## Babes-Bolyai University of Cluj-Napoca Faculty of Mathematics and Computer Science Study Cycle: Master SUBJECT

 Code Subject MMM1001 Continuum Mechanics
 Section Semester Hours: C+S+L Category Type Applied Mathematics 1 2+1+0 speciality compulsory
 Teaching Staff in Charge
 Prof. KOHR Mirela, Ph.D.,  mkohrmath.ubbcluj.ro
 Aims The aim of this course is the acquirement and thoroughgoing study of certain fundamental notions of continuum mechanics related to movement and deformation of continuum media. The study of certain special models of continuum mechanics. Applications of the complex function theory to the study of steady potential flow of incompressible ideal fluids. Special problems concerning viscous fluid flows. Special problems of Elasticity. The students will be involved in the research activity.
 Content 1. Kinematics of Continuous Media: Continuous medium, fluid, configuration, motion. The velocity and acceleration fields of the motion of continuous medium. Descriptions of the motion of a continuous medium: Lagrangean and Eulerian descriptions. Stream lines. Material derivatives. 2. Dynamics of Continuous Media: The principle of mass conservation. The continuity equation. Cauchy@s stress principle. Cauchy@s fundamental theorem. The principle of the momentum variation. Cauchy@s equations. The principle of the moment of momentum variation. The symmetry of the stress tensor. The principle of initial data. 3. The principle of thermodynamics. The energy equation. Applications. 4. Constitutive equations of Fluid Mechanics: The constitutive equation of ideal fluid. Euler@s equation. The constitutive equation of Newtonian viscous fluid. The Navier-Stokes equations. 5. The model of the ideal fluid. The motion equations. Boundary and initial conditions. Uniqueness theorems. Complex potential. The plane potential flow of incompressible ideal fluid. Translation motion. Source and vortex potential. The flow in the presence of a circular obstacle. The Riemann-mapping theorem. The flow in the presence of a given obstacle. Applications. 6. The method of boundary integral equations in the study of steady potential flow of incompressible fluid. 7. Elasticity: Material description. The deformation theory. The constitutive equation of classical linear elasticity. Hooke@s law. The motion equation. Boundary and initial conditions. The Navier-Lamé equations of equilibrium. Uniqueness theorems. Applications. 8. The Navier-Stokes equations. Boundary and initial conditions. Uniqueness theorems. Exact solutions of the Navier-Stokes equations. Applications.
 References 1. Kohr, M., Modern Problems in Viscous Fluid Mechanics, Cluj University Press, Cluj- Napoca, 2 vols. 2000 (in Romanian). 2. Kohr, M., Pop, I., Viscous Incompressible Flow for Low Reynolds Numbers, WIT Press (Wessex Institute of Technology Press), Southampton (UK) – Boston, 2004. 3. Dragoş, L., Mecanica Fluidelor. Editura Academiei Române, Bucureşti, 1999. 4. Dragoş, L., Principiile Mecanicii Mediilor Continue, Editura Tehnică, Bucureşti. 5. Truesdell, C., Rajagopal, K.R., An Introduction to the Mechanics of Fluids, Birkhäuser, Basel, 2000 6. Truesdell, C., A First Course in Rational Continuum Mechanics, Vol. 1, Academic Press, New York, 1991 7. Hunter, S.C., Mechanics of Continuous Media, Ellis Horwood Ltd., 1983. 8. Kiselev, S.P., Vorozhtsov, E.V., Fomin, V.M., Foundations of Fluid Mechanics with Applications. Problem Solving Using Mathematica, Birkhäuser, Boston, 1999 9. Brǎdeanu P., Mecanica fluidelor, Editura Tehnică, Bucureşti, 1973. 10.Saad, M., Elasticity. Theory, Applications and Numerics, Elsevier, 2005.
 Assessment Final mark is given by: Written exam: 70% Seminar activity: 30%
 Links: Syllabus for all subjects Romanian version for this subject Rtf format for this subject