Exact invariant stress and deformation functions for doubly curved (nondevelopable) shells are derived. The invariant stress function reduces the six shell equilibrium equations into a single equation in the stress function and moment resultants. The deformation function reduces the three surface strain-displacement relations into a single compatibility equation in the strains and deformation function, in terms of which the changes of curvature are also expressed. Application of these functions in the formulation of an approximate bending theory for shells is presented.

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