Journal of Materials Engineering and Performance

, Volume 21, Issue 2, pp 180–190 | Cite as

A Numerical Method for Inverse Thermal Analysis of Steady-State Energy Deposition in Plate Structures

  • S. G. Lambrakos
  • A. D. Zervaki
  • G. N. Haidemenopoulos


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.


aluminum modeling processes welding 



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.


  1. 1.
    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 793–815Google Scholar
  2. 2.
    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 907–923Google Scholar
  3. 3.
    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 847–879Google Scholar
  4. 4.
    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 1025–1055Google Scholar
  5. 5.
    J. Xie and J. Zou, Numerical Reconstruction of Heat Fluxes, SIAM J. Numer. Anal., 2005, 43(4), p 1504–1535CrossRefGoogle Scholar
  6. 6.
    A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, PA, 2005CrossRefGoogle Scholar
  7. 7.
    H.S. Carslaw and J.C. Jaegar, Conduction of Heat in Solids, Vol 374, 2nd ed., Clarendon Press, Oxford, 1959Google Scholar
  8. 8.
    S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, New York, 1980Google Scholar

Copyright information

© ASM International 2011

Authors and Affiliations

  • S. G. Lambrakos
    • 1
  • A. D. Zervaki
    • 2
  • G. N. Haidemenopoulos
    • 2
  1. 1.Materials Science and Technology Division, Center for Computational MaterialsNaval Research LaboratoryWashingtonUSA
  2. 2.Department of Mechanical EngineeringUniversity of ThessalyVolosGreece

Personalised recommendations