Variational design of open cross-section thin- walled beam under stability constraints

摘要

A thin-walled beam is in pure bending subjected to couples Mo. The open cross-section profile has two ribs with cross-section Ao and it is shaped symnletrically towards the plane perpendicular to the bending plane. Tbe ribs are located at the proble ends. The shape of the profile line is searched for. Criterion is the minimal value of the cross-section area A, of the beam. The problem is described by means of variational calculus. Within the numerical calcu- lations a RungeKutta method is used. The optimal shapes of beam profiles are shown graphi- cally.