Abstract
In this chapter we consider minimization of functionals that depend on the solution of the stationary conductivity problem. Energy minimization is one such problem. Other examples include minimization of the mean temperature within some area in the body, minimization of a norm of the difference between the desired and actual temperature, or maximization of the total current through a boundary component. Again, microstructures appear in these optimal designs. We describe an approach based on homogenization and demonstrate that the optimal composites are surprisingly simple: Laminates are the optimal structures for a large class of cost functionals.
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© 2000 Springer-Verlag Berlin Heidelberg
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Cherkaev, A. (2000). Optimal Conducting Structures. In: Variational Methods for Structural Optimization. Applied Mathematical Sciences, vol 140. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1188-4_5
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DOI: https://doi.org/10.1007/978-1-4612-1188-4_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7038-6
Online ISBN: 978-1-4612-1188-4
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