Abstract
A numerical method for inverse thermal analysis of steady-state energy deposition in plate structures is constructed according to the general physical characteristics of energy deposition within a volume of material from a beam energy source. This numerical method represents implementation of a general methodology using basis functions that was introduced previously. The formal structure of the numerical method presented follows from a specific definition of the inverse heat transfer problem, which is well posed for inverse analysis of heat deposition processes. This definition is based on the assumption of the availability of information concerning spatially distributed boundary and constraint values. This information would be obtained in principle from both experimental measurements obtained in the laboratory, as well as numerical simulations performed using models having been constructed using basic theory. Experimental measurements include solidification cross sections, thermocouple measurements, and microstructural changes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S.G. Lambrakos, A.D. Zervaki, G.N. Haidemenopoulos, and V. Stergiou, Basis Functions and Parameterizations for Inverse Analysis of Welding Processes, Mathematical Modelling of Weld Phenomena, Vol 9, Verlag der Technischen Universite, Graz, 2011, p 793–815
A.D. Zervaki, G.N. Haidemenopoulos, and S.G. Lambrakos, Analysis of Heat Affected Zone using Direct and Inverse Modelling in 6XXX Aluminum Alloys, Mathematical Modelling of Weld Phenomena, Vol 8, Verlag der Technischen Universite, Graz, 2007, p 907–923
S.G. Lambrakos and S.G. Michopoulos, Algorithms for Inverse Analysis of Heat Deposition Processes, Mathematical Modelling of Weld Phenomena, Vol 8, Verlag der Technischen Universite, Graz, 2007, p 847–879
S.G. Lambrakos and J.O. Milewski, Analysis of Welding, Heat Deposition Processes Using an Inverse-Problem Approach, Mathematical Modelling of Weld Phenomena, Verlag der Technischen Universite, Graz, 2005, p 1025–1055
J. Xie and J. Zou, Numerical Reconstruction of Heat Fluxes, SIAM J. Numer. Anal., 2005, 43(4), p 1504–1535
A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, PA, 2005
H.S. Carslaw and J.C. Jaegar, Conduction of Heat in Solids, Vol 374, 2nd ed., Clarendon Press, Oxford, 1959
S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, New York, 1980
Acknowledgments
One of the authors (SGL) acknowledges the support by the Naval Research Laboratory (NRL) internal core program and active scientific collaboration with the University of Thessaly. The authors (ADZ, GNH) would like to thank the German Research Foundation DFG for the support of the depicted research within the Cluster of Excellence “Integrative Production Technology for High-Wage Countries” at RWTH Aachen University.” Also ADZ acknowledges the support of Dr. Alexander Drenker of Fraunhofer-Institut für Lasertechnik during experimental work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lambrakos, S.G., Zervaki, A.D. & Haidemenopoulos, G.N. A Numerical Method for Inverse Thermal Analysis of Steady-State Energy Deposition in Plate Structures. J. of Materi Eng and Perform 21, 180–190 (2012). https://doi.org/10.1007/s11665-011-9963-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11665-011-9963-7