Exact analytic solutions of the nonlinear partial differential equations governing rigid perfect plasticity problems

Stampouloglou, IH; Theotokoglou, EE; Panayotounakos, DE

dc.contributor.author	Stampouloglou, IH	en
dc.contributor.author	Theotokoglou, EE	en
dc.contributor.author	Panayotounakos, DE	en
dc.date.accessioned	2014-03-01T01:22:19Z
dc.date.available	2014-03-01T01:22:19Z
dc.date.issued	2005	en
dc.identifier.issn	0001-5970	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16529
dc.subject	Analytic Solution	en
dc.subject	Boundary Condition	en
dc.subject	Large Classes	en
dc.subject	Nonlinear Partial Differential Equation	en
dc.subject	Numerical Solution	en
dc.subject	Second Order	en
dc.subject.classification	Mechanics	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Derivatives	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Strain	en
dc.subject.other	Stresses	en
dc.subject.other	Theorem proving	en
dc.subject.other	Governing equations	en
dc.subject.other	Nonlinear partial differential equations	en
dc.subject.other	Strain increments	en
dc.subject.other	Velocity distribution	en
dc.subject.other	Plasticity	en
dc.title	Exact analytic solutions of the nonlinear partial differential equations governing rigid perfect plasticity problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00707-004-0187-x	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00707-004-0187-x	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	We provide exact analytic solutions for the stress and velocity states in statically determinate rigid, perfectly plastic bodies under plane-strain conditions. The extracted solutions include more than one arbitrary function, a fact that permits us to use them for large classes of boundaries and boundary conditions. In addition, other solutions by making use of several ad hoc assumptions are constructed including one arbitrary function. For the stresses the solutions are extracted by the full decoupling of the system of the equilibrium equations and the appropriate von Mises-Hencky nonlinear condition, leading to a second order nonlinear partial differential equation (PDE) of the Monge type; for the velocities we use the Saint Venant-von Mises theory of plasticity PDEs. Several applications concerning the so-called direct problem are examined. The advantage of the proposed analytical solution methodology compared to the technique of characteristics is the general applicability delivered from the a priori construction of slip lines, as well as the demanded numerical solutions of the corresponding equations of characteristics.	en
heal.publisher	SPRINGER WIEN	en
heal.journalName	Acta Mechanica	en
dc.identifier.doi	10.1007/s00707-004-0187-x	en
dc.identifier.isi	ISI:000227072700001	en
dc.identifier.volume	174	en
dc.identifier.issue	1-2	en
dc.identifier.spage	1	en
dc.identifier.epage	20	en