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Mechanics Colloquim

 

PROGRAM


MATEMATIČKI INSTITUT SANU
ODELJENJE ZA MEHANIKU

PROGRAM ZA MART 2010.

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

SREDA, 10. mart 2010. u 18 sati:


Jovo Jaric, Matematicki fakultet Beograd; Zoran Golubovic, Masinski fakultet Beograd; Dragoslav Kuzmanovic Saobracajni fakultet Beograd
ON ENTROPY FLUX OF ANISOTROPIC ELASTIC BODIES

Exploitation of entropy principle based on the Clausius-Duhem inequality has been widely adopted in the development of modern continuum thermodynamics following The simple Colman-Noll procedure. The main assumption, that the entropy flux is defined as the heat flux divided by the absolute temperature is referred as the classical Entropy flux relation. On the other hand, a new theory of the entropy principle based on the general inequality has been proposed by Mueller and the method of Lagrange multipliers proposed by Liu. For isotropic elastic and viscoelastic materials it is proved that the classical entropy relation remains valid in the new theory. However for anisotropic elastic materials in general, the validity of the classical entropy flux relation is yet to be explored. Very recently Liu considered transversely isotropic elastic bodies, and show that the classical entropy flux relation does not hold in general. Based on modified Liu's approach we further investigate the entropy flux relation for several other crystal systems: Orthotropy, Triclinic systems, Monoclinic Systems and Rhombic Systems. Our Investigation shows that the classical entropy flux relation does not hold not only for transversely isotropic elastic bodies but also for other crystal systems, in general.



SREDA, 17. mart 2010. u 18 sati:


Katica (Stevanovic) Hedrih, Matematicki institut SANU Beograd
TRIGGER OF COUPLED SINGULARITIES IN NONLINEAR DYNAMICS OF A HEAVY MASS PARTICLE ALONG ROTATE ROUGH CIRCLE

In previous published papers lecturer presented a series of the theorems of coupled singularities existence in nonlinear dynamical systems as well as theorem of homoclinic orbit in the form of number eight. Also, in corresponding published papers some examples of the nonlinear dynamics of the engineering system shown improvement of previous defined theorems. Some new research results of fascinating non-linear dynamics of a heavy mass particle along rotate rough circle with Coulomb’s type friction, accepted for publishing, will be presented. Also, for the case that circle rotate around an axis, the differential double equation is derived and analysed in the particular cases in the phase plane. Trigger of coupled singularities and bifurcations of the singularities into sub-triggers of singularities caused by Coulomb’s type friction will be analysed. The alternations of the Coulomb’s type friction force are analysed. A visualization of the phase trajectories and homoclinic orbits will be presented, also. Key words: Non-linear dynamics, coupled rotation, mass particle, rough circle, Coulomb’s frictions, homoclinic points, homoclinic orbit, trigger, sub-trigger, coupled singularities, bifurcation, phase plane portrait, separatrice layering, phase trajectory in the form of number eight.



SREDA, 24. mart 2010. u 18 sati:
Bojan Medjo, Tehnolosko-metalurski fakultet Beograd; Marko Rakin, Tehnolosko-metalurski fakultet Beograd; Nenad Gubeljak, Masinski fakultet Maribor; Aleksandar Sedmak, Masinski fakultet Beograd
ANALIZA NASTANKA ZILAVOG LOMA U ZAVARENIM SPOJEVIMA PRIMENOM LOKALNOG PRISTUPA

Predvidjanje nastanka zilavog loma u zavarenim konstrukcijama je veoma vazno za procenu njihovog integriteta, jer spojevi cesto sadrze pocetne greske, koje mogu biti mesta nastanka prslina. Lokalni pristup je pogodan za razmatranje ovakvih struktura, jer koristi parametre kojima se kvantifikuje ostecenje na lokalnom nivou - usled postojanja supljina u materijalu. Odgovarajuca primena ovog pristupa podrazumeva ispitivanje mikrostrukture, karakterizaciju materijala, ispitivanja mehanike loma, modeliranje ponasanja materijala pri razvoju ostecenja primenom mikromehanickih modela, kao i proracune metodom konacnih elemenata (MKE). Lokalni pristup zilavom lomu je ovde primenjen u analizi nastanka i rasta prline u zavarenim spojevima. Korisceni mikromehanicki model - kompletni Gursonov model (CGM) se zasniva na Gursonovom kriterijumu plasticnog tecenja, prema kome se materijal razmatra kao porozna sredina - cime se uzima u obzir uticaj supljina na naponsko stanje i tecenje materijala. Bice prikazani rezultati koji ukljucuju analizu uticaja razlike u osobinama osnovnog materijala i metala sava (tzv. mismatch effect), sirine spoja, velicine i formulacije konacnog elementa u ligamentu ispred vrha prsline i duzine pocetne prsline na predvidjanje nastanka zilavog loma u ispitivanim spojevima. Posebna paznja bice posvecena vezi izmedju mikrostrukturnih parametara i ponasanja materijala pri lomu.

Sednice se održavaju u zgradi SANU, Knez Mihailova 35, u sali 2 na prvom spratu.

Sekretar Odeljenja
Bojan Međo
Upravnik Odeljenja
Akademik Teodor Atanacković, s.r.