Abstract
Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in three dimensional (3D) solid objects, subjected to nonlinear boundary conditions, and with temperature dependent material properties, is shown to generate an accurate and economical approach for the computation of shape sensitivities. The theoretical formulation for primary response (surface temperature and normal heat flux) sensitivities and secondary response (surface tangential heat flux components and internal temperature and heat flux components) sensitivities is given. Iterative strategies are described for the solution of the resulting sets of nonlinear equations and computational performances examined. Multi-zone analysis and zone condensation strategies are demonstrated to provide substantial 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 sensitivity example problems are presented that have closed form solutions. Sensitivities computed using the boundary formulation are shown to be in excellent agreement with these exact expressions.
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Communicated by S. N. Atluri, July 7, 1992
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Wang, H., Guru Prasad, K. & Kane, J.H. Three dimensional boundary formulations for nonlinear thermal shape sensitivities. Computational Mechanics 11, 123–139 (1993). https://doi.org/10.1007/BF00350047
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DOI: https://doi.org/10.1007/BF00350047