Complete solutions of elastic-plastic discretized structures by linear programming

The method developed in this paper combines limit and elastic-plastic analysis in a twofold sense: (a) although it is based on the elastic-plastic (in contrast to rigid-plastic) assumption, it is centered on a linear programming algorithm slightly modified with a complementarity constraint ('restricted basis entry') and, hence, the relevant computational effort is of the same order of magnitude as in classical limit analysis; (b) the information provided encompasses both the complete deformation hitory up to plastic collapse and the collapse mechanism along with the collapse load (or the safety factor). Possible local unloadings are allowed for by means of suitable modifications of the current tableau. The method is expounded and illustrated with reference to frames with concentrated plastic deformability ('critical section' assumption). Its applications to finite element or lumped-parameters models of other continua, can be carried out straightforwardly, provided that the yield surfaces in the generalized stress space be replaced by approximating polyhedra. Also the applicability of the method to nonproportional loading process, to hardening and to elastoplastic-brittle behavior is briefly pointed out at the end of the paper