Global error estimates in Reissner theory of thin elastic shells (Q1114486)

The accuracy of a shell theory which is an extension of Reissner's theory of plates is studied as an approximation to three-dimensional elasticity. Refined three-dimensional displacement and stress fields are constructed in terms of the two-dimensional shell theory solutions for transversely loaded shells of arbitrary geometry with midsurface elastic symmetry and constant thickness. Under so-called regular edge conditions on the lateral boundary, these fields are proved to have a relative mean square error of order \(h/R+h^ 3/L^ 3\) (h,R,L-thickness, radius of curvature, deformation wave length) with respect to the solutions of elasticity. Known error estimates in classical theory are \(O(h/R+h^ 2/L^ 2)\).