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Optimal arrangement of holes in a two‐dimensional heat conductor by a special boundary integral method
Author(s) -
Barone M. R.,
Caulk D. A.
Publication year - 1982
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.1620180505
Subject(s) - discretization , conductor , thermal conduction , boundary (topology) , boundary value problem , finite element method , optimal design , surface (topology) , position (finance) , geometry , boundary element method , mechanics , thermal , mathematics , materials science , mathematical analysis , physics , thermodynamics , composite material , statistics , finance , economics
The position, size and surface temperature of circular holes inside a two‐dimensional heat conductor are optimized to produce a minimum variation in surface temperature over a portion of the outer boundary. This problem, whic arises in thermal desing of moulds and dies, resembles those encountered in structural shape optimization because the internal geometry of the heat conductor depends on the design variables. In this paper, some of the traditional difficulties associated with shape optimization are overcome by analysing steady heat conduction with a special boundary integral method developed for two‐dimensional regions with circular hole. This approach eliminates the need to regenerate a finite element mesh over the interior of the region each time the geometry is changed during the design process. It also increases the efficiency of the analysis by reducing the number of unknowns in the numerical discretization of the region. Since the objective function depends only on the boundary temperatures, there is no need to determine temperatures in the interior. The analysis method is applied to two problems arising in optimal thermal design of compression moulds. These examples show that the number of holes choson for the design strongly affects their resulting optimal arrangement as well as the ultimate uniformity of the cavity surface temperature.