339-0907/01 – Mechanics of Materials (PaP)
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 | |
| | Study language | Czech |
Year of introduction | 2000/2001 | Year of cancellation | 2012/2013 |
Intended for the faculties | FS | Intended for study types | Doctoral |
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, virtual 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
BORESI,A.P.-SCHMIDT,R.J.-SIDEBOTTOM,O.M.: Advanced Mechanics of Materials,
John Wiley & Sons,Inc., 1993
Recommended literature:
HEARN,E.J.: Mechanics of Materials, Pergamon Press, 1985
BORESI,A.P.-SCHMIDT,R.J.-SIDEBOTTOM,O.M.: Advanced Mechanics of Materials,
John Wiley & Sons,Inc., 1993
Additional study materials
Way of continuous check of knowledge in the course of semester
Příprava zadané problematiky v písemné formě.
E-learning
Other requirements
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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