# 339-0909/02 – 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 2013/2014 Year of cancellation 2014/2015 Intended for the faculties FS Intended for study types Doctoral
Instruction secured by
FRY72 doc. Ing. Karel Frydrýšek, Ph.D.
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 Examination 25+0
Part-time 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.

### E-learning

The student prepare individual account on selected topic

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

The stress tensor and deformation tensor components transform, the main component tensor, determine the principal planes, invariants of the stress tensor and deformation. Mohr circle for stress and strain. Physical elastomechaniky linear equations, orthotropic material, isotropic material, plane strain condition, the planar state

### Conditions for subject completion

Full-time form (validity from: 2013/2014 Winter semester, validity until: 2014/2015 Summer semester)
Min. number of points
Examination Examination
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2014/2015 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner