# 339-0920/02 – Mechanics of Continuum (MK)

 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 prof. 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 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.

### Other requirements

The student prepare individual account on selected topic

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Specifically, the following issues are discussed : stress and strain tensor , transformation tensor components , the main components of a tensor, determining the principal planes , invariants of the stress tensor and deformation. Mohr's circle for stress and strain . Physical linear equations elastomechaniky orthotropic material , isotropic material , plane strain condition , plane stress state , energy principles , work and potential energy , complementary energy principle of virtual work , boundary conditions. Equilibrium equations, compatibility conditions , equilibrium equations feeds in folders , folders solutions through feeds . some problems planar and spatial elastomechaniky . Torsion bars with constant circular section, bending of prismatic bars , center of shear , bending stress plates, torsion of prismatic rods of non-circular cross-section , membrane analogy , the function voltage , the voltage distribution in the rotationally symmetrical bodies , the circular cylinder, rotating ring strain of rotationally symmetric plates , thermal stresses. Fundamentals of mechanics of materials komozitních . Types of material , homogeneous, heterogeneous , anisotropic and isotropic , anisotropic , orthotropic material material response , cutting composite materials , lamina , laminate , basic lamina properties , degree of anisotropy of elastic behavior unidirectional lamina, dependence of stress and strain , relations between the elastic constants and physical constants , transformation tensor components of stress and strain , elastic behavior multidirectional composite laminate layers constitutive equation , force and torque resultant laminate layer symmetric laminate.

### 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 (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner