MATHEMATICAL JUSTIFICATION OF A ONE-DIMENSIONAL MODEL FOR GENERAL ELASTIC SHALLOW ARCHES

We present a bending model for a shallow arch, namely the type of curv ed rod where the curvature is of the order of the diameter of the cros s section. The model is deduced in a rigorous mathematical way from cl assical tridimensional linear elasticity theory via asymptotic techniq ues, by taking the limit on a suitable re-scaled formulation of that p roblem as the diameter of the cross section tends to zero. This model is valid for general cases of applied forces and material, and it allo ws us to calculate displacements, axial stresses, bending moments and shear forces. The equations present a more general form than in the cl assical Bernoulli-Navier bending theory for straight slender rods, so that flexures and extensions are proved to be coupled in the most gene ral case. (C) 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.