Bounds on the Volume Fraction of the Two-Phase Shallow Shell Using One Measurement

Author: Kang Hyeonbae   Milton Graeme   Wang Jenn-Nan  

Publisher: Springer Publishing Company

ISSN: 0374-3535

Source: Journal of Elasticity, Vol.114, Iss.1, 2014-01, pp. : 41-53

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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.