| Course Unit Code | 228-0239/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Fourth Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| KRE13 | prof. Ing. Martin Krejsa, Ph.D. |
| HOR0218 | Ing. Marie Horňáková |
| Summary |
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| The course Special Numerical Methods focuses on advanced use of computer technology for engineering tasks and to deepen the theoretical foundations in the field of structural mechanics. The prerequisite is knowledge of algorithm engineering problems, numerical mathematics and creating applications in MATLAB. |
| Learning Outcomes of the Course Unit |
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| Objective of the course in terms of learning outcomes and competences The aim of the course is to deepen the knowledge of the Matlab programming system to create engineering applications, to master advanced numerical mathematical methods and to use them in solving the problems of building mechanics, deepening the knowledge of programming and algorithms. |
| Course Contents |
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Lectures:
1. Direct stiffness method I.: The principle of the method, the degree of deformational uncertainty of planar structures.
2. Direct stiffness method II.: Analysis of the direct beam with different supports, local coordinate system, its selection and transformation into the global coordinate system.
3. Direct stiffness method III.: Analysis of the beam system, calculation of the deformation state, determination of components of internal forces of the members and reaction components.
4. Direct stiffness method IV.: Creation of system of equations. Solving the system of equations. Matrix band and sparse systems of linear equations.
5. Direct stiffness method V.: Solution of continuous beams, rectangular and angular plane frames, planar trusses by direct stiffness method. Force and strain loads. Irregular temperature change.
6. Direct stiffness method VI.: Spatial beam systems and planar frames transversally loaded.
7. Transmission matrices: Derivation, load assignment, demonstration examples.
8. Geometric non-linear solution of trusses: Derivation, direct stiffness method and its application, iterative solution of geometrically non-linear calculation of planar truss structure according to theory of IInd order, demonstration examples.
9. Stability of compressed members using the principle of virtual works: Stability of slender compressed members using the principle of virtual works and theory of IInd order, derivation, application, iterative solution of buckling load bearing capacity of slender pressed rods, comparison with exact Euler analytical solution, demonstration examples.
10. Eigenvalues of matrices and eigenvectors: Introduction, numerical methods for solving eigenvalues of matrices and corresponding eigenvectors, partial and complete problem of eigenvalues, practical use in the tasks of building mechanics.
11. Eigenmodes and eigenfrequencies of free vibration: Introduction to the problem, orthogonality of its eigenmodes, standardized eigenmodes. Determination of eigenfrequencies and eigenmodes of free vibration in simple constructions.
12. Random variables and probabilistic simulation calculations I.: Random variable - discrete random variable, continuous random variable. Parametric probability distribution, nonparametric (empirical) probability distribution.
13. Random variables and probabilistic simulation calculations II.: Generate random variables in Matlab. Probabilistic assessment of the support element.
14. Sample solution for selected tasks. |
| Recommended or Required Reading |
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| Required Reading: |
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1. Olek C Zienkiewicz, Robert L Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Seventh Edition, 756 pages, 2013, ISBN-13: 978-1856176330, ISBN-10: 1856176339.
2. Eugenio Oñate, Structural Analysis with the Finite Element Method. Linear Statics: Volume 1: Basis and Solids (Lecture Notes on Numerical Methods in Engineering and Sciences), 446 pages, 2009, ISBN-13: 978-1402087325, ISBN-10: 1402087322.
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1. Kadlčák, Kytýr, Statika stavebních konstrukcí II, VUTIUM Brno, 2001.
2. Krejsa, M., Speciální numerické metody, učební texty v obrazovkové verzi i ve verzi pro tisk, VŠB-TU, Ostrava, 2018. |
| Recommended Reading: |
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1. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to Algorithms, 3rd Edition, 1312 pages, 2009, ISBN-13: 978-0262033848, ISBN-10: 0262033844.
2. Sauer T. Numerical Analysis. George Mason University. Pearson Education, Inc., 2006. (669 s). ISBN 0-321-26898-9.
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1. Sauer, T., Numerical Analysis. George Mason University. Pearson Education, Inc., 2006. (669 s). ISBN 0-321-26898-9.
2. Ralston, A., Základy numerické matematiky. 1. vydání. Academia, Praha, 1973. (635 s).
3. Wirth, N., Algoritmy a štruktúry údajov. 1. vydanie. Alfa, vydavateľstvo technickej a ekonomickej literatúry, Bratislava, 1988. (488 s).
4. Steven C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists (4th Edition), 720 pages, 2017, ISBN-13: 978-0073397962, ISBN-10: 0073397962.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 35 | 18 |
| Examination | Examination | 65 | 33 |