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Mathematical justification of a one‐dimensional model for general elastic shallow arches
Author(s) -
ÁlvarezDios J. A.,
Viaño J. M.
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19980310)21:4<281::aid-mma951>3.0.co;2-o
Subject(s) - arch , mathematics , curvature , bernoulli's principle , bending , elasticity (physics) , bending moment , mathematical analysis , springing , section (typography) , geometry , structural engineering , physics , engineering , thermodynamics , advertising , business
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. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.