337-0504/01 – FEM II (MKPII)
| Gurantor department | Department of 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 | summer |
| | Study language | Czech |
| Year of introduction | 2004/2005 | Year of cancellation | 2014/2015 |
| Intended for the faculties | FS | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
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
Teaching methods
Lectures
Tutorials
Project work
Summary
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
Compulsory literature:
Recommended literature:
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
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
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Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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