339-0920/01 – Mechanics of Continuum (MK)

Gurantor departmentDepartment of Mechanics of MaterialsCredits10
Subject guarantorprof. Ing. Jiří Lenert, CSc.Subject version guarantorprof. Ing. Jiří Lenert, CSc.
Study levelpostgraduateRequirementChoice-compulsory
Year1Semesterwinter + summer
Study languageCzech
Year of introduction1999/2000Year of cancellation2012/2013
Intended for the facultiesFSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
LEN30 prof. Ing. Jiří Lenert, CSc.
VAC10 doc. Ing. Leo Václavek, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 25+0
Combined Credit and Examination 25+0

Subject aims expressed by acquired skills and competences

Teach a students derive benefit from the newest knowledge of subject with possibility the knowledge further evolve and apply for complicated problems.

Teaching methods

Individual consultations
Project work

Summary

Vectors and Tensors. Physical components of vectors and tensors.Strain. Strain tensor, coordinate transformations for strains, principal strains, determination of planes of principal strains, principal strain invariants, maximum shear strains, Mohr circle representation, deviatoric strain tensor. Stress. Forces and stresses, stress tensor, coordinate trans-formations for stresses, principal stresses, determination of planes of principal stresses, principal stress invariants, maximum shear stresses, Mohr circle representation, deviatoric stress tensor. Elastic Solids. Constitutive equations for linear elastic solid, orthotropic material, isotropic material, plane strain, plane stress, wirtual work and total potential energy, complementary energy, energy principles, boundary conditions.General Theories. Differential equations of equilibrium, condition of compatibility, equations of equilibrium in terms of displacement, general solution for the displacements.Elementary Problems of Elasticity in two and three Dimensions. Twist of circular shafts of constant cross section, pure bending of prismatic bars, shear centre, pure bending of plates, torsion of prismatic bars with non circle cross section, membrane analogy, stress function, axially symmetrical stress distribution in a solid, circular cylinder, twist of circular ring, pure bending of a circular plates, thermal stresses. The Grounds of Mechanics of Composite Materials. Type of material, homogenity, heterogenity or inhomogenity, isotropy, anisotropy, orthotropy, material response, types and classification of composite materials,lamina, laminate, basic lamina properties, degree of anisotropy, elastic behaviour of unidirectional lamina, stress-strain relations, relations between mathematical and engineering constants, transformation of stress and strain, transformation of elastic parameters, transformations of stress-strain relations in terms of engineering constants, elastic behaviour of multidirectional laminates, strain displacements relations, stress-strain relations of layer, force and moment resultants, symmetrical laminates.

Compulsory literature:

[1] TIMOSHENKO, S. P.-GOODIER, J. N.: Theory of elasticity. New York-Toronto- London: Mc Graw-Hill, 1951, 3.ed.1970. [2] LEIPHOLZ, H.:Theory of elasticity. Noordhoff International Publishing Leyden, 1974. ISBN 90 286 0193 7

Recommended literature:

[1] TIMOSHENKO, S. P.-GOODIER, J. N.: Theory of elasticity. New York-Toronto- London: Mc Graw-Hill, 1951, 3.ed.1970. [2] LEIPHOLZ, H.:Theory of elasticity. Noordhoff International Publishing Leyden, 1974. ISBN 90 286 0193 7

Way of continuous check of knowledge in the course of semester

Příprava zadané problematiky v písemné formě.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Konkrétně jsou probírány následující problémy:Tenzor napětí a deformace, transformace složek tenzor, hlavní složky tenzoru, stanovení hlavních rovin, invarianty tenzoru napětí a deformace. Mohrova kružnice pro napětí a deformace. Fyzikální rovnice lineární elastomechaniky, ortotropní materiál, izotropní materiál, rovinný stav deformace, rovinný stav napjatosti, energetické principy, práce a potenciální energie, doplňková energie, princip virtuálních prací, okrajové podmínky. Rovnice rovnováhy, podmínky kompatibility, rovnice rovnováhy ve složkách posuvů, řešení prostřednictvím složek posuvů. Některé problémy rovinné a prostorové elastomechaniky. Kroucení tyčí s konstantním kruhovým průřezem, ohyb prizmatických tyčí, středisko smyku, ohybové namáhání desek, kroucení prizmatických tyčí nekruhového průřezu, membránová analogie, funkce napětí, rozložení napětí v rotačně symetrických tělesech, kruhový válec, rotující prstenec, namáhání rotačně symetrických desek, teplotní namáhání. Základy mechaniky komozitních materiálů. Typy materiálu, homogenní, heterogenní, nehomogenní izotropní, anizotropní, ortotropní materiál, materiálová odezva, dělení kompozitních materiálů, lamina, laminát, základní vlastnosti laminy, stupeň anizotropie, elastické chování jednosměrné laminy, závislost napětí a deformace, vztahy mezi elastickými konstantami a fyzikálními konstantami, transformace složek tenzoru napětí a deformace, elastické chování vícesměrných kompozitů, konstituční rovnice vrstvy laminátu, silové a momentové výslednice vrstvy laminátu, symetrický laminát.

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
2012/2013 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K 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 (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K 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 (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2005/2006 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2004/2005 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

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