Gurantor department | Department of Applied Mechanics | Credits | 5 |

Subject guarantor | prof. Ing. Petr Horyl, CSc., dr.h.c. | Subject version guarantor | prof. Ing. Petr Horyl, CSc., dr.h.c. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2015/2016 | Year of cancellation | 2020/2021 |

Intended for the faculties | FS | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

FUS76 | doc. Ing. Martin Fusek, Ph.D. | ||

MAW007 | Ing. Pavel Maršálek, Ph.D. | ||

POD10 | doc. Ing. Jiří Podešva, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

Outline principle of derivation mass matrix in slope-deflection variant of FEM
Identify meaning solution of natural frequencies and mode shapes and classify differences for Bernoulli and Timoshenko beam
Define methods for numerical computing of eigenvalues and eigenvectors for undamped systems
Construct reduction method for easy problem of natural frequency
Solve matrix equation of motion by modal method
Classify direct integration method, compare implicit and explicit method
Clarify solution principle of nonlinear static problems
Relate methods for analysis contacts problem by FEM

Lectures

Tutorials

Project work

1. Dynamics and FEM
2. Mass matrix
3. Equations of motion of elastic systems
4. Natural frequencies and mode shapes
- properties and normalization of mode shapes
- methods for computing eigenvalues and eigenvectors
5. Reduction of the number of DOf in dynamics
6. Response history: modal method
- proportional damping matrix
- vibration caused by initial conditions
- harmonic response
- general excitation
7. Response history: direct integration method (implicit and explicit methods)
8. Principles of solution nonlinear static problems, fundamental numeric solution of contacts in FEM
9. Newton-Raphson method, arc-length method

Cook R. D., Malkus D.S., Plesha M.E., Witt R.J. CONCEPTS AND APPLICATIONS OF
FINITE ELEMENT ANALYSIS. 4th edition. J. Wiley & Sons, Inc. NY, 2002, p. 719,
ISBN 0-471-35605-0
Examples for ANSYS solutions: http://www.mece.ualberta.ca/tutorials/ansys/
REDDY, J.N., An Introduction Nonlinear Finite Element Analysis, Oxford
University Press, 2004, p. 463, ISBN 0-19-852529-X
BHATTI, M. A., Fundamental Finite Element Analysis and Applications: with
Mathematica and Matlab Computations, Wiley, 2005, p.590, ISBN 0-471-64808-6
HORYL, P. FEM Finite Element Method Introduction,2014,https://www.fs.vsb.cz/330/cs/MKP-II/

BHATTI,M.A., Advanced Topics in Finite Element Analysis of Structures: with
Mathematica and Matlab Computations, Wiley, 2006, p.590, ISBN-13 978-0-471-
64807-9

Good knowledge of numerical mathematics, especially Voight notation of matrix calculus.

Subject has no prerequisities.

Subject has no co-requisities.

1.0 Comparison of static and dynamic problems solved by FEM
2.0 Finite element mass matrix
2.1 Bar element
2.2 Beam element
2.2.1 Bernoulli‘s beam, diagonal mass matrix
2.2.2 Thimoshenko‘s beam, the second spectrum of natural frequencies
2.3 Plane and space frame finite element
2.4 Selected types of finite elements
3.0 Natural frequencies and mode shapes of un-damped vibration
3.1 Matrix equation for solving natural frequencies and mode shapes (eigenvectors)
3.2 Normalization of the eigenvectors
3.3 Solution methods
3.3.1 Solutions using determinant, disadvantages
3.3.2 Power method (method of inverse iterations)
3.3.3 Subspace method (method of simultaneous iterations)
3.3.4 Lanczos method
4.0 Reduction method in dynamics
5.0 Damping matrix
6.0 Solving response of the linear mechanical system by using mode shapes (Modal analysis method)
6.1 Self-induced oscillations by changing the initial conditions
6.2 Harmonic excitation
6.3 General continuous excitation
7.0 The response solution of nonlinear dynamical systems
7.1 Implicit method
7.2 Explicit method
8.0 Buckling (collapse of structures shape)
8.1 Introduction
8.2 Geometric stiffness matrix of bar FE
8.3 Geometric stiffness matrix of plane frame FE (compression-tension + bending)
8.4 Practical examples
9.0 Solution of nonlinear static tasks
9.1 Introduction
9.2 Newton-Raphson method
10. Contacts in FEM
10.1. Introduction
10.2. Penalty method
10.3. Langrange multiplier method
10.4. Augmented Lagrange method
10.5. Partitioning (Semi-analytical) method
10.6. Example

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 35 | 20 |

Examination | Examination | 65 | 16 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2020/2021 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner | |
---|---|---|---|---|---|---|---|---|---|

ECTS - MechEng - Master Studies | 2015/2016 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block |