Finite Element Method I.

Course guarantor:

Ctirad Novotný

Lecturer:

Ctirad Novotný

Tutor:

Michal Bartošák, Martin Nesládek, Ctirad Novotný

Supervisor:

Department of Mechanics, Biomechanics and Mechatronics

Synopsis:

The course is focused on the interpretation of the essence and basic apparatus of FEM in the mechanics of a deformable body. The variational principles in the statics (principle of virtual displacements and the principle of minimum total potential energy), deformation variant of FEM (construction of shape functions, expression of total potential energy, kinematic boundary conditions) in one-, two- and three-dimensional continuum are explained.

Requirements:

Syllabus of lectures:

1. Deformation and force approach in mechanics

2. Fundamental ideas of elastostatics - tensor, index and matrix notation, variational principles: statically amissible stress, kinematically admissible strain, principle of virtual displacements. Example for 1D.

3. Minimum of total potential energy principle. Example for 1D.

4. Variational principles in mechanics - extension for 3D-continuum.

5. Approximate solutions - Ritz's method. Example with Fourier base and with piecewise linear base on the tension-compression bar.

6. Basic concepts of FEM - node, element, shape functions, u-delta operator, stiffness matrix, equivalent nodal loads

7. Triangular plane element.

8. Choose of interpolation model.

9. Isoparametric element.

10. Theory of Kirchhoff plates. Plate elements, flat shell elements

11. Shells classification, stress.

12. Generalized linear constraint equation.

13. Numerical integration.

Syllabus of tutorials:

Study Objective:

- understanding variational principles particularly of deformation approach

- understandig FEM as particular case of Ritz's method

Study materials:

Lecturers's slides and other resources are placed in http://moodle.fs.cvut.cz.

Bathe, K.J.: Finite Element Procedures, Prentice Hall, 1996

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomT4:A1-405b Bartošák M. 14:15–15:45 ODD WEEK (lecture parallel1 parallel nr.101) Dejvice
Wed
Thu	roomT4:A1-307a Novotný C. 09:45–12:15 (lecture parallel1) Dejvice
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: