HSDM and BFGS method for determining the heat generation and range of heat distribution in 2-D ultrasonic seam welding problems

References

• S. Koellhoffer, J. W. Gillespie, S. G. Advani, and T. A. Bogetti, Role of Friction on the Thermal Development in Ultrasonically Consolidated Aluminum Foils and Composites, J. Mater. Process. Technol., vol. 211, pp. 1864–1877, 2011.
   Web of Science ®Google Scholar
• G. S. Kelly, A Thermo-Mechanical Finite Element Anlysis of Acoustic Softening during Ultrasonic Concolidation of Aluminum Foils, Master of Science Thesis, Mechanical Engineering, University of Delaware, 2012.
   Google Scholar
• S. Elangovan, S. Semeer, and K. Prakasan, Temperature and Stress Distribution in Ultrasonic Metal Welding—An FEA-Based Study, J. Mater. Process. Technol., vol. 209, pp. 1143–1150, 2009.
   Web of Science ®Google Scholar
• N. K. R. Naidu and S. G. S. Raman, Effect of Contact Pressure on Fretting Fatigue Behaviour of Al–Mg–Si Alloy AA6061, Int. J. Fatigue, vol. 27, pp. 283–291, 2005.
   Web of Science ®Google Scholar
• M. R. Sriraman, M. Gonser, H. T. Fujii, S. S. Babu, and M. Bloss, Thermal Transients during Processing of Materials by Very High Power Ultrasonic Additive Manufacturing, J. Mater. Process. Technol., vol. 211, pp. 1650–1657, 2011.
   Web of Science ®Google Scholar
• G. S. Kelly, S. G. Advani, J. W. Gillespie, and T. A. Bogetti, A Model to Characterize Acoustic Softening during Ultrasonic Consolidation, J. Mater. Process. Technol., vol. 213, pp. 1835–1845, 2013.
   Web of Science ®Google Scholar
• M. R. Sriraman, M. Gonser, D. Foster, H. T. Fujii, S. S. Babu, and M. Bloss, Thermal Transients during Processing of 3003 Al-H18 Multilayer Build by Very High-Power Ultrasonic Additive Manufacturing, Metall. Mater. Trans. B, vol. 43, pp. 133–144, 2012.
   Web of Science ®Google Scholar
• Y. Yang, G. D. Janaki Ram, and B. E. Stucker, Bond Formation and Fiber Embedment during Ultrasonic Consolidation, J. Mater. Process. Technol., vol. 209, pp. 4915–4924, 2009.
   Web of Science ®Google Scholar
• D. T. W. Lin, C. C. Wang, C. Y. Yang, and J. C. Li, Inverse Estimation of Temperature Boundary Conditions with Irregular Shape of Gas Tank, Int. J. Heat Mass Transfer, vol. 53, pp. 4651–4662, 2010.
   Web of Science ®Google Scholar
• D. T. W. Lin, C. Y. Yang, J. C. Li, and C. C. Wang, Inverse Estimation of the Unknown Heat Flux Boundary with Irregular Shape Fins, Int. J. Heat Mass Transfer, vol. 54, pp. 5275–5285, 2011.
   Web of Science ®Google Scholar
• C. C. Wang and C. Y. Yang, Inverse Method in Simultaneously Estimate Internal Heat Generation and Root Temperature of the T-Shaped Fin, Int. Commun. Heat Mass Transfer, vol. 37, pp. 1312–1320, 2010.
   Web of Science ®Google Scholar
• N. D’Souza, Numerical Solution of one-Dimensional Inverse Transient Heat Conduction by Finite Difference Method, ASME Paper, 1975.
   Google Scholar
• G. W. Krutz, R. J. Schoenhals, and P. S. Hore, Application of the Finite-Element Method to the Inverse Heat Conduction Problem, Numer. Heat Transfer, vol. 1, pp. 489–498, 1978.
   Google Scholar
• C. H. Huang and J. Y. Wu, Two-Dimensional Inverse Problem in Estimating Heat Fluxes of an Enclosure with Unknown Internal Heat Source, J. Appl. Phys., vol. 76, pp. 133–141, 1994.
   Web of Science ®Google Scholar
• W. L. Chen and Y. C. Yang, Inverse Problem of Estimating the Heat Flux at the Roller/Workpiece Interface during a Rolling Process, Appl. Therm. Eng., vol. 30, pp. 1247–1254, 2010.
   Web of Science ®Google Scholar
• C. H. Huang and C. W. Chen, A Boundary-Element-Based Inverse Problem of Estimating Boundary Conditions in an Irregular Domain with Statistical Analysis, Numer. Heat Transfer B, vol. 33, pp. 251–268, 1998.
   Web of Science ®Google Scholar
• M. Prud’homme and T. H. Nguyen, On the Iterative Regularization of Inverse Heat Conduction Problems by Conjugate Gradient Method, Int. Commun. Heat Mass Transfer, vol. 25, pp. 999–1008, 1998.
   Web of Science ®Google Scholar
• C. H. Cheng and C. Y. Wu, An Approach Combining Body-Fitted Grid Generation and Conjugate Gradient Methods for Shape Design in Heat Conduction Problems, Numer. Heat Transfer B, vol. 37, pp. 69–83, 2000.
   Web of Science ®Google Scholar
• Y. C. Yang, W. L. Chen, and H. L. Lee, A Nonlinear Inverse Problem in Estimating the Heat Generation in Rotary Friction Welding, Numer. Heat Transfer A, vol. 59, pp. 130–149, 2011.
   Web of Science ®Google Scholar
• K. K. Hong and C. Y. Lo, An Inverse Analysis for the Heat Conduction during a Grinding Process, J. Mater. Process. Technol., vol. 105, pp. 87–94, 2000.
   Web of Science ®Google Scholar
• C. C. Wang and C. K. Chen, Three-Dimensional Inverse Heat Transfer Analysis during the Grinding Process, Proc. IME C. J. Mech. Eng. Sci., vol. 216, pp. 199–212, 2002.
   Web of Science ®Google Scholar
• J. Y. Jang, C. H. Cheng, and Y. X. Huang, Optimization of Channel Width Distribution of a Gas Flow Field by Integrating Computational Fluid Dynamics Code with a Simplified Conjugate-Gradient Method, Energy & Fuels, vol. 24, pp. 570–580, 2010.
   Web of Science ®Google Scholar
• C. H. Cheng and M. H. Chang, A Simplified Conjugate-Gradient Method for Shape Identification Based on Thermal Data, Numer. Heat Transfer B, vol. 43, pp. 489–507, 2011.
   Web of Science ®Google Scholar
• H. Q. Li, J. Lei, and Q. B. Liu, An Inversion Approach for the Inverse Heat Conduction Problems, Int. J. Heat Mass Transfer, vol. 55, pp. 4442–4452, 2012.
   Web of Science ®Google Scholar
• C. M. Murea, The BFGS Algorithm for a Nonlinear Least Squares Problem Arising from Blood Flow in Arteries, Comput. Math. Appl., vol. 49, pp. 171–186, 2005.
   Web of Science ®Google Scholar
• C. Zhu, R. H. Byrd, and J. Nocedal, Algorithm 778: L-BFGS-B: Fortan Routines for Large Scale Bound Constrained Optimization, ACM Trans. Math. Softw., vol. 23, pp. 550–560, 1997.
   Web of Science ®Google Scholar
• Y. A. Cengel and A. J. Ghajar, Heat and Mass Transfer: Fundamentals and Applications, 4th ed., pp. 19–23, John Wiley, New York, 2010.
   Google Scholar
• C. C. Wang, L. P. Chao, and W. J. Liao, Hybrid Spline Difference Method (HSDM) for Transient Heat Conduction, Numer. Heat Transfer B, vol. 61, pp. 129–146, 2012.
   Web of Science ®Google Scholar
• C. C. Wang, J. H. Huang, and D. J. Yang, Cubic Spline Difference Method for Heat Conduction, Int. Commun. Heat Mass Transfer, vol. 39, pp. 224–230, 2012.
   Web of Science ®Google Scholar
• C. C. Wang, H. Chen-Hung, and D. J. Yang, Hybrid Spline Difference Method for Steady-State Heat Conduction, Numer. Heat Transfer B, vol. 60, pp. 472–485, 2011.
   Web of Science ®Google Scholar
• C. C. Wang, W. J. Liao, and C. Y. Yang, Hybrid Spline Difference Method for Heat Transfer and Thermal Stresses in Annular Fins, Numer. Heat Transfer B, vol. 64, pp. 71–88, 2013.
   Web of Science ®Google Scholar
• C. C. Wang, W. J. Liao, and Y. S. Hsu, Hybrid Spline Difference Method for the Burgers’ Equation, Appl. Math. Comput., vol. 219, pp. 1031–1039, 2012.
   Web of Science ®Google Scholar
• O. M. Alifanov, Inverse Heat Transfer Problems, Springer-Verlag, Berlin, 1994.
   Google Scholar
• C. H. Huang and H. H. Wu, An Iterative Regularization Method in Estimating the Base Temperature for Non-Fourier Fins, Int. J. Heat Mass Transfer, vol. 49, pp. 4893–4902, 2006.
   Web of Science ®Google Scholar