Bounds on the volume fraction of the two-phase shallow shell using one measurement

TL;DR

This paper derives bounds on the volume fraction of two-phase shallow shells using a single measurement, employing the translation method and linking shallow shell equations to thin plate equations.

Contribution

It introduces a novel approach to estimate phase volume fractions in shallow shells from limited data, connecting shell equations to plate theory.

Findings

Derived explicit bounds on phase volume fractions

Established a connection between shallow shell and plate equations

Validated bounds through theoretical analysis

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.