# 339-0909/01 – Selected Topics of Continuum Mechanics (VSMK)

 Gurantor department Department of Mechanics of Materials Credits 10 Subject guarantor prof. Ing. Jiří Lenert, CSc. Subject version guarantor prof. Ing. Jiří Lenert, CSc. Study level postgraduate Requirement Choice-compulsory Year Semester winter + summer Study language Czech Year of introduction 2000/2001 Year of cancellation 2012/2013 Intended for the faculties FS Intended for study types Doctoral
Instruction secured by
LEN30 prof. Ing. Jiří Lenert, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 25+0
Part-time 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 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, coordinate transformations 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, energy principles, complementary energy, boundary conditions. Linear Stress-Strain-Temperature Relations. 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 three Dimensions. Twist of circular shafts of constant cross section, pure bending of a prismatic bars, pure bending of plates, torsion of a prismatic bars with non circle cross section, other elementary solution, membrane analogy, bending of a prismatic bars, stress function, shear centre, axially symmetrical stress distribution in a solid, circular cylinder, twist of circular ring, pure bending of a circular plates, thermal stresses. Selected Advanced Topics. Stress concentrations, stress concentration factors- theory of elasticity, stress concentration factor-combined loads, fracture mechanics, failure criteria, contact stresses, geometry of the contact surface, expressions for principal stresses, deflection of bodies in point of contact, stress for two bodies in line contact.

### Compulsory literature:

HEARN,E.J.: Mechanics of Materials, Pergamon Press, 1985

### Recommended literature:

BORESI,A.P.-SCHMIDT,R.J.-SIDEBOTTOM,O.M.: Advanced Mechanics of Materials, John Wiley & Sons,Inc., 1993

### Way of continuous check of knowledge in the course of semester

Příprava zadané problematiky v písemné formě.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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)
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.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2012/2013 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K 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 (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P 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
2006/2007 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P 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
2005/2006 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava 1 Choice-compulsory study plan

### Occurrence in special blocks

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