457-0914/01 – Non-linear Problems of Continuums Mechanics (NPMK)

Gurantor departmentDepartment of Applied MathematicsCredits0
Subject guarantorprof. RNDr. Radim Blaheta, CSc.Subject version guarantorprof. RNDr. Radim Blaheta, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1992/1993Year of cancellation2002/2003
Intended for the facultiesIntended for study typesDoctoral
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 2+0

Subject aims expressed by acquired skills and competences

Student bude znát různé typy nelineárních úloh, které se objevují v mechanice deformovatelných těles a bude umět navrnout metody jejich řešení.

Teaching methods

Summary

Předmět seznamuje s různými typy nelineárních úloh, které se objevují v mechanice deformovatelných těles. Výklad je soustředěn na matematické aspekty formulace úloh a na jejich řešení metodou konečných prvků. Předmět navazuje na předměty: "Matematické modelování a metoda konečných prvků" a "Maticová analýza".

Compulsory literature:

Blaheta: Nonlinear system solvers with applications in nonlinear elasticity, Report DAM 01-06, Institute of Geonics AS CR, Ostrava 2001. Blaheta: Numerical methods in elasto-plasticity, Documenta Geonica, Peres Publ. Prague 1999. Z. Dostál, F. A. M. Gomes, S. A. Santos, Solution of contact problems by FETI domain decomposition with natural coarse space projections, Comput. Methods Appl. Mech. Engrg. 190 (2000)1611-1627. N. Kikuchi, J.-T. Oden, Contact Problems in Elasticity, SIAM, Philadelphia 1988. J. Nečas, I. Hlaváček: Úvod do matematické teorie pružných a pružně plastických těles, SNTL Praha 1983

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Fyzikálně nelineární pružnost. Nelineární vztah napětí-deformace. Variační formulace úlohy. Vlastnosti variační formulace. Monotónní operátory a jejich vlastnosti. Potenciální operátory. Numerické řešení úloh fyzikálně nelineární pružnosti. Aplikace metody konečných prvků. Řešení nelineárních soustav Picardovou a Newtonovou metodou. Elasto-plasticita. Evoluční formulace úloh elasto-plasticity. Přírůstková metoda konečných prvků. Základní diskretizační schéma. Explicitní a implicitní Eulerova metoda. Metoda zpětného zobrazení (return mapping). Adaptivní diskretizace. Řešení nelineárních soustav Newtonovou metodou. Kontakt bez tření. Podmínky nepronikání a jejich linearizace. Podmínky rovnováhy soustavy těles ve vzájemném kontaktu, semikoercivní úlohy. Primární, smíšená a duální variační formulace podmínek rovnováhy soustavy těles ve vzájemném kontaktu. Diskretizace založená na variační formulaci. Řešitelnost kontaktních úloh bez tření. Kontakt s Coulombovým třením. Coulombovské tření. Variační formulace podmínek rovnováhy s daným třením a s Coulombovým třením. Řešitelnost úloh s Coulombovým třením. Algoritmy řešení kontaktních úloh. Využití metod pevného bodu a kvadratického programování. FETI metody.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
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2009/2010 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
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2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
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2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
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2007/2008 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
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2007/2008 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2006/2007 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
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2005/2006 (P2301) Mechanical Engineering (2301V999) Volitelné předměty pro doktorské studium K Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

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