Finite Element Method

Lecturer:

Miroslav Španiel (gar.)

Tutor:

Miroslav Španiel (gar.), Martin Nesládek, Jan Růžička

Supervisor:

Department of Mechanics, Biomechanics and Mechatronics

Synopsis:

Variational principles in statics (virtual displacements, minimum of total potential energy). Finite element method with deformation approach (base functions, total potential energy formulation, loads and kinematic boundary conditions) in 1-,2 and 3D continuum. General finite elements requirements. Plate and shell structures/elements. bar and frame strucures/elements. Generalized linear constraint equations.

Requirements:

Syllabus of lectures:

1.- Fundamental ideas of elastostatics

- tensor, index and matrix notation

- variational principles: statically amissible stress, kinematically admissible strain, principle of virtual displacements,

minimum of total potential energy principle

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

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

3.- Discretization of continuum generalized requirements to guarantee displacements continuity.

4.- Triangular plane element example

4.- Triangular plane element example - finishing

5.- Data structure and organisation of computational process in FEA.

- Simple kinemtic constraints

6.- Stress computation and smoothing.

- Beam elements

7.- Beam elements - finishing

8.- Numerical integration

- Isoparametric elements with serendipity shape functions

9.- Shells - Theory of Kirchhoff plates

10.- Shells - plate elements, displacements compatibility

- Flat shell elements

11.- Shells - Flat shell elements

- shells classification

12.- Shells - stress

- shell structures modelling

13.- Generalized linear constraint equations

14.- Generalized linear constraint equations

Syllabus of tutorials:

Basic course of FE modelling using programs ANSYS or ABAQUS. Student individually carries out simple computation of given structure.

Study Objective:

Variational principles in statics (virtual displacements, minimum of total potential energy). Finite element method with deformation approach (base functions, total potential energy formulation, loads and kinematic boundary conditions) in 1-,2 and 3D continuum. General finite elements requirements. Plate and shell structures/elements. bar and frame strucures/elements. Generalized linear constraint equations.

Study materials:

Lecture slides, lectures records (on web, in Czech), -Bathe, K.J., Wilson, E.L.: Numerical methods in finite element analysis. Prentice--Hall, Inc., -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:

Time-table for winter semester 2011/2012:

	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	roomT4:C2-334 Španiel M. 12:30–15:00 (lecture parallel1) Dejvice Poslucharna 334
Tue
Fri	roomT4:A1-405b Růžička J. 12:30–14:00 ODD WEEK (lecture parallel1 parallel nr.101) Dejvice Poc.ucebna 405b roomT4:A1-405b Růžička J. 12:30–14:00 EVEN WEEK (lecture parallel1 parallel nr.102) Dejvice Poc.ucebna 405b
Thu	roomT4:A1-405b Nesládek M. 16:45–18:30 ODD WEEK (lecture parallel1 parallel nr.103) Dejvice Poc.ucebna 405b
Fri

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: