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Lecturer(s)
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Adámek Vítězslav, Ing. Ph.D.
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Course content
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1.Fundamental equations of theory of elasticity 2.Classic formulation of FEM, variational principles 3.Problem formulation and weak solution. 4.Isoparametric elements. 5.Numerical integration. 6.Mass matrix, equations of motion, modal analysis. 7.Plate and shell elements. 8.Nonlinear problems. 9.Convergence, test problems. 10.Coupling, contact problems, substructures. 11.Non-stationary state of stress. 12.Multiphysics problems. 13.Boundary element method.
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Learning activities and teaching methods
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Lecture, Practicum
- Graduate study programme term essay (40-50)
- 35 hours per semester
- Contact hours
- 65 hours per semester
- Preparation for an examination (30-60)
- 35 hours per semester
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| prerequisite |
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| Knowledge |
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| know and orientate yourself in classical mechanics (statics, kinematics, dynamics) of mass points and rigid bodies |
| know the issues of mechanics of material (uniaxial tension, plane tension and deformation, spatial tension) |
| know the basic types of stress (tension-compression, torsion, bending) of rod and beams |
| know the basic behavior of materials (homogeneous, isotropic, linear, elastic) |
| know matrix and vector calculus (determinant, Gaussian elimination, inverse matrix) |
| Skills |
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| define the problem of statics, kinematics and dynamics of a mass point and a body |
| define the basic terms of mechanics of materials |
| describe and solve the basic problems of elasticity and strength (tension-compression, torsion and bending of straight rods and beams) |
| solve systems of algebraic equations using matrix calculus (determinant, Gaussian elimination, inverse matrix) |
| Competences |
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| N/A |
| learning outcomes |
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| Knowledge |
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| explain the difference between an exact and an approximate solution to an elasticity problem |
| define the role of mechanics of materials |
| classify approximate methods (Ritzova, finite element method, boundary element method) |
| classify different types of finite elements and describe their properties |
| explain the principles of numerical integration |
| define and describe the properties of isoparametric elements |
| Skills |
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| solve elasticity problems using the finite element method in a commercial software |
| choose and justify the appropriate dimension of the problem and types of elements for the numerical solution |
| create a numerical model for a specified deformable problem (statics, dynamics, modal analysis) |
| analyze and assess the necessary level of detail of the numerical model for the required accuracy of the solution |
| create a high-quality technical report with a description of the performed numerical analysis |
| Competences |
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| N/A |
| teaching methods |
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| Knowledge |
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| Lecture with visual aids |
| Task-based study method |
| Skills |
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| Practicum |
| Individual study |
| Competences |
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| Lecture |
| Practicum |
| Self-study of literature |
| Interactive lecture |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Skills |
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| Skills demonstration during practicum |
| Individual presentation at a seminar |
| Competences |
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| Combined exam |
| Individual presentation at a seminar |
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Recommended literature
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Bathe, Klaus-Jürgen. Finite element procedures. [S.n. : s.l.], 2006.
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Belytschko, Ted; Liu, W. K.; Moran, B. Nonlinear finite elements for continua and structures. Chichester : Wiley, 2000. ISBN 0-471-98773-5.
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Bittnar, Zdeněk; Šejnoha, Jiří. Numerické metody mechaniky 1.. 1. vyd. Praha : ČVUT, 1992. ISBN 80-01-00855-X.
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Bittnar, Zdeněk; Šejnoha, Jiří. Numerické metody mechaniky 2.. 1. vyd. Praha : ČVUT, 1992. ISBN 80-01-00901-7.
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Bucalem, Miguel Luiz; Bathe, Klaus-Jürgen. The Mechanics of solids and structures : hierarchical modeling and the finite element solution. Berlin : Springer, 2011. ISBN 978-3-540-26331-9.
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Cook, Robert Davis. Finite element modeling for stress analysis. [1st ed.]. New York : John Wiley & Sons, 1995. ISBN 0-471-10774-3.
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Reddy, J. N. An introduction to nonlinear finite element analysis. Oxford : Oxford University Press, 2004. ISBN 0-19-852529-X.
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Zienkiewicz, O. C.; Taylor, Robert L.; Fox, D. D. The finite element method for solid and structural mechanics. Seventh edition. 2014. ISBN 978-1-85617-634-7.
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