Three dimensional boundary formulations for nonlinear thermal shape sensitivities
Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in three-dimensional 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 are examined.
temperature dependent material properties
scientific article; zbMATH DE number 167092