A bonded bilayer has equal layer thickness d, equal Young moduli, width b and α 2 α 1 . It is free of external force and moment; plane sections remain plane. What is small-strain curvature magni

Question

A bonded bilayer has equal layer thickness d, equal Young moduli, width b and α 2 ​ > α 1 ​ . It is free of external force and moment; plane sections remain plane. What is small-strain curvature magnitude after positive heating Δ T ?

TestHub · Accepted Answer

Let interface y = 0 , layers -d to 0 and 0 to d. Stress σ = Y ( ϵ 0 ​ + κ y − α i ​ Δ T ) . Zero axial force gives ϵ 0 ​ = 2 ( α 1 ​ + α 2 ​ ) Δ T ​ . Zero moment gives κ ( 3 2 d 3 ​ ) = 2 Δ T ( α 2 ​ − α 1 ​ ) d 2 ​ . Therefore κ = ( 4 d ) 3 ( α 2 ​ − α 1 ​ ) Δ T ​ , B. Elastic constraints matter.

Physics - Heat & Thermo Question with Solution | TestHub

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