Research Papers

An Integrated Computational Welding Mechanics With Direct-Search Optimization for Mitigation of Distortion in an Aluminum Bar Using Side Heating

[+] Author and Article Information
Mahyar Asadi

Mechanical Engineering,
The University of Ottawa, Ottawa,
ON K1N 6N5, Canada
e-mail: masadi@uottawa.ca

John A. Goldak

Mechanical and Aerospace Engineering,
Carleton University, Ottawa,
ON K1S 5B6, Canada
e-mail: jgoldak@mrco2.carleton.ca

1Corresponding author.

Manuscript received October 16, 2012; final manuscript received August 29, 2013; published online November 5, 2013. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 136(1), 011007 (Nov 05, 2013) (10 pages) Paper No: MANU-12-1308; doi: 10.1115/1.4025406 History: Received October 16, 2012; Revised August 29, 2013

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.

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Lindgren, L., 2001, “Finite Element Modeling and Simulation of Welding. Part 1: Increased Complexity,” J. Therm. Stresses, 24, pp. 141–192. [CrossRef]
Lindgren, L., 2001, “Finite Element Modeling and Simulation of Welding. Part 2: Improved Material Modeling,” J. Therm. Stresses, 24, pp. 195–231. [CrossRef]
Lindgren, L., 2001, “Finite Element Modeling and Simulation of Welding. Part 3: Efficiency and Integration,” J. Therm. Stresses, 24, pp. 305–334. [CrossRef]
Goldak, J. A., and Akhlaghi, M., 2005, “Computational Welding Mechanics,” Technology & Engineering, Springer, New York.
Okerblom, N. O., 1958, The Calculations of Deformations of Welded Metal Structures, Department of Scientific and Industrial Research, London, Translation from Russian.
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.
Michaleris, P., Dantzig, J., and Tortorelli, D., 1999, “Minimization of Welding Residual Stress and Distortion in Large Structures,” Weld. J., pp. 361–366.
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. [CrossRef]
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.
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. [CrossRef]
Kadivar, M. H., Jafarpur, K., and Baradaran, H. G., 2000, “Optimizing Welding Sequence With Genetic Algorithm,” Comput. Mech., 26, pp. 514–519. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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.
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.
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.
Goldak Technologies, Inc., 2013, http://www.goldaktec.com/vrweld.html
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.
Gu, M., and Goldak, J. A., 1993, “Steady State Thermal Analysis of Welds With Filler Metal Addition,” Can. Metall. Q., 32, pp. 49–55. [CrossRef]
Zienkiewicz, O., and Taylor, R., 1989, The Finite Element Method, 4th ed., Vol. 2, McGraw-Hill, New York.
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.
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Taguchi, G., 1990, “Introduction to Quality Engineering,” Asian Productivity Organization, Eighth Symposium on Taguchi Methods, American Supplier Institute, Dearborn, MI.
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.


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Fig. 3

Deflection in y direction at the end of the process (×50). Horizontal and vertical axis are x and y.

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Fig. 2

A 2D view of the 3D mesh employed in the analysis

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Fig. 1

Specimen dimensions, fixities, welding direction, and locations of thermocouples, strain gauges, a dial gauge, and extensometers used in validation activity [18]

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Fig. 4

Double ellipsoid parameters; front a2, rear a1, width b, and depth c

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Fig. 5

Relative position of side heater torch to the welding torch in aluminium bar to mitigate the distortion

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Fig. 6

Constraint showing the feasible region for two side heater parameters; power and area. Nodes on the gray zone have the maximum temperature in the side heater below 480 K and therefore generate no-plastic strain.

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Fig. 7

Taguchi main effects plots for r, η, y, and x

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Fig. 11

Final deflection for the weld with no mitigation, when the side heater only applied and the weld mitigated by the side heater. Distance is from the left bottom corner to the right bottom corner of the bar and unit is meter.

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Fig. 8

The objective function response from Table 3

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Fig. 9

The original direct-search algorithm results (Table 4) is illustrated graphically to show the path followed by the algorithm to the minimum

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Fig. 10

The least-square direct-search algorithm results (Table 5) is illustrated in the short path. It is compared to the original direct search, i.e. longer path (Table 4), to show the path followed by either algorithms to the minimum.

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Fig. 12

Longitudinal residual stress in the bar after welding is complete for the weld with no mitigation, when the side heater is only applied and the weld mitigated by the side heater. Residual stress is plotted for a line normal to the weld from the top edge to the bottom edge of the bar at the midlength of the bar. Units are Pa and m for stress and distance, respectively.



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