Description:

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.

Contents:

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.

Recommended literature:

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

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar