An ECCOMAS Advanced Course on Computational Structural Dynamics

Computational Structural Dynamic Short Course

logo Eccomas logo CEACM logo CSM logo UT

The program of the short course

Monday

1. Basics of dynamics (M. Okrouhlík)
- Historical background
- Newton’s laws
- Newtonian, Lagrangian and Hamiltonian mechanics
2. Continuum mechanics I (J. Plešek)
- Kinematics of deformation
- Strains and stresses
- Governing equations
3. Continuum mechanics II (J. Plešek)
- Convexity condition
- Basics of thermodynamics
- Constitutive equations for small and large strains
4. Continuum mechanics III (R. Ohayon)
- Variational formulations in linear dynamics and vibrations
- Modal analysis
- Rayleigh quotient, Hamilton’s principle
5. Dynamics of multibody systems (A. Ibrahimbegovic)
- Governing equations
- Constrains
- Lagrange equations and Lagrange multipliers
- Numerical methods in multibody dynamics

Tuesday

6. Finite element method I (J. González)
- Principle of virtual work
- Finite Element Formulation
- Assembly of global matrices
- Convergence properties
- Examples
7. Finite element method II (A. Ibrahimbegovic)
- Shape functions and higher order FEM
- Isoparametric formulation
- Numerical integration
- Hybrid and mixed formulation, inf-sup condition
8. Finite element method III (A. Tkachuk)
- Locking phenomena and hourglass effect
- Assumed strain, enhanced strain FEM, B-bar formulation
- Reduced integration and stabilization
9. Finite element method IV (J. Kruis)
- Linear solvers in FEM
- Matrix factorization
- Sparse solvers, Krylov methods (especially conjugate gradient method)
10. Finite element method V (A. Ibrahimbegovic)
- FEM for nonlinear problems
- Solvers for nonlinear static problems - NR, BGFS, semi-Newton methods, etc.
- Convergence criteria

Wednesday

11. Finite element method VI (J. Kruis)
- FEM in vibration problems, mass matrix
- Spectral and modal analysis
- Numerical methods for eigen-value problem (subspace iteration, etc)
- Convergence of FEM in eigen-value problem
- Dynamic steady state response
12. Direct time integration in dynamics I (R. Kolman)
- FEM in linear dynamics, formulation of dynamic problems
- Introduction into direct time integration
- Basic methods (Newmark method and central difference method)
- Lumping techniques for mass matricesStability of time schemes
- Stability of time schemes
13. Finite element method VII (A. Ibrahimbegovic)
- Dynamic problems
- Solving of nonlinear time-depend problems
14. Finite element method VIII (A. Combescure)
- Basics of shell theory
- FEM shell models 
- FEM for shells in dynamics
- Mass matrices for shells 
15. Direct time integration in dynamics II (A. Tkachuk)
- Time step size estimates – global/local estimate in FEM
- Treatment of time step size – mass scaling, bi-penalty, etc
- Application in crash problems

Thursday

16. Modal reduction and reduction methods in dynamics (R. Ohayon)
- Variational analysis of dynamic sub-structuring
- Substructuring analysis in discretized (finite element) case
- Hurty and Craig-Bampton methods
17. Partitioned analysis I – basic theory (K.C. Park)
- Theory of Lagrange multipliers
- Basic theory of partitioned analysis
- Equations of motion for partitioned systems
18. Partitioned analysis II (K.C. Park)
- Domain decomposition methods
- Finite element tearing and interconnect (FETI)
- Coupling of FEM/FEM
19. Dynamic contact problems (A. Tkachuk)
- FEM in contact problems
- Penalty method
- Augmented Lagrangian method
- Mortar methods 
20. Finite element method - wave propagation (R. Kolman)
- Theory of wave propagation in elastic solids
- Wave speeds in solids
- Dispersion and frequency analysis of FEM
- Numerical benchmarks

Friday

21. Modern methods of direct time integration (A. Combescure)
- Generalized time schemes
- Asynchronous and variational schemes
- Sub-cycling methods, coupling of different time schemes
22. Coupled problems – Fluid-structures interactions (K.C. Park)
- Variational  formulation
- Methods of discretizations
- Staggered analysis
23. Boundary element method (J. González)
- Introduction into Boundary Element Method
- Linear Acoustics
- Coupling FEM/BEM 
24. Numerical methods for dynamic crack propagation (A. Combescure)
- Extended finite element method (XFEM)
- Meshless methods and Level-set methods
- Cohesive FEM
25. Vibroacoustic/elastoacoustic modelling (R. Ohayon)
- General local equations of vibroacoustic problem
- Choice of unknown fields and variational formulations of the problem
- Finite element discretization and Reduced Order Models for the interior problem

 

imce   Powered by Imce 3.01  © 2015, Pavel Formánek, Institute of Thermomechanics AS CR, v.v.i. [generated: 0.0284s]