Limit load and deformation analysis forframe structures with mathematical programming

DSpace/Manakin Repository

Show simple item record

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

Files in this item

This item appears in the following Collection(s)

Show simple item record