Finite Element Method II.

Lecturer:

Tutor:

Supervisor:

Department of Mechanics, Biomechanics and Mechatronics

Synopsis:

Continuation of FEM (2111030), dealing with:

Non-linearities (fundamentals of geometric and material non-linearity in continuum mechanics,

tangential stiffness matrix, Newton-Raphson incremental solution, stability loss under critical loading). Contact. Non-linear constitutive models (plasticity, hyperelasticity)

Dynamics, direct (implicit and explicit) integration of equations of motion. Modal analysis.

Requirements:

Syllabus of lectures:

1. Dynamics, direct (implicit and explicit) integration of equations of motion.

2. Dynamics, modal analysis

3. Dynamics, modal analysis - continuation

4. Non-linear constitutive models (plasticity, hyperelasticity)

5. Tangential stiffness matrix, Newton-Raphson incremental solution

6. Geometric non-linearity

7. Geometric non-linearity - tangential stiffness matrix

8. Critical loads, buckling

9. Contact

10. Contact - continuation

11 - 13. Examples

Syllabus of tutorials:

Study Objective:

Continuation of FEM (2111030), dealing with: Non-linearities (fundamentals of geometric and material non-linearity in continuum mechanics, tangential stiffness matrix, Newton-Raphson incremental solution, stability loss under critical loading). Contact. Non-linear constitutive models (plasticity, hyperelasticity). Dynamics, direct (implicit and explicit) integration of equations of motion. Modal analysis.

Study materials:

Lecture slides; -Bathe, K.J., Wilson, E.L.: Numerical methods in finite element analysis. Prentice--Hall, Inc., 1976; -Zienkiewicz, O. C.: The Finite Element Method in Engineering Science. McGraw--Hill, London; -Kanócz, A. Španiel, M.: Metoda konečných prvků v mechanice poddajných těles. ČVUT v Praze, 1998. In Czech. -Bittnar, Z.Šejnoha, J.: Numerické metody mechaniky 1, 2. ČVUT v Praze, 1992. In Czech., -Valenta, F. at al.: Pružnost a pevnost III. ČVUT v Praze, 2002. In Czech

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: