Asymptotic approximation of an elastic beam with a rotating cross section

Abstract

In the framework of linearized elasticity, the asymptotic expansion method is used to obtain an approximation of the displacement field of a beam with a variable cross section (in the sense that the section rotates along the longitudinal axis of the beam, keeping its form). We give a complete characterization of the equations governing the bending, stretching and torsion components, generalizing, in this way, previous results for straight beams.