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Boundary formulations for shape sensitivity of temperature dependent conductivity problemsUsed in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.
Document ID
19920042779
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Kane, James H.
(NASA Lewis Research Center Cleveland, OH, United States)
Wang, Hua
(Clarkson University Potsdam, NY, United States)
Date Acquired
August 15, 2013
Publication Date
February 28, 1992
Publication Information
Publication: International Journal for Numerical Methods in Engineering
Volume: 33
ISSN: 0029-5981
Subject Category
Structural Mechanics
Accession Number
92A25403
Funding Number(s)
CONTRACT_GRANT: NAG3-1089
CONTRACT_GRANT: NSF DDM-89-96171
Distribution Limits
Public
Copyright
Other

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