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Finite Element Method I. (E111057)
 Departments: ústav mechaniky, biomech.a mechatr. (12105) Abbreviation: FEM1 Approved: 16.01.2015 Valid until: ?? Range: 3P+1C Semestr: Credits: 5 Completion: Z,ZK Language: EN
Annotation
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.
Teacher's
Zimní 2023/2024
Zimní 2022/2023
Zimní 2021/2022
Structure
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.
Literarture
Lecturers's slides and other resources are placed in http://moodle.fs.cvut.cz.

Bathe, K.J.: Finite Element Procedures, Prentice Hall, 1996
Keywords
variational principles, finite element method
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