A MODEL FOR PLANE ELASTICA WITH SIMPLE SHEAR DEFORMATION PATTERN

Several existing theories of elastic rods that take into account shear effects are classified. Then, a new model for the influence of sheari ng force, based on simple shear of finite amount, is proposed. The pro perties of the model are examined on the stability problem for a heavy elastic rod. It is shown that the rod may exhibit sub- and super-crit ical bifurcation patterns at the trivial equilibrium configuration. A comparison is made between the results for the critical load of the ro d predicted by the new and the three different existing models.