Mehčanje materiala in lokalizacija deformacij v geometrijsko točni teoriji prostorskih nosilcev z vgrajeno nezveznostjo

doktorska disertacija

Klara Štrus (Author), Miran Saje (Mentor), Igor Planinc (Thesis defence commission member), Sebastjan Bratina (Thesis defence commission member), Simon Schnabl (Thesis defence commission member), Dejan Zupan (Co-mentor)

Abstract

Ko je v materialni točki trdnega telesa doseženo neko kritično stanje, se začnejo razvijati lokalizirane deformacije, kar povzroča nezveznosti v polju deformacij in močno pospeši lokalno deformiranje materiala. V doktorski nalogi obravnavamo te vrste lokalizacije deformacij v teoriji geometrijsko točnih prostorskih nosilcev. Predstavimo novo formulacijo prostorskih linijskih nosilcev, ki upošteva mehčanje materiala prek vgrajenih nezveznosti deformacij. Gre za razširitev osnovne deformacijske metode končnih elementov tako, da omogoča zaznavanje pojava lokalizacije in razširi sistem enačb, iz katerega lahko nato izračunamo tudi skoke deformacij, pomikov in rotacij pri nadaljnjem deformiranju. Zahteva po enakosti konstitucijskih in ravnotežnih sil in momentov se izkaže za primerno pri implementaciji v nezvezno formulacijo, nastanek lokalizacije pa je povezan z izgubo enoličnosti konstitucijskih enačb prečnega prereza. Takoj ko njihov inverzni več enoličen, sta rešitvi za deformacije prečnega prereza lahko dve. Pri nadaljnjem deformiranju ena od teh rešitev sledi mehčanju materiala. Nezvezne inkremente deformacij, pomikov in rotacij mehčajočega prečnega prereza dobimo iz enačb konstrukcije, ki jih dopolnimo z dodatnimi konstitucijskimi pogoji mehčajočega prečnega prereza. Osnovne neznanke interpoliramo in zvezne enačbe diskretiziramo po metodi končnih elementov, pri čemer izberemo kolokacijsko metodo. Enačbe rešujemo z Newtonovo iteracijsko metodo, zato podrobno predstavimo njihovo linearizacijo in dodajanje popravkov. Nov element vgradimo v računalniški program in testiramo na numeričnih primerih, pri čemer uporabimo metodo ločne dolžine za sledenje obtežno-deformacijski poti in plastični konstitucijski zakon materiala.

Keywords

Grajeno okolje;gradbeništvo;disertacije;geometrijsko točni prostorski nosilci;materialno mehčanje;lokalizacija deformacij;izguba enoličnosti;vgrajena nezveznost;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.08 - Doctoral Dissertation
Organization:	UL FGG - Faculty of Civil and Geodetic Engineering
Publisher:	[K. Pirmanšek]
UDC:	539.3:624.046+624.075(043)
COBISS:	8182881
Views:	1077
Downloads:	829
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Material softening and strain localization in spatial geometrically exact beam finite element method with embedded discontinuity
Secondary abstract:	When some critical condition is reached at a material point of a solid body, a localized strain starts developing which makes the strain field discontinuous and highly accelerates local damaging of material. The present thesis addresses this kind of strain localization in spatial geometrically exact beams. Here we propose a new beam finite element formulation which accounts for softening of material by applying the embedded strong strain discontinuity technology. The formulation is essentially an extension of the original strain-based formulation and upgraded such to allow for detecting the onset of strain localization and to introduce additional equations for evaluating singular strain peaks and jumps of displacements and rotations at the localized section in further deformation. The consistency condition that the equilibrium and the constitutive stress-resultants are equal is shown to be naturally suited for the implementation into the discontinuous formulation. The condition for the onset of strain localization at a beam cross-section is here related to the loss of uniqueness of the beam cross-sectional constitutive equations. If the condition for a unique inverse is violated, two solutions are possible for cross-sectional strains. In a subsequent deformation, one of the two solutions follows the softening regime of material. The discontinuous increments in strains, displacements and rotations at the softening cross-section are obtained from the equations of the structure supplemented by the consistency conditions of the softening cross-section. The primary unknowns are interpolated and a collocation method is chosen for discretization of the continuous equations. The system of equations is solved by the iterative Newton method, therefore the linearization of equations and the update procedure are presented. The computer code is generated and the performance of the formulation is tested on numerical examples where the arc-length method is used to track the load-deformation path of constructions and a plastic material constitution model implemented.
Secondary keywords:	Built Environment;civil engineering;doctoral thesis;geometrically exact beam finite element;material softening;localization of deformation;loss of uniqueness;embedded discontinuity;
Type (COBISS):	Doctoral dissertation
Thesis comment:	Univ. v Ljubljani, Fak. za gradbeništvo in geodezijo
Pages:	XVIII, 50 str., 4 pril.
ID:	10895418