Jm. Rodriguez et Jm. Viano, ASYMPTOTIC DERIVATION OF A GENERAL LINEAR-MODEL FOR THIN-WALLED ELASTIC RODS, Computer methods in applied mechanics and engineering, 147(3-4), 1997, pp. 287-321
In this work we derive from three-dimensional elasticity a general mat
hematically justified theory for thin-walled elastic rods. This theory
is obtained as an asymptotic approximation of the three-dimensional l
inear model as the area and the thickness of the cross-section becomes
successively small. It constitutes an extension of the classical Vlas
sov's theory for thin-walled beams (the most complete among models cur
rently used in engineering).