
2001
, “
Finite Element Modeling and Simulation of Welding. Part 2: Improved Material Modeling
,”
J. Therm. Stresses
,
24
, pp.
195
231
.10.1080/014957301300006380
3.
Lindgren
,
L.
,
2001
, “
Finite Element Modeling and Simulation of Welding. Part 3: Efficiency and Integration
,”
J. Therm. Stresses
,
24
, pp.
305
334
.10.1080/01495730151078117
4.
Goldak
,
J. A.
, and
Akhlaghi
,
M.
,
2005
, “
Computational Welding Mechanics
,”
Technology & Engineering
,
Springer
,
New York
.
5.
Okerblom
,
N. O.
,
1958
,
The Calculations of Deformations of Welded Metal Structures
,
Department of Scientific and Industrial Research
,
London
, Translation from Russian.
6.
Asadi
,
M.
, and
Goldak
,
J. A.
,
2011
, “
Mitigation of Distortion in an Edge-Welded-Bar by Clamping Parameters
,”
Proceedings of the International ASME 2011 Pressure Vessel and Piping Division Conference
, Baltimore, MD, Paper No. PVP2011-57955.
7.
Michaleris
,
P.
,
Dantzig
,
J.
, and
Tortorelli
,
D.
,
1999
, “
Minimization of Welding Residual Stress and Distortion in Large Structures
,”
Weld. J.
, pp.
361
366
.
8.
Deo
,
M.
, and
Michaleris
,
P.
,
2003
, “
Mitigation of Welding Induced Buckling Distortion Using Transient Thermal Tensioning
,”
Sci. Technol. Weld. Joining
,
8
(
1
), pp.
49
54
.10.1179/136217103225008919
9.
Tsai
,
C. L.
,
Park
,
S. C.
, and
Cheng
,
W. T.
,
1999
, “
Welding Distortion of a Thin-Plate Panel Structure
,”
Weld. J.
,
78
(
5
), pp.
157
165
.
10.
Mochizuki
,
M.
,
Hayashi
,
M.
, and
Hattori
,
T.
,
1999
, “
Residual Stress Distribution Depending on Welding Sequence in Multi-Pass Welded Joints With X-Shaped Groove
,”
ASME J. Pressure Vessel Technol.
,
122
(
1
), pp.
27
32
.10.1115/1.556142
11.
Kadivar
,
M. H.
,
Jafarpur
,
K.
, and
Baradaran
,
H. G.
,
2000
, “
Optimizing Welding Sequence With Genetic Algorithm
,”
Comput. Mech.
,
26
, pp.
514
519
.10.1007/s004660000195
12.
Voutchkov
,
I.
,
Keane
,
A.
,
Bhaskar
,
A.
, and
Olsen
,
T.
,
2005
, “
Weld Sequence Optimization: The Use of Surrogate Models for Solving Sequential Combinatorial Problems
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
30–33
), pp.
3535
3551
.10.1016/j.cma.2005.02.003
13.
Asadi
,
M.
, and
Goldak
,
J. A.
,
2011
, “
Combinatorial Optimization of Weld Sequence by Using a Surrogate Model to Mitigate a Weld Distortion
,”
Int. J. Mech. Mater. Des.
,
7
(
2
), pp.
123
139
.10.1007/s10999-011-9154-6
14.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
,
1992
,
Numerical Recipes in C: The Art of Scientific Computing
,
2nd ed.
, Cambridge University Press, Cambridge, UK.
15.
Lewis
,
R. M.
,
Torczon
,
V.
, and
Trosset
,
M. W.
,
2000
, “
Direct Search Method: Then and Now
,”
J. Comput. Appl. Math.
,
124
(
2000
), pp.
191
207
.10.1016/S0377-0427(00)00423-4
16.
Trosset
,
M. W.
,
1997
, “
I Know it When I See it: Toward a Definition of Direct Search Methods
,”
SIAG/OPT Views-and-News: A Forum for the SIAM Activity Group on Optimization
, Vol.
9
, pp.
7
10
.
17.
Goldak
,
J. A.
, and
Asadi
,
M.
,
2013
, “
Challenges in Verification of Computational Weld Mechanics Software to Compute Residual Stress and Distortion in Welds
,”
J. Pressure Vessels Technol.
, PVT-10-1158.
18.
Masabuchi
,
K.
,
1983
, Analysis of Welded Structures (International Series on Materials Science and Technology), Vol. 33, Sec. 5 Transient Thermal Stress, Pergamon Press, MIT USA, pp.
172
187
.
19.
Goldak Technologies, Inc.
,
2013
, http://www.goldaktec.com/vrweld.html
20.
Asadi
,
M.
, and
Goldak
,
J. A.
,
2010
, “
Challenges in Verification of CWM Software to Compute Residual Stress and Distortion in Weld
,”
Proceedings of the ASME 2010 Pressure Vessel and Piping Division Conference
, Bellevue, Washington, Paper No. PVP2010-25770.
21.
Gu
,
M.
, and
Goldak
,
J. A.
,
1993
, “
Steady State Thermal Analysis of Welds With Filler Metal Addition
,”
Can. Metall. Q.
,
32
, pp.
49
55
.10.1179/000844393795544168
22.
Zienkiewicz
,
O.
, and
Taylor
,
R.
,
1989
,
The Finite Element Method
,
4th ed.
, Vol.
2
,
McGraw-Hill
,
New York
.
23.
Francis
,
J. D.
,
2002
, “
Welding Simulations of Aluminium Alloy Joints by Finite Element Analysis
,” M.Sc. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
24.
Simo
,
J. C.
,
1998
, “
Numerical Analysis of Classical Plasticity
,”
Handbook for Numerical Analysis
, Vol.
IV
,
P. G.
Ciarlet
and
J. J.
Lions
, eds.,
Elsevier
,
Amsterdam
.
25.
Song
,
J.
,
Shanghvi
,
J. Y.
, and
Michaleris
,
P.
,
2004
, “
Sensitivity Analysis and Optimization of Thermo-Elasto-Plastic Processes With Applications to Welding Side Heater Design
,”
Computer Methods in Applied Mechanics and Engineering
,
193
, pp.
4541
4566
.10.1016/j.cma.2004.03.007
26.
Goldak
,
J. A.
,
Chakravarti
,
A.
, and
Bibby
,
M. J.
,
1984
, “
A New Finite Element Model for Welding Heat Sources
,”
Metall. Trans. B
,
15
, pp.
299
305
.10.1007/BF02667333
27.
Kolda
,
T. G.
,
Lewis
,
R. M.
, and
Torczon
,
V.
,
2003
, “
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods
,”
SIAM Rev.
,
45
(
3
), pp.
385
482
.10.1137/S003614450242889
28.
Taguchi
,
G.
,
1990
, “
Introduction to Quality Engineering
,”
Asian Productivity Organization, Eighth Symposium on Taguchi Methods, American Supplier Institute, Dearborn, MI
.
29.
Unal
,
R.
, and
Dean
,
E. B.
,
1991
, “
Taguchi Approach to Design Optimization for Quality and Cost: An Overview
,”
Annual Conference of the International Society of Parametric Analysts
.
You do not currently have access to this content.