Asymptotic theories for thin-walled beams
Roberto Paroni (University of Sassari)
SES Medal Symposium in honor of D.J. Steigmann
Tue 9:00 - 10:30
MacMillan 115
Geometrically, a thin-walled beam is a slender structural element whose length is much larger than the diameter of the cross section which, in turn, is larger than the thickness of the thin wall. These beams have been used for a long time in civil and mechanical engineering and, most of all, in flight vehicle structures because of their high ratio between maximum strength and weight. From a mathematical point of view, these beams present two scaling factors: one is the ratio between the diameter of the cross-section and the length of the beam, the other is the ratio between the wall thickness and the diameter of the cross-section. In this talk, starting from the three-dimensional theory of elasticity we shall deduce one dimensional models for these kind of beams by means of an asymptotic analysis in which the two scaling factors go to zero.