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An inverse finite element minimization‐based method for solution of multi‐dimensional phase‐change and material boundary shapes
Author(s) -
Keanini Russell G.,
Rubinsky Boris
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620370703
Subject(s) - finite element method , minification , boundary (topology) , inverse problem , inverse , boundary value problem , thermocouple , mathematics , algorithm , mathematical analysis , mathematical optimization , geometry , materials science , structural engineering , engineering , composite material
An inverse finite element method for solution of unknown multidimensional phase‐change and material boundary shapes is presented. The method is based on minimization and requires boundary shape parametrization. The unknown boundary parameters are determined by minimizing the error between a limited number of known (e.g. measured) temperatures and the temperatures associated with the iteratively altered boundary. The algorithm presented is based on the multidimensional downhill simplex minimization method. The inverse method is illustrated and verified using a model of the plasma arc welding process. In particular, it is shown that the technique is capable of accurately determining a specified weld pool capillary interface shape using a limited number of simulated thermocouple measurements. The code's ability to determine the interface shape is investigated under various interface‐thermocouple separations, using varying numbers of simulated thermocouples.