# Department of Mechanics

The Department of Mechanics is part of the Faculty of Technical Sciences at the University of Novi Sad, Serbia

An interesting problem...

# Euler's disk...

Mechanics is a science that deals with motion and deformation of bodies under the action of forces. Its essential ingredients are axioms, theorems, proofs, definitions, principles, but at the heart of it, what mechanics really consist of, are problems and solutions.

## Recent events

ICFDA16 , International Conference on Fractional Differentiation and its Applications, Novi Sad, Serbia, 2016

Fractional Calculus for Modelling Phenomena from our Life, Workshop, Novi Sad, Serbia, September 9th, 2016

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### Personal Data

**Dragan T. Spasić, Full Professor**

Location: Wing F/Room 203

Phone: +381 (0)21 485 2234, ~2240, ~2235

Fax: +381 (0)21 450 207

E-mail: spasic@uns.ac.rs

Address: University of Novi Sad, 21000 Novi Sad, Trg D. Obradovica 6, Serbia

Details: March 25, 1961, Born, Novi Sad, Yugoslavia

Status: Married, Children: Kristina (1991), Relja (1994) and Dimitrije (2005)

**Educational and professional experience**

- 1967-1979 Schools in Novi Sad
- 1979-1984 B Sc in Mechanical Engineering, University of Novi Sad
- September 18, 1991 M Sc in Applied Mathematics, University of Belgrade
- December 29, 1993 Doctor of Philosophy, University of Novi Sad
- 1985-1995 Assistant, Department of Mechanics, University of Novi Sad, full time
- 1995 - 2000 Assistant Professor, Department of Mechanics, University of Novi Sad, full time
- 2000 - 2005 Associate Professor, Department of Mechanics, University of Novi Sad, full time
- 2005 - to present, Full Professor, Department of Mechanics, University of Novi Sad, full time

**Responsibilities and main objectives**

- Teaching:
- Supervising graduate and postgraduate works
- Investigator of sponsored research projects
- Administrative:
- 1996-1998, 2007 to present Head of Department
- 2007-2012, 2015, Member of the Faculty of Technical Sciences Council
- 2013-2015 President of Serbian Society of Mechanics

Mechanics in the Departments of Architecture, Industrial Systems and Biomedical Engineering(A207)

Kinematics and Dynamics in the Departments of Mechantronics and Traffic engineering (H112)

Analytical Mechanics in the Department of Mechantronics (H201)

Variational Principles and Non-Smooth Mechanics in the Department of Mechantronics (H303)

Biomechanics and Sports Mechanics in the Department of Mechanics (M4302) and in the State University of Novi Pazar

Dynamics of Non-Smooth Systems in the Department of Mechanics (M404)

Biomechanics of Cardio-Vascular System in the Departments of Mechanics and Biomedical Engiineering (M45991)

Biomechanics in the Departments of Biomedical Engineering and Medical Rehabilitation (BFM.1.1, at the Medical Faculty)

Non-Smooth Mechanics and Optimization (DM406)

Impact Theories (SDI5)

Biomechanical Analysis of Accidents (DSIM7)

**Current research projects:**

- Mechanics of nonlinear and dissipative systems: contemporary models, analysis and applications, Serbian Ministry of Science Project No. 174016
- Engineering analysis of mechanical systems, UNS-FTS-2016-054
- MEDLEM, Cost-effective microfluidic electronic devices for optimal drug administration based on fractional pharmacokinetics for leukemia treatments, no. 690876, (H2020-RISE)
- The optimization of methotrexate pharmacokinetics in personalized leukemia treatments by means of fractional calculus and microfluidic electronic devices, Autonomous Province of Vojvodina, Program 0201

**Recent visiting possitions:**

- Bordeaux University 1, (2013)
- Basic Course on Technical Mechanics at Hubei University of Science and Technology, on behalf of SRH Heidelberg University, (2016)
- Genochem, molecules design and synthesis, Grasse, (2016)

**Recent talks:**

- J. Kolarovic, M.M. Zigic, N.M. Grahovac, M. Mikov, D.T. Spasic, On fractional methotrexate deposition/restoring model in the presence of pleural effusion, (2016), The poster presented at the International Conference on Fractional Differentiation and its Applications ICFDA16, University of Novi Sad, Serbia
- A.S. Okuka, N.M. Grahovac, M.M. Zigic, D.T. Spasic, A seismic protection system comprising an active device, fractional damping and dry friction(2016), The poster presented at the International Conference on Fractional Differentiation and its Applications ICFDA16, University of Novi Sad, Serbia
- D.T. Spasic, N. M. Grahovac, M.M. Zigic, J. Kolarovic, S. Golocorbin-Kon, M. Mikov, On the optimal high dose methotrexate administration in the consolidation phase of acute lymphoblastic leukaemia in children,(2016), The poster presented at the International Conference on Fractional Differentiation and its Applications ICFDA16, University of Novi Sad, Serbia
- D.T. Spasic, On applications of fractional calculus in biomedical engineering, Bulgarian-Serbian symposium “Fractional Calculus and Applications 2015”, 8 December, 2015, IMI-BAS, Sofia, Bulgaria
- D.T Spasic, On not-so-ordinary approach, Mechanics through Mathematical Modelling (MTMM2015 - Symposium in the honour of 70th birthday of Academician Teodor Atanackovic), September 7 - 10, 2015, Branch of the Serbian Academy of Arts and Sciences, Novi Sad, Serbia.
- D.T. Spasic, A solution of fractional Cattaneo-type heat conduction equation in a semi-infinite medium, 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015
- A. Okuka and D.t. Spasic, On active seismic protection combined with both passive fractional damping and dry friction, 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015
- Z.C. Dolicanin and D. T. Spasic (2015), An ocular biomechanics model describing early glaucoma caused alterations in the peripapillary sclera, Presented at 7th Polyahov Readings, Saint-Petersburg, Russia
- I.M. Mitic, V. Crnobrnja, D.T. Spasic and T. M. Atanackovic (2014), On fractional hemodialysis model with endochrone term and flow within compartments, Presented at International Conference on Fractional Differentiation and its Applications, University of Catania, Italy
- M.M. Zigic, N.M. Grahovac and D.T. Spasic (2014), An optimal control problem for a sliding isolated seismically excited structure with passive fractional damping, Presented at International Conference on Fractional Differentiation and its Applications, University of Catania, Italy
- D. Kuzmanovic and D. Spasic, (2012), A case study: an accident reconstruction by use of nonholonomic mechanics and the Hertz theory of impact, Presented at CPMMI 2012, State University of Novi Pazar, Serbia
- D.T. Spasic, (2012), A note on the Atanackovic-Stankovic expansion formula for fractional derivatives and the Leibniz rule, Presented at FDA12, Nanjing, China
- M.M. Zigic and D.T. Spasic, (2012), Response of a column-like structure under a seismic load based on multivalued fractional differential equations, Presented at FDA12, Nanjing, China
- N.I. Kovincic and D.T. Spasic, (2012), Fractional derivative considerations on simplified earthquake dynamics of a column like structure in the presence of dry friction, Presented at FDA12, Nanjing, China
- S.A. Zegzhda, M.P. Yushkov (Saint Petersburg), Sh.Kh. Soltakhanov (Groznyi), D.T. Spasic (Serbia), (2012), Non-holonomic mechanics with high-order constrains and motion control, Plenary lecture at International Scientific Conference on Mechanics 6th Polyahov Readings, Saint-Petersburg, Russia
- D.T. Spasic, (2012), A Note on the Kane Equations for a Rigid Body Motion, Presented at 6th Polyahov Readings, Saint-Petersburg, Russia

**Selected publications of Dragan T. Spasic**

- Proceedings of ICFDA16: International Conference on Fractional Differentiation and its Applications, Novi Sad, Serbia, July 18-20, 2016, Eds: D.T. Spasic, N. Grahovac, M. Zigic, M. Rapaic, T.M. Atanackovic, ISBN 978-86-7892-830-7
- M. Mikov, S. Golocorbin-Kon, N. Grahovac, M. Zigic, D.T. Spasic, (2016), The influence of 12-monoketocholic acid on methotrexate oral absorption in the rat by the means of fractional calculus, Proceedings of ICFDA16: International Conference on Fractional Differentiation and its Applications, Novi Sad, Serbia, Eds: D.T. Spasic, N. Grahovac, M. Zigic, M. Rapaic, T.M. Atanackovic, 146-149, ISBN 978-86-7892-830-7
- N.M. Grahovac, M.M. Zigic, A. Okuka, D.T. Spasic, (2016), On creep/recovery and pulse heating models, Proceedings of ICFDA16: International Conference on Fractional Differentiation and its Applications, Novi Sad, Serbia, Eds: D.T. Spasic, N. Grahovac, M. Zigic, M. Rapaic, T.M. Atanackovic, 582 - 585, ISBN 978-86-7892-830-7
- N. I. Kovincic and D.T. Spasic (2016), Dynamics of a middle ear with fractional type of dissipation, Nonlinear Dynamics, doi:10.1007/s11071-016-2832-z
- D.T. Spasic , N.I. Kovincic , D.V. Dankuc (2016), A new material identification pattern for the fractional Kelvin-Zener model describing biomaterials and human tissues, Communications in Nonlinear Science and Numerical Simulation 37, 193 - 199
- Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, D.T. Spasic, M. Lazarevic, N. Grahovac, M. Zigic, (Editors) ISBN 978-86-7892-715-7
- M. Medic-Stojanoska, T. Icin, I. Pletikosic, I. Bajkin, J. Novakovic-Paro, E. Stokic, D.T. Spasic, B. Kovacev-Zavisic, and L. Abenavoli, Risk factors for accelerated atherosclerosis in young women with hyperprolactinemia, Medical Hypotheses, 84 (2015) 321-326
- J.K. Popovic, D.T. Spasic, J. Tosic, J.L. Kolarovic, R. Malti, I.M. Mitic, S. Pilipovic and T.M. Atanackovic, Fractional model for pharmacokinetics of high dose methotrexate in children with acute lymphoblastic leukaemia, Communications in Nonlinear Science and Numerical Simulation 22 (2015) 451–471.
- D.T. Spasic: ''A Thermodynamically Consistent Rheological Model for Engineering Applications'', book chapter in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, (Eds: V. Mladenov, N. Mastorakis; Com. M. Lazarevic), WSEAS Press, 2014.
- M. Medic-Stojanoska, G. Mitic, I.M. Mitic, D.T. Spasic, N. Curic, S. Pekic, B. Kovacev-Zavisic, and V. Popovic, The Influence of Hyperprolactinemia on Coagulation Parameters in Females with Prolactinomas, Srp Arh Celok Lek. (2014) 314-319 DOI: 10.2298/SARH1406314M
- Nenad M. Grahovac and Dragan T. Spasic, Multivalued fractional differential equations as a model for an impact of two bodies, Journal of Vibration and Control, 2014, Vol. 20, No. 7, 1017-1032. DOI: 10.1177/1077546312471069
- N. Challamel, D. Zorica, T.M. Atanackovic and D. T. Spasic, On the fractional generalization of Eringen’s nonlocal elasticity for wave propagation, Comptes Rendus de Mécanique, (2013).
- D.T. Spasic: ''Mechanics - Part I: Fundamental considerations - Part II: General considerations - Part III: Extensions'', to appear in Novi Sad University Press, (in Serbian), 2013.
- V.B. Glavardanov, D.T. Spasic, T.M. Atanackovic, Stability and optimal shape of Pflüger micro/nano beam. International Journal of Solids and Structures, 49, 2559–2567 (2012).
- N. M. Grahovac, M. M. Zigic and D. T. Spasic, (2012), On impact scripts with both fractional and dry friction type of dissipation, Int. J. Bifircation and Chaos, 22, 4, 1250076, DOI:10.1142/S0218127412500769.
- G. Mitic, M. Kovac, D. Jurisic, V. Djordjevic, V. Ilic, I. Salatic, D. Spasic, A. Novakov Mikic, (2011), Clinical Characteristics and Type of Thrombophilia in Women with Pregnancy-Related Venous Thromboembolic Disease. Gynecol Obstet Invest, 72, p. 103-108 (DOI: 10.1159/000323828)
- John. T. Katsikadelis, "Boundary elements, theory and applications", Elsevier 2002, English to Serbian translation done by D.T. Spasic, 2011. Gradjevinska Knjiga, Beograd.
- A. A. Tikhonov, D. T. Spasic, K. A. Antipov, M. V. Sablina, (2011), Optimizing the electrodynamical stabilization method for a man-made Earth satellite, Avtomatika i Telemekhanika, 9, 2011, c. 112-121. (in Russian), (in English).
- D. T. Spasic (2011), A new impact model with both fractional and dry friction type of energy dissipation pattern, 4th Serbian-Greek Symposium "Recent Advances in Mechanics" Vlasina Lake, Serbia, July, 9-10.
- Sh.Kh.Soltakhanov, D.Spasic, M.P.Yushkov, S.A.Zegzhda (2011), On the possibility of a shockless motion control of a troley with pendulums, Third Serbian Congress on Theoretical and Applied Mechanics, Vlasina lake, Serbia, July 5-8.
- Sh.Kh.Soltakhanov, D.Spasic, M.P.Yushkov, S.A.Zegzhda (2011), Nonholonomic mechanics and motion control, Third Serbian Congress on Theoretical and Applied Mechanics, Vlasina lake, Serbia, July 5-8.
- M.P.Yushkov, S.A. Zegzdha, Sh.Kh. Soltakhanov and D.T. Spasic, (2011), Applications of the generalized Gauss principle in controlling the vibration of a cantilever, Vestnik Nizhegorodskog Universiteta N.I. Lobachevskog, 4, 269-230.
- D. V. Dankuc, N. I. Kovincic and D. T. Spasic (2010), "A new model for middle ear structures with fractional type dissipation pattern", Proceedings of FDA'10. The 4th IFAC Workshop Fractional Differentiation and its Applications. Badajoz, Spain, October 18-20, 2010 (Eds: I. Podlubny, B. M. Vinagre Jara, YQ. Chen, V. Feliu Batlle, I. Tejado Balsera). ISBN 9788055304878, Article No FDA10_156
- N. M. Grahovac, M. M. Zigic and D. T. Spasic (2010), "On impact scripts with both fractional and dry friction type of dissipation", Proceedings of FDA'10. The 4th IFAC Workshop Fractional Differentiation and its Applications. Badajoz, Spain, October 18-20, 2010 (Eds: I. Podlubny, B. M. Vinagre Jara, YQ. Chen, V. Feliu Batlle, I. Tejado Balsera). ISBN 9788055304878, Article No FDA10_142
- D. T. Spasic and V. B. Glavardanov, "Does generalized elastica lead to bimodal optimal solutions?", International Journal of Solids and Structures, (2009), 46, 14-15, 2939-2949
- Proceedings IConSSM 2009 - 2nd International Congress of Serbian Society of Mechanics, Palic (Subotica), 1-5 June 2009, T. Atanackovic, D. Spasic, S. Simic (Editors) ISBN 978-86-7892-173-5
- G. Mitic, Lj. Povazan, R. Lazic, D. T. Spasic and M. Maticki-Sekulic, "Deficiency of the natural anticoagulant proteins in women with pregnancy related venous thromboembolism", Medical Review, (2009), LXII, 1-2, 53-62
- Vujanovic B.D. and Spasic D.T. (2009): "Optimization Methods - Part I: Applied Calculus of Variations with Elements of Analytical Mechanics - Part II: Fundamentals of Optimal Control Theory", Novi Sad University Press, Novi Sad, (
**book**- Third, revised edition in Serbian). - G. Mitic, Dj. Jurisic, M. Scekic, D. Spasic, M. Petkovic, B. Jakovljevic, Z.D. Jelicic, P14 Correlation between the low molecular weight heparin prophylactic dose and the plasma levels of anti Xa activity in pregnant women Page S143, Thrombosis Research, Volume 123, Supplement 2, Pages S1-S165 (2009) Papers and Abstracts of 3rd International Symposium on Women's Health Issues in Thrombosis and Haemostasis, Prague, Czech Republic, 0206-0208 Edited by Benjamin Brenner and Ian A. Greer
- M. M. Zigic, N. M. Grahovac and D. T. Spasic, A simplified earthquake dynamics of a column like structure with fractional type of dissipation, Proceedings of 1st International Congress of Serbian Society of Mechanics, 11-13th April 2007, Kopaonik, Serbia, Eds. D. Sumarac and D. Kuzmanovic.
- N. M. Grahovac, M. M. Zigic, and D. T. Spasic, On multiple impacts with fractional type of dissipation, Proceedings of 1st International Congress of Serbian Society of Mechanics, 11-13th April 2007, Kopaonik, Serbia, Eds. D. Sumarac and D. Kuzmanovic.
- D. T. Spasic and I. M. Mitic, A new model for biomechanics of soft tissue in cardiovascular systems, Proceedings of 1st International Congress of Serbian Society of Mechanics, 11-13th April 2007, Kopaonik, Serbia
- Lj. Petrovic, D. T. Spasic and T. M. Atanackovic (2005), ''On a mathematical model of a human root dentin'', Dental Materials, 21, 125-128
- D. T. Spasic, Analysis of impact dynamics by use of the regularized model approach, Conference on Nonconservative and Dissipative Problems in Mechanics - Book of Abstracts, Novi Sad, 11-14 September 2005.
- D. T. Spasic and T. M. Atanackovic (2004), "Bimodal optimization of a compressed rotating rod", Acta Mechanica, 173, N 1-4, 77-87
- T. M. Atanackovic and D. T. Spasic, (2004): "On viscoelastic compliant contact-impact models", Transactions of ASME Journal of Applied Mechanics, 71, 134-138
- D. T. Spasic, M. Nedeljkov and M. Milutinovic (2004), "A note on airplane landing problem", Proceedings of the First IFAC workshop on Fractional Differentiation and Applications", Bordeaux, France. p.626-629, (Keywords: Nonlinear Fractional Differential Equations)
- Radovic R., Spasic D.T., Karadzic B., Novakovic B., Atanackovic J., Jelicic Z.. and Tepavcevic B., (2002), ''New challenges and opportunities for the city of Novi Sad'', Coordinated by T. Atanackovic, The Danube Commision and The University of Novi Sad, (
**monograph**- 157 pages in English and Serbian) - D. T. Spasic and N. C. Charalambakis (2002): "Forced vibrations with fractional type of dissipation", Proceedings of the International Conference on Nonsmooth/Nonconvex Mechanics with Applications in Engineering, Thessaloniki, p. 323-330
- D. T. Spasic (2002): "Optimal shape of elastic rod against buckling under compression and non-conservative torsion", Proceedings of the International Conference on Nonsmooth/Nonconvex Mechanics with Applications in Engineering, Thessaloniki, p. 249-254).
- I Mitic, ..., D.T. Spasic, ..., (2002), Long term survival in lupus nephropathy, Serbian Archives of Medicine, Journal of Serbian Medical Society, Vol 130, 32-37
- D. T. Spasic and T. M. Atanackovic, (2001): ''A model for three spheres in colinear impact'', Archive of Applied Mechanics Ingenieur-Archive, Springer-Verlag, 71, 327-340
- T. M. Atanackovic and D. T. Spasic, (1999): ''On the Impact of Elasctic Bodies with Adhesive Forces'', Meccanica, 34, 367-377, Kluwer AP
- Petrović Lj. and Spasić D. T. (1998): "Investigation of the bond strength of various composites to tooth structure", Proceedings of 5th International Conference on Composites Engineering, Las Vegas, 723-724
- Atanackovic T. M., Guran A. and Spasic D. T. (1998): "A variational principle for equation of Hertz's theory of impact", In Volume 14 of Stability, Vibration and Control of Systems, Series B, 207-210, Ed. A. Guran (Proceedings of First International Symposium on Impact and Friction of Solids, Structures and Inteligent Mashines: Theory and Applications in Engineering and Science).
- Milanov V., Milutinovic M. and Spasic D. T. (1998): "One Problem of Linear Optimization for Vojvodina Region", Proceedings of 3rd International Interdisciplinary Regional Research, Novi Sad, 195-197.
- Spasic, D. T. (1997), "Optimal design of elastic columns for maximal buckling load",
**book chapter**in Volume 3 of Stability, Vibration and Control of Systems, A. Guran and D. Inman Eds. - Stojsic Dj., Spasic D., Obradovic M., Benc D., Jung R., Srdic S., Bikicki M., Dodic S. , Stojsic-Milosavljevic A., (1997): "Does left ventricular hypertrophy correlates with aortic regurgitations?", 10th Annual Meeting of Mediterranean Association of Cardiology and Cardiatic Surgery, Beirut-Lebanon (Research done at Institute of Cardiovascular Diseases, Sremska Kamenica)
- Kovac M., Stojsic A., Jancic B., Grujic S., Stojsic Dj., Spasic D., Cikos J., (1997): "Quantification of mitral regurgitation with 2D and Doppler echocardiography", 9th International Congress on Echocardiography "Clinical Cardiology", Book of Abstracts, Roma (Italy) 1997, pp. 111, (Research done at Institute of Cardiovascular Diseases, Sremska Kamenica), also in The Journal of Heart Failure, Vol. 4, No 1, May 1997, pp. 93, (371)
- D. T. Spasic and B. V. Glavardanov, (1996): ''Stability of a rigid sphere supported by a thin elastic column'', Eur. J. Mech., A/Solids, 15, 2, 337-350, Gauthier-Villars
- Spasić D.T. (1995): "On nonlinear oscillatory motion with force acting on nonconvex domain", Proceedings of 21st, Yugoslav Congress of Applied Mechanics, Nis, (in Serbian).
- T. M. Atanackovic and D. T. Spasic, (1994): ''A model for plane elastica with simple shear deformation pattern'', Acta Mechanica 104, 241-253, Springer-Verlag
- Spasic D.T. (1994): "Optimal shape of water tower against buckling", Proceedings of Symposia in Mechanics, Novi Sad, (in Serbian).
- D.T. Spasic, (1993), "On stability of a compressed and twisted linearly elastic rod", University of Novi Sad,
**PhD Thesis**, written under direction of Prof. Dr.-Ing. Teodor M. Atanacković, - T. M. Atanackovic and D. T. Spasic, (1991): ''Effect of shear and compressibility on stability of a heavy column with an end load'', Q. J. Mech. appl. Math., 44, 4, 601-617, Oxford UP
- Spasic D.T. (1988): "A note on the existence of non-symmetric solutions of symmetric non-linear two-point boundary value problems", Proceedings of 18th Yugoslav Congress of Applied Mechanics, Vrnjačka Banja, (in Serbian).
- Spasic D.T. (1988): "On estimation of blood function in the process of drug transmission", Proceedings of 3rd YUREMA Symposia in Medicine and Engineering, Zagreb, (in Serbian).

**Leisure activities:**

- Very small vineyard arround the house in Srem.
- Traditional Karate School of Novi Sad, awarded Sho-Dan from Master Slobodan Milicevic, Shichi-Dan (ITKF).