330-0913/04 – Probabilistic Calculations in Mechanics (PVvM)
| Gurantor department | Department of Applied Mechanics | Credits | 10 |
| Subject guarantor | prof. Ing. Karel Frydrýšek, Ph.D., FEng. | Subject version guarantor | prof. Ing. Karel Frydrýšek, Ph.D., FEng. |
| Study level | postgraduate | Requirement | Choice-compulsory type B |
| Year | | Semester | winter + summer |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FS | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
This subject responds to the contemporary trend of changes from the deterministic approach to the fully probabilistic approach in the design and reliability of parts of machines, structures and systems in human society. Students get to know the theoretical and application approaches for solutions of the stochastic (probabilistic, statistic) tasks (process of data, model creation, numerical modelling, experiments).
Teaching methods
Lectures
Individual consultations
Project work
Summary
This subject responds to the contemporary trend of changes from the deterministic approach to the fully probabilistic approach in the design and reliability of parts of machines, structures and systems in human society. This subject relates to theory of reliability, statics and probability. Important terms are random (stochastic) variables and their interpetations, identifications and ways of generation. Main focus is on the application of SBRA (Simulation-Based Reliability Assessment ) Method, i.e. application of the Monte Carlo (MC) Method, as a tool for fully probabilistic reliability assessment determination (i.e. specific applications in mechanics, technics, connection with another numerical methods, familiarization with application software etc.). In the introduction are explained the basic conceptions of the theory of probability, statistics, reliability, MC method, SBRA method and their new development tendencies "Integrated – fully probabilistic Design" (ID). Into ID, which can exert a direct influence of economy, ecology, politics etc., belongs Performance-Based Design (PBD), Life-Cycle Assessment (LCA), Risk Engineering (RE) etc. Acquired knowledge are needed for success scientific work, research, development and innovations in industry.
Compulsory literature:
MAREK, P., BROZZETTI, J., GUŠTAR M. Probabilistic Assessment of Structures Using Monte Carlo Simulation Background, Exercises and Software, 2nd edition, ITAM CAS, Prague, 2003, Czech Republic, ISBN 80-386246-08-6, pp.471 (cd attached).
Recommended literature:
Way of continuous check of knowledge in the course of semester
Oral examination
E-learning
Other requirements
Semestral project on the defined topic and its presentation before examiner
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Stochastic mechanics, statistics and theory of probability and reliability
2. Monte Carlo Method - history, simulation techniques, examples of solving typical problems, random number generators (natural, pseudo-random), quality testing of random number generators, applications in the AntHill program.
3. SBRA Method - probability analysis of load, geometry and construction material, probability assessment of structures and components, reliability theory, application in AntHill program.
4. SBRA Method – truss, beams, frames, plates and shell structures, structures on elastic foundation, application in the AntHill program.
5. SBRA Method - basic dynamic tasks of the mechanics (determination of critical frequencies, ...), applications in the AntHill program.
6. SBRA Method - combined load (bending + torsion + tension/compression), shafts, AntHill application.
7. SBRA Method - high-cycle fatigue of material, fracture mechanics, creep, application in AntHill program.
8. SBRA Method – biomechanics, geomechanics, application in AntHill program.
9. SBRA Method - applications in commercial programs ANSYS and MSC.MARC.MENTAT.
10. Another stochastic approaches
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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