228-0239/02 – Special numerical methods (SNM)
| Gurantor department | Department of Structural Mechanics | Credits | 5 |
| Subject guarantor | prof. Ing. Martin Krejsa, Ph.D. | Subject version guarantor | prof. Ing. Martin Krejsa, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 4 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FAST | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Tutorials
Summary
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.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Written and oral exam.
E-learning
Other requirements
Ability of partial self-study
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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