A 1993 result of J. Llibre, and M. Misiurewicz, (Theorem A [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. Also a 1980 result of L.S. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young (Lemma 1.5 [3]) states that if G is an A-graph of f then h(G) ? h( f ). In this pap...

In this paper the eccentric forward extrusion of sections has been simulated and analyzed using FEM Abaqus-explicit. The results have been compared to those obtained from upper bound theorem and experimental works. Close agreements was observed between the FEM and experimental work and as compared with the upper bound data more realistic and better predictions were made by the authors’ method. ...

In rigid plastic analysis one of the most widely applicable methods that is based on the minimum principle, is the combination of elementary mechanisms which uses the upper bound theorem. In this method a mechanism is searched which corresponds to the smallest load factor. Mathematical programming can be used to optimize this search process for simple fra...