prikaz prve stranice dokumenta Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala
Access restricted to authenticated users
master's thesis
Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala
2021. urn:nbn:hr:179:032818
Samardžić, Domagoj
University of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
Department of Mechanical Engineering and Naval Architecture

Cite this document

Samardžić, D. (2021). Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala (Master's thesis). Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture. Retrieved from https://urn.nsk.hr/urn:nbn:hr:179:032818

Samardžić, Domagoj. "Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala." Master's thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2021. https://urn.nsk.hr/urn:nbn:hr:179:032818

Samardžić, Domagoj. "Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala." Master's thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2021. https://urn.nsk.hr/urn:nbn:hr:179:032818

Samardžić, D. (2021). 'Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala', Master's thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, accessed 07 April 2025, https://urn.nsk.hr/urn:nbn:hr:179:032818

Samardžić D. Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala [Master's thesis]. Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture; 2021 [cited 2025 April 07] Available at: https://urn.nsk.hr/urn:nbn:hr:179:032818

D. Samardžić, "Analiza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala", Master's thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:179:032818

Please login to the repository to save this object to your list.
Metadata
TitleAnaliza deformacija i naprezanja elemenata izrađenih od hiperelastičnih materijala
Title (english)Strain and stress analysis of elements made of hyperelastic materials
AuthorDomagoj Samardžić
MentorŽeljan Lozina (mentor)
GranterUniversity of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
(Department of Mechanical Engineering and Naval Architecture)
Split
Defense date and country2021-03-17, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Mechanical Engineering
Abstract
U mehanici kontinuuma, posebno kod analize čvrstoće deformabilnih tijela, najveću zastupljenost imaju metali i njihove slitine čije su konstitutivne jednadžbe naprezanja i deformacija razrađene do najmanjih detalja. Međutim, u zadnjoj polovici 20. stoljeća hiperelastični materijali imaju sve veću zastupljenost u praksi zbog razvoja i porasta znanja o njihovim ponašanjima. Sadržaj ovog rada usmjeren je na nelinearnu mehaniku krutih tijela odnosno pojam hiperelastičnog materijala i njegovih... More karakteristika, zajedno s postupcima rješavanja. Na samom početku predstavljeni su temeljni pojmovi vezani za gibanje i naprezanja tijela s velikim deformacijama i promjenama volumena. Opisane su bitne kinematske veličine iz teorije konačnih deformacija kao i njihovi intenziteti vremenskih promjena. Izvedene su jednadžbe naprezanja i stanja ravnoteže, uz opis i izvod jednadžbe virtualnog rada u materijalnoj i prostornoj konfiguraciji. Prikazani su alternativni prikazi naprezanja (prvo i drugo Piola-Kirchhoff-ovo naprezanje) te njima konjugirane veličine deformacije koje se koriste u formulaciji jednadžbe virtualnog rada. Uveden je pojam hiperelastičnog materijala uz izraze koji definiraju nelinearno ponašanje i velike deformacije. Također, ukratko su opisani neki od modela hiperelastičnih materijala te njihove odgovarajuće jednadžbe akumulirane funkcije energije deformacije iz kojih slijede izrazi za odgovarajuća naprezanja i tenzore elastičnosti. S obzirom na to da se radi o nelinearnom ponašanju materijala, potrebno je primijeniti linearizaciju konstitutivnih jednadžbi da bi se mogao implementirati Newton-Raphson iterativni postupak. U tu svrhu linearizirane su jednadžbe virtualnog rada u materijalnoj i prostornoj konfiguraciji. Pri tome, svaka linearizirana komponenta jednadžbe virtualnog rada predstavlja doprinos temeljnoj jednadžbi formulacije konačnih elemenata: K u=F. Objašnjena je nelinearna formulacija metode konačnih elemenata, uz diskretizaciju bitnih kinematskih veličina i jednadžbi ravnoteže s ciljem uspostave tangentne matrice krutosti K i vektora ekvivalentnih čvornih sila. Na samom kraju, za numeričku primjenu odabran je softver FLagSHyP koji sadrži biblioteku potrebnih funkcija koje se koriste za rješavanje nelinearnih statičkih problema. Dane su kratke upute korištenja softvera te riješeni određeni primjeri kako bi se prikazale nelinearne ovisnosti između naprezanja i deformacije. Riješeni primjeri opisani su hiperelastičnim modelom materijala s jednakim svojstvima s namjerom utvrđivanja ponašanja određenog modela u različitim slučajevima opterećenja. Zaključno, pokazan je utjecaj svojstva hiperelastičnog materijala na njegovu krutost. Less
Abstract (english)
In continuum mechanics, particularly at solid mechanics analysis of deformable bodies, metals and their alloys have the largest share, whose constitutive stress and strain equations have been worked out to smallest detail. However, in the last half of 20th century, hyperelastic materials have an increasing presence in practice due to the development and thus increase of knowledge about their behaviours. Content of this thesis is focused on nonlinear solid mechanics respectively, on... More concept of hyperelastic material and its characteristics, together with resolution procedures. Initially, basic terms related to motion and stresses of bodies with great deformations and volume change are introduced. Important kinematic quantities from the finite strain theory as well as their time change intensities are described. Stress and equlibrium equations have been derived, with description and derivation of principle of virtual work in material and spatial configuration. Alternative stress representations are shown (first and second Piola-Kirchhoff stress) and their conjugate deformation quantities which are used in formulation of principle of virtual work. The notion of hyperelastic material is introduced with expressions that define nonlinear behaviour and large deformations. Some models of hyperelastic materials are also briefly described and their corresponding stored strain energy functions, from which the expressions for coresponding stresses and elasticity tensors follow. Since it is a matter of nonlinear material behavior, it is necessary to apply linearization of constitutive equations in order to implement Newton-Raphson iterative procedure. For this purpose, virtual work equations in material and spatial configuration are linearized. Thereby, every component of linearized virtual work equation represents a contribution to the fundamental equation of finite element formulation: K u=F. The nonlinear finite element method formulation is explained, with discretization of essential kinematic quantities and equilibrium equations with the aim of establishing tangent stiffness matrix K and vectors of equivalent nodal forces. At the very end, the software FLagSHyP was selected for numerical application, which contains a library of necessary functions used to solve nonlinear static problems. Brief instructions regarding the use of software are given and certain examples are solved in order to show and explain nonlinear dependence between stress and strain. Solved examples are described by the same hyperelastic material model with the equal properties with the goal to present behavior of a certain model in different load cases. In conclusion, influence of the properties of hyperelastic material on its stiffness is shown. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:179:032818
Study programmeTitle: Mechanical Engineering; specializations in: Structures and Energy Technology, Computer Aided Design and Engineering, Production Mechanical Engineering
Course: Computer Aided Design and Engineering
Study programme type: university
Study level: graduate
Academic / professional title: Magistar/magistra inženjer/inženjerka strojarstva (Magistar/magistra inženjer/inženjerka strojarstva)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
Terms of useLicence In copyright icon
Created on2021-11-29 11:51:45
accessibility

closeAccessibilityrefresh

If you wish to permanently save changes, click on Save, if not - your settings will be reset when you restart the browser.