Physical instability and geometric effects in frames

The interaction between physical instability and geometric (2nd-order) effe cts in plane frames is investigated herein within a finite element based ma thematical programming framework, under the assumptions of quasistatic load ing and lumped plasticity. The sources of physical instability consist of i nelastic bending hinges characterized by softening nonholonomic (irreversib le) moment versus rotation constitutive laws. The complex and insightful re sponse spectrum which can arise is illustrated with the aid of simple, albe it instructive, reference examples. Stability domains are obtained for thes e examples in the space of the parameters characterizing the level of membe r axial force and the amount of hinge softening. Such domains highlight var ious key features, which are briefly commented upon, of the interplay betwe en physical and geometric effects. (C) 1998 Elsevier Science Ltd. All right s reserved.