Abstract
We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in this paper is based on the translation method. One of the key steps is to connect the shallow shell equations to the thin plate equation.
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Acknowledgements
HK was partially supported by National Research Foundation of Korea through NRF grants No. 2009-0085987 and 2010-0017532. GWM was partially supported by the National Science Foundation of the USA through grant DMS-0707978 and DMS-1211359. JNW was partially supported by the National Science Council of Taiwan through grants 100-2628-M-002-017 and 99-2115-M-002-006-MY3.
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Kang, H., Milton, G.W. & Wang, JN. Bounds on the Volume Fraction of the Two-Phase Shallow Shell Using One Measurement. J Elast 114, 41–53 (2014). https://doi.org/10.1007/s10659-012-9425-y
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DOI: https://doi.org/10.1007/s10659-012-9425-y