Direct computation of instability points with inequality constraints using the finite element method

Abstract

In structural mechanics buckling phenomena often have seriousconsequences as they mean a loss of stability or a shape change of the whole structure. Typical examples for these phenomena are the buckling of rods, plates, beams, arches and shell structures. Further examples for phenomena that are connected with a stability loss are diffuse necking bifurcation problems or the formation of shear bnds in elastic-plastic solids. With the weight opyimization of mechanical components, an important issue in e.g. aeronautics, structures become thinner and thus more susceptible to buckling.