Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Theory of impact (17.DTM02)

Native organizations units: Chair of Machine Elements, Machine and Mechanism Theory and Mechanical Engineering in Agriculture

Type of studies	Title
Doctoral Academic Studies	Mechanical Engineering (Year: 1, Semester: Winter)
Doctoral Academic Studies	Mechatronics (Year: 2, Semester: Winter)
Doctoral Academic Studies	Mechatronics (Year: 1, Semester: Winter)
Doctoral Academic Studies	Traffic Engineering (Year: 1, Semester: Winter)

General information:

Category	Scientific-professional
Scientific or art field	Deformable Body Mechanics Mechanics
ECTS	10

Professor`s intention is through this course to: - expand terms of classic analytical mechanics to the set of general functions (distributions) as well as to involve differential equations of mechanic systems movement with interrupted right sides (differential inclusions) what is directly applied in problems including collision and dry friction, - understand how mechanic methods can be applied in bio system problem analysis which are more complex and principally less defined than technical problems mainly consisting of simple geometric forms, in order to analyse problems that include vehicle collision and participants injuries.

Upon completion of this course student acquires knowledge to: - utilize acquired knowledge in engineering disciplines which as tool use non smooth mechanics, and deal with collision analysis, - recognize through models various movements of real systems, effects of various actions (forces and force coupling, regular and impact), analyse friction and energy balance, as well as to simulate forecasting of various models by using computers, - apply acquired knowledge in analysing movement and collision of actual mechanical systems including biological, i.e., to identify, formulate (idealise practical problems by using appropriate mathematical model) and solve problem in the field covered by following content, with special insight to restrains resulting from entopic inequality,- communicate and work with other engineers on the team.

Elements of collision theory. Derivative in the distribution sense. Distribution model of collision. General Euler-Lagrange equations of second type. Theorem on kinetic energy application on collision. Collision theory of Hertz type – regularization. Zener model. Constrains deriving from Clausius – Duhem inequality. Fremont approach. Herz-Signorini-Moreau law of unilateral contact. Linear complementarity problems. Generated derivative and differential. Different models of force of dry friction. Differential inclusions. Theorem by Phillip. Mechanical systems with forces which are modelled by multi-value functions. Non smooth potentials. Method of wider Lagrange. Application of Gaussian principle. Methods of numerical integration. Moreau algorithm. Human body structure. Mechanical features of biomaterials. Inner forces in human body. Dynamic modelling of human joints with special emphasis on knee and connection neck head. Models for collision analysis with special emphasis on biodynamic response of human body in frontal collision as head response to crash. Air bag models.

Lectures, study research work and consultations. The lectures provide a theoretical part of the material using modern equipment and information and communication technologies. Through lectures, a student acquires and mastered contemporary scientific knowledge, scientific methods and procedures that enable him to become independent research work. In addition to lectures, consultations are also held regularly. Study research work includes all forms of teaching that are in the function of directly training a student for research, writing scientific papers and making a doctoral dissertation. Study research work includes active monitoring of primary scientific sources, organization and execution of numerical simulations and experimental research.

Authors	Title	Year	Publisher	Language
B. Brogliato	Non-smooth mechanics, Springer, London	1999	Springer, London	English
R. Leine and H. Nijimeijer	Dynamics and bifurcations of nonsmooth mechanical systems	2004	Springer, Berlin	English
N. Ayache (ed.)	Computational models for the human body	2004	Elsevier, Amsterdam	English
Ch. Glocker	Set valued force laws, Dynamics of non-smooth systems	2001	Springer, Berlin	English