On a viscoplastic Shanley-like model under constant load

Motivated by applications devoted to study the behavior of steel and alumin um alloys columns, inelastic Shanley-like models have been extensively stud ied in the literature, mainly to investigate buckling and post buckling pro blems (see Sewell, 1971; Hutchinson, 1974 for a complete review). On the other hand, recent papers discussing geotechnical problems point out that those models may be useful for the study of the essential features of the equilibrium of towers. In this case, the structure's proper weight (wh ich is a conservative load with constant magnitude), and the verticality im perfection, appear to be responsible for the leaning evolution, as well as the time variation of the mechanical property of the soil. Throughout this paper, a 'T' shaped rigid rod on two no-tension viscoplasti c springs under constant load with initial imperfection is considered. Unde r fairly general assumptions, a viscoplastic constitutive law is derived as a particular case of the theory developed in (Gurtin et al., 1980), studyi ng its behavior under loading processes. By virtue of a time rescaling proc edure, extreme retardation leads to determine a yielding parameter, which a llows to distinguish between viscoelastic and viscoplastic ranges. For all the states attained by the rod, explicit expressions for the two di splacement parameters characterizing its evolution are given. Noting that f ailure may occur if the reaction of one spring goes to zero, sufficient con ditions under which no bifurcation and no failure occur are given for all t he phases, leading so to determine the minimum upper bound for the load par ameter. This new result turns out to depend only on the relaxation surface parameters at equilibrium, irrespective of the behavior under non-zero fini te deformation velocities. (C) 1999 Elsevier Science Ltd. All rights reserv ed.