## Other Lectures

### Content:

(1) Introduction to the Thermodynamics of a compressible fluid. (2) A short review of the Thermodynamics: Basic expressions and basic relations, first and second law of thermodynamics. State and process variables, closed and open systems, work of expansion (and compression), shaft work and technical work, specific heat, dissipation, enthalpy, entropy. (3) Thermomechanics of a compressible fluid: The perfect-gas relationship, speed of sound waves, Mach number, isentropic flow, shock waves, Fanno and Rayleigh line, adiabatic flow with friction in conduits, frictionless flow with heat transfer, steady isothermal flow, isothermal flow in long pipes, subsonic and supersonic flow in pipes. (4) Non-deformable bodies in a flow of compressible fluids. Three important speed ranges: high speed subsonic, trans-sonic and supersonic. Approaching the speed of sound, the transsonic flight, normal and oblique shock waves, the effects of shockwaves. Movement of soundlines and shockwaves on the surface of an airofoil. Supersonic flow round a corner (sharp edged or rounded). The centre of pressure position.

### Content:

d’Alembert's principle, Lagrange equations, variational principle, action, Hamilton's principle, Euler-Lagrange equations, gauge transformation, Legendre transformation, canonical systems, symmetries & conservation, Noether's theorem, rotation group, Lie algebra, canonical transformation, Liouville's theorem, Poisson brackets, conserved quantities, Hamilton-Jacobi differential equation, integrable systems, perturbation of quasiperiodic systems, KAM theorem.

### Content:

Continuum-mechanical and thermodynamical basis rheological models elasticity, hyperelasticity, viscoelasticity, plasticity, viscoplasticity, porous plasticity, crystal plasticity, various hardening models using the material libraries of finite element software packages algorithmic preparation, explicit and implicit integration algorithms, algorithms for the solution of systems of non-linear equations, consistent tangent operator coding a material subroutine for a finite element program design of experiments for the verification of the simulation results, determination of free parameters.

### Content:

Total differential, state functions, first, second and third law, fundamental equations, generalized Gibbs-Duhem equation, Maxwell's relations, method of Lagrange multipliers, fundamental inequalities, principle of maximum dissipation; applications to problems in metallic systems, independent development of a Gibbs energy minimizer with "Maple", diffusive phase transformations, grain growth and coarsening; an introduction to the thermodynamics of small systems.

### Content:

Different lecturers of great industries report on the application of the finite element method in their respective business. The topic choices are wide-spread, for example: classical mechanical and industrial plant engineering, automotive industry, material development, polymer engineering, refractory materials, mining engineering and many more.