A direct method to predict cyclic steady states of elastoplastic structures

Spiliopoulos, KV; Panagiotou, KD

dc.contributor.author	Spiliopoulos, KV	en
dc.contributor.author	Panagiotou, KD	en
dc.date.accessioned	2014-03-01T02:07:15Z
dc.date.available	2014-03-01T02:07:15Z
dc.date.issued	2012	en
dc.identifier.issn	00457825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29534
dc.subject	Alternating plasticity	en
dc.subject	Cyclic loading	en
dc.subject	Direct methods	en
dc.subject	Elastic shakedown	en
dc.subject	Fourier series	en
dc.subject	Ratcheting	en
dc.subject.other	Applied loading	en
dc.subject.other	Computational advantages	en
dc.subject.other	Cyclic loadings	en
dc.subject.other	Cyclic steady state	en
dc.subject.other	Cyclic stress	en
dc.subject.other	Direct method	en
dc.subject.other	Elastic shakedown	en
dc.subject.other	Elastic-perfectly plastics	en
dc.subject.other	Elasto-plastic structures	en
dc.subject.other	External loads	en
dc.subject.other	Plastic straining	en
dc.subject.other	Ratcheting	en
dc.subject.other	Steady-state behaviors	en
dc.subject.other	Time points	en
dc.subject.other	Time-stepping	en
dc.subject.other	Two-dimensional structures	en
dc.subject.other	Von Mises	en
dc.subject.other	Yield surface	en
dc.subject.other	Zero load	en
dc.subject.other	Cyclic loads	en
dc.subject.other	Finite element method	en
dc.subject.other	Fourier series	en
dc.subject.other	Mathematical programming	en
dc.subject.other	Plasticity	en
dc.subject.other	Residual stresses	en
dc.subject.other	Stress analysis	en
dc.subject.other	Stress concentration	en
dc.subject.other	Loading	en
dc.title	A direct method to predict cyclic steady states of elastoplastic structures	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cma.2012.03.004	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cma.2012.03.004	en
heal.publicationDate	2012	en
heal.abstract	The asymptotic steady state behavior of an elastic-perfectly plastic structure under cyclic loading may be determined by time consuming incremental time-stepping calculations. Direct methods, alternatively, have a big computational advantage as they attempt to find the characteristics of the cyclic state right from the start of the calculations. Most of these methods address an elastic shakedown state through the shakedown theorems and on the basis of mathematical programming algorithms. In the present paper, a novel direct method that has a more physical basis and may predict any cyclic stress state of a structure under a given loading is presented. The method exploits the cyclic nature of the expected residual stress distribution at the steady cycle. Thus, after equilibrating the elastic part of the total stress with the external load, the unknown residual stress part is decomposed into Fourier series whose coefficients are evaluated iteratively by satisfying compatibility and equilibrium with zero loads at time points inside the cycle and then integrating over the cycle. A computationally simple way to account for plasticity is proposed. The procedure converges uniformly to the true cyclic residual stress for a loading below the elastic shakedown limit or to an unsafe cyclic total stress, which may be used to mark the regions with plastic straining inside the cycle. The method then continues to determine whether the applied loading would lead the structure to ratcheting or to regions that alternate plastically. The procedure is formulated within the finite element method. A von Mises yield surface is typically used. Examples of application of one and two dimensional structures are included. © 2012 Elsevier B.V.	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.doi	10.1016/j.cma.2012.03.004	en
dc.identifier.volume	223-224	en
dc.identifier.spage	186	en
dc.identifier.epage	198	en