Limit load and deformation analysis forframe structures with mathematical programming

Manola, Marina-Myrto

dc.contributor.author	Manola, Marina-Myrto	en
dc.date.accessioned	2015-09-08T08:39:27Z
dc.date.available	2015-09-08T08:39:27Z
dc.date.issued	2015-09-08
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/41214
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.2104
dc.rights	Default License
dc.subject	limit analysis, mathematical programming, complementarity conditions, stress resultant interaction, holonomic behavior	en
dc.title	Limit load and deformation analysis forframe structures with mathematical programming	en
dc.contributor.department	Εργαστήριο Στατικής και Αντισεισμικών Ερευνών	el
heal.type	doctoralThesis
heal.secondaryTitle	Οριακή και παραμορφωσιακή ανάλυση πλαισιωτών κατασκευών με χρήση μεθόδων μαθηματικού προγραμματισμού	el
heal.classification	Structural analysis (Engineering)	en
heal.classificationURI	http://id.loc.gov/authorities/subjects/sh85129216
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2015-03-30
heal.abstract	This thesis concerns the determination of the ultimate structural state using mathematical programming techniques. Its main objective is to highlight the inner structure and drawbacks of the existing methods and to propose new approaches that improve and enhance their performance. The ultimate load and state of a structure is determined by solving an optimization problem that is based on the piecewise linearization of yield condition and constitutive laws. For rigid-perfectly plastic behavior, limit analysis is formulated as a Linear Programming (LP) problem expressing both the static and kinematic theorem. Incorporation of deformation constraints and/or softening behavior leads to the formulation of an optimization problem that aims at the maximization of the load factor subjected to equilibrium, compatibility, yield and complementarity constraints. Due to the disjunctive nature of the latter, the problem becomes nonsmooth, nonconvex and numerical unstable. Thus, a penalty function formulation is used to reformulate it to a nonlinear programming (NLP) problem, the size of which is strictly related to the discretization of the yield surface and the constitutive laws. In this work, the main research objectives revolve around the expression of yield condition and the incorporation of hardening/softening behavior in a more efficient way. Therefore, yield condition is expressed following three different schemes: i) a convex hull formulation, ii) a cone identification approach and iii) a local linearization technique. According to the convex hull formulation, yield condition is given in the form of a linear combination of the vectors corresponding to all vertices that define the a priori linearized yield hypersurface. The cone identification approach is based on the fact that for every cross section and at each optimization iteration only one yield constraint is potentially or truly activated and thus only one yield constraint is required. Extending this concept for the local linearization technique, the critical hyperplane for each cross section is not a priori defined, but it is determined at each optimization iteration for every stress point by locally linearizing the yield surface. In addition, multi-linear and nonlinear hardening/softening structural behavior is embedded efficiently without affecting the size of the problem. The herein proposed approaches uncouple the size of the problem from the linearization of the yield surface and constitutive laws, reducing accordingly the size of the complementarity condition that is the source of numerical difficulties for the solution of the problem. Numerical results of plane and 3D steel frames prove the computational advantages of the proposed formulations for multi-component interaction and multi-linear or nonlinear structural behavior. The main conclusions of this dissertation may constitute the central points of future research concerning limit analysis not only in the field of structural engineering, but also in fracture and soil mechanics applications.	en
heal.sponsor	Χορήγηση υποτροφίας: Ηράκλειτος ΙΙ	el
heal.advisorName	Koumousis, Vlasis	en
heal.committeeMemberName	Sapountzakis, Evangelos	en
heal.committeeMemberName	Tsopelas, Panagiotis	en
heal.committeeMemberName	Papadrakakis, Manolis	el
heal.committeeMemberName	Bisbos, Christos	el
heal.committeeMemberName	Vayas, Ioannis	en
heal.committeeMemberName	Lagaros, Nikolaos	en
heal.academicPublisher	Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.fullTextAvailability	true