Finite Element Method I

Course guarantor:

Miroslav Španiel

Lecturer:

Miroslav Španiel

Tutor:

Michal Bartošák, Jiří Kuželka, Martin Nesládek, Miroslav Španiel

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. FEM data structure. Shell and frame models in scope of FEM.

Requirements:

Syllabus of lectures:

- Fundamental of variational principles: statically amissible stress, kinematically admissible strain, principle of virtual displacements, minimum of total potential energy principle.

- Ritz's method. Example with Fourier base and with piecewise linear base applied to bar under tension load.

- Basic consepts of FE (node, element, shape functions, u-delta operator, stiffness matrix, equivalent nodal loads) using the bar under tension load example.

- Triangular plane element. Outline of element operators example. Constraints and load.

- Data structure and organisation of computational process in FEM.

- Isoparametric elements with serendipity shape functions in 3D continuum

- Overview of thin-walled structures, Reisner-Mindlin hypothesis.

- Kirchhoff theory of plates. Plate elements formulation.

- Heuristic outline of flat shell element by plane and plate element, stiffness matrix transformations, stress and strains on shell elements.

- Beam elements. Compliance to stiffness matrix using regular kernell.

- Generalized linear constraint equations.

Syllabus of tutorials:

Study Objective:

The aim of the subject is to provide students with theoretical background of the method including implementation aspects as a preparation to use FEM programs for modeling the mechanical response of deformable bodies. It is not focucused to any specific MKP system or specific tasks. The student should become more familiar with relevant physical and mathematical apparatus (variational principles in mechanics of deformable bodies, tensor/matrix notation), understand the essence of FEM discretization of continuum, principles of FEM models data structure, fundamentals of the theories of thin-walled structures and their modeling with specific shell or beam elements. The aforementioned knowledge will enable student not only to understand and use available FEM programs, but also to critically evaluate the results of his models and effectively search for the causes of potential problems.

Study materials:

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

Note:

For english version of the subject see E111057.

Further information:

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:D1-266 Španiel M. 13:15–15:45 (lecture parallel1) Dejvice
Wed
Thu
Fri	roomT4:A1-405a Nesládek M. 09:00–10:30 EVEN WEEK (lecture parallel1 parallel nr.101) Dejvice roomT4:A1-405a Nesládek M. 09:00–10:30 ODD WEEK (lecture parallel1 parallel nr.102) Dejvice

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: