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Issue ESAIM: Proc.
Volume 2, 1997
Elasticity, viscoelasticity and optimal control
Page(s) 145 - 152
DOI http://dx.doi.org/10.1051/proc:1997001

ESAIM: Proc., 1997, Vol. 2, pp. 145-152
DOI: 10.1051/proc:1997001

A bending and stretching asymptotic theory for general elastic shallow arches

José A. Alvarez-Dios1 and Juan M.Viaño1

1  Departamento de Matematica Aplicada, Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain.


Abstract
We present a bending model for a shallow arch, namely the type of curved rod where the curvature is of the order of the diameter of the cross section. The model is deduced in a rigorous mathematical way from classical tridimensional linear elasticity theory via asymptotic techniques, by taking the limit on a suitable re-scaled formulation of that problem as the diameter of the cross section tends to zero. This model is valid for general cases of applied forces and material, and it allows us to calculate displacements, axial stresses, bending moments and shear forces. The equations present a more general form than in the classical Bernoulli-Navier bending theory for straight slender rods, so that flexures and extensions are proved to be coupled in the most general case.



© EDP Sciences, ESAIM 1997


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