An ECCOMAS Advanced Course on Computational Structural Dynamics

Computational Structural Dynamic Short Course

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The program of the short course



1. Basics of dynamics and introduction with motivation (K.C. Park)

Introduction of the course

Historical background of dynamics

Newtonian, Lagrangian and Hamiltonian mechanics

2. Continuum mechanics I  (J. Plešek)

Kinematics of deformation

Strains and stresses

Governing equations, Strong form

3. Continuum mechanics II  (J. Plešek)

Overview of continuum termomechanics

Constitutive equations for small strains - elasticity, hyper-elasticity, plasticity

4. Continuum mechanics III (A. Tkachuk)

Variational formulations in dynamics Mixed formulations, Tonti diagram

Hamilton’s principle,Weak forms

5. Dynamics of multibody systems (J. Kim)

Governing equations, Constrains

Lagrange equations and Lagrange multipliers

Numerical methods in multibody dynamics


6. Finite element method I - Basics  (J. Gonzalez)

Principle of virtual work

Finite Element Formulation

Assembly of global matrices

Convergence properties

7. Finite element method II (J. Gonzalez)

Shape functions and higher order FEM

Isoparametric formulation

Numerical integration

Hybrid and mixed formulation, inf-sup condition

8. Finite element method III - Mass matrices (A. Tkachuk)

Properties of mass matrix

Consistent and lumped mass matrices

Higher-order mass matrix

Direct inversion of mass matrix

9. Finite element method IV    (J. Gonzalez)

Implementation of FE codes for linear dynamics (Matlab)

10. Poster section of participants


11. Finite element method V – Beams and Plates (A. Combescure)

Basics of beam theory – Euler-Bernoulli and Timoshenko theory

Basics  of plate theory  - Kirchoff-Love and  Mindlin theory

FEM for beams and plates 

Free vibration of beams and plates

12. Finite element method VI – Shells  (A. Combescure)

Basics of shell theory

FEM shell models 

Shells in dynamics

13. Finite element method VII  (A. Tkachuk)

Locking phenomena and hourglass effect

Assumed strain, enhanced strain FEM, B-bar formulation

Reduced integration and stabilization

14. Finite element method VIII– Linear Solvers (J. Kruis)

Linear solvers in FEM

Matrix factorization

Sparse solvers, Krylov methods (especially conjugate gradient method)

15. Finite element method IX (J. Kruis)

FEM in vibration problems

Spectral and modal analysis

Numerical methods for eigen-value problem (subspace iteration, etc)

Convergence of FEM in eigen-value problem

Dynamic steady state response


16. Finite element method X (A. Popp)

Basics of nonlinear continuum mechanics

FEM for nonlinear problems, Total Lagrangian formulation

Nonlinear solvers - Newton-Raphson method

17. Finite element method XI - Direct time integration in dynamics  (R. Kolman)

FEM in dynamics, formulation of dynamic problems

Introduction into direct time integration

Basic methods (Newmark method and central difference method)

Solving of nonlinear time-depend problems

Time step size estimates, mass scaling

18.  Buckling phenomena (A. Combescure)

Linear theory of stability

Solution methods, path following techniques

Identification of critical points

Pre-buckling analysis and nonlinear stability analysis

19.  Wave propagation (R. Kolman)

Theory of wave propagation in elastic solids, Wave speeds in solids

Dispersion and frequency analysis of FEM,

20. Partitioned analysis (K.C. Park)

Theory of Lagrange multipliers

Basic theory of partitioned analysis

Equations of motion for partitioned systems

Domain decomposition methods and FETI


21. Model reduction in dynamics (J. Kim)

Variational  analysis of dynamic sub-structuring

Hurty and Craig-Bampton method D

Dynamic reduction, mode selection, error estimation,

22. Contact problems I (A. Popp)

Basics of contact mechanics, FEM for contact problems

Penalty, Lagrange multiplier and Augmented Lagrangian methods

23. Contact problems II (A. Popp)

Modeling of friction

Advanced discretization techniques and solution algorithms

Mortar methods, Semi-smooth Newton methods

24. Coupled problems – Fluid-structures interactions (K.C. Park)

Variational  formulation, Methods of discretizations, Staggered analysis


Partitioned Formulation and Interface Mechanics (K.C. Park)

Methods for interface mechanics, gap finite elements

25. Closing and discussion


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