FEM II

1. Dynamics and FEM
2. Mass matrix
3. Equations of motion of elastic systems
4. Natural frequencies and mode shapes
- properties and normalization of mode shapes
- methods for computing eigenvalues and eigenvectors
5. Reduction of the number of DOf in dynamics
6. Response history: modal method
- proportional damping matrix
- vibration caused by initial conditions
- harmonic response
- general excitation
7. Response history: direct integration method (implicit and explicit methods)
8. Principles of solution nonlinear static problems, fundamental numeric solution of contacts in FEM
9. Newton-Raphson method, arc-length method