On Stress-Strain Relations and Strain-Energy Expressions in the Theory of Thin Elastic Shells

The stress-strain relations of Flu¨gge and Byrne for thin elastic shells are inverted to express strain quantities, and therewith the strain energy, in terms of stress resultants and couples. In this form, and upon omission of terms which are small of order h²/R², the stress-strain relations and the strain-energy expression are shown to be simply related to corresponding results of Trefftz. The strain-energy formula of Trefftz is generalized to arbitrary orthogonal middle surface co-ordinates.