Metoda končnih elementov za izračun polja napetosti iz polja deformacij ob upoštevanju enakosti glavnih smeri

magistrsko delo magistrskega študijskega programa II. stopnje Strojništvo

Dalibor Hranjec (Author), Miroslav Halilovič (Mentor), Bojan Starman (Co-mentor)

Abstract

Sodobne tehnike in algoritmi omogočajo merjenje polja deformacij z visoko prostorsko in časovno ločljivostjo. Ker je materialni odziv določen s poljem deformacij in napetosti, želimo na osnovi dobljenega polja deformacij določiti še polje napetosti. Temu pravimo inverzni problem. Dosedanji pristopi reševanja inverznega problema so v splošnem predoločeni in zahtevajo uporabo statističnih metod. Reševanje poteka z minimizacijo ciljne funkcije, ki vključuje razlike med merjenimi in računskimi vrednostmi. Takšno reševanje je težavno z vidika implementacije, natančnosti in računskega časa, poleg tega pa je potrebno predpostaviti še konstitutivni model. V magistrski nalogi je predstavljena deterministična formulacija inverznega problema, ki temelji na eni sami predpostavki – predpostavki o sousmerjenosti glavnih osi napetosti in deformacij. Prednost takšnega pristopa je, da pridemo do sistema enačb, ki ga lahko rešimo eksaktno brez uporabe statističnih metod in brez predpostavljenega konstitutivnega modela za širok spekter materialov. Razvili smo enačbo končnega elementa za reševanje inverznega problema in delovanje metode potrdili z numeričnim eksperimentom. Ugotovili smo, da lahko inverzni problem na ta način rešimo s primerljivo natančnostjo in bistveno hitreje kot z obstoječimi pristopi.

Keywords

magistrske naloge;inverzni problem;predpostavka o sousmerjenosti;numerično modeliranje;metoda končnih razlik;metoda končnih elementov;hiperbolična formulacija;enačba končnega elementa;izoparametrični končni elementi;

Data

Language:	Slovenian
Year of publishing:	2023
Typology:	2.09 - Master's Thesis
Organization:	UL FS - Faculty of Mechanical Engineering
Publisher:	[D. Hranjec]
UDC:	519.61:539.37(043.2)
COBISS:	156541443
Views:	353
Downloads:	92
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Finite element method for full-field stress computation from deformation fields under alignment assumption
Secondary abstract:	Modern day imaging techniques and algorithms enable measurement of strain fields with high spatial and temporal resolution. Since the material response is determined by the deformation and stress field, we want to calculate the stress field based on the obtained deformation field. This in known as the inverse problem. The existing approaches to solving the inverse problem are generally overdetermined and require the use of statistical methods. The solution is performed by minimizing the cost function, which includes the differences between the measured and calculated values. Such a solution is difficult from the point of view of implementation, accuracy and computational time, and it is also necessary to assume a constitutive model. This thesis presents a deterministic formulation of the inverse problem, which is based on a single assumption – the codirectionality assumption. The advantage of such an approach is that we arrive at a system of equations that can be solved exactly without an assumed constitutive model for a wide range of materials. We developed a finite element equasion for solving the inverse problem and confirmed the performance of the method with a numerical experiment. We found that the inverse problem can be solved in this way with comparable accuracy and significantly faster than with existing approaches.
Secondary keywords:	master thesis;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. Ljubljana, Fak. za strojništvo
Pages:	XXII, 84 str.
ID:	19356498