330-0913/03 – Probabilistic Calculations in Mechanics (PVvM)

Gurantor departmentDepartment of Applied MechanicsCredits10
Subject guarantorprof. Ing. Karel Frydrýšek, Ph.D.Subject version guarantorprof. Ing. Karel Frydrýšek, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
FRY72 prof. Ing. Karel Frydrýšek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 25+0
Part-time Examination 25+0

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:

HALDAR, A., MAHADEVAN, S. Probability, Reliability and Statistical Methods in Engineering Design, John Willey & Sons, Inc, ISBN 0-471-33119-8, New York, USA, 2001.

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

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2027/2028 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan
2027/2028 (P0715D270013) Applied Mechanics K Czech Ostrava Choice-compulsory type B study plan
2026/2027 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan
2026/2027 (P0715D270013) Applied Mechanics K Czech Ostrava Choice-compulsory type B study plan
2025/2026 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan
2025/2026 (P0715D270013) Applied Mechanics K Czech Ostrava Choice-compulsory type B study plan
2024/2025 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan
2024/2025 (P0715D270013) Applied Mechanics K Czech Ostrava Choice-compulsory type B study plan
2023/2024 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan
2022/2023 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan
2022/2023 (P0715D270013) Applied Mechanics K Czech Ostrava Choice-compulsory type B study plan
2021/2022 (P0715D270013) Applied Mechanics K Czech Ostrava Choice-compulsory type B study plan
2021/2022 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan
2020/2021 (P0715D270013) Applied Mechanics K Czech Ostrava Choice-compulsory type B study plan
2020/2021 (P0715D270013) Applied Mechanics P Czech Ostrava Choice-compulsory type B study plan

Occurrence in special blocks

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