Abstract
In this paper, we present a Continuous Sensitivity Equation (CSE) that describes the sensitivity of temperature with respect to shape parameters, physical properties and other parameters. We begin by introducing the notion of sensitivities using a one-dimensional, steady-state conduction problem for a composite rod. The model is extended to incorporate contact resistance at the interface between different materials. These examples illustrate some of the difficulties involved in computing sensitivities: accurate evaluation of boundary conditions for shape sensitivities and discontinuities across material interfaces. We conclude with a finite element formulation for CSE applied to phase change problems.
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Dedicated to the memory of Professor P.D. Panagiotopoulos.
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© 2001 Kluwer Academic Publishers
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Borggaard, J., Pelletier, D. (2001). A Sensitivity Equation Method for Conduction and Phase Change Problems. In: Gao, D.Y., Ogden, R.W., Stavroulakis, G.E. (eds) Nonsmooth/Nonconvex Mechanics. Nonconvex Optimization and Its Applications, vol 50. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0275-9_3
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DOI: https://doi.org/10.1007/978-1-4613-0275-9_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7973-7
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