339-0907/02 – 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 | 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 |
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
Way of continuous check of knowledge in the course of semester
Příprava zadané problematiky v písemné formě.
E-learning
Other requirements
The student prepare individual account on selected topic
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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
stress , energy principles , work and potential energy , complementary
energy , principle of virtual work , boundary conditions . Equilibrium equations,
compatibility conditions , equilibrium equations in the components of displacements, the solution
through folders of feeds . Some problems of planar and spatial
elastomechaniky . Torsion bars having a constant circular cross-section , bend
prismatic bars , center of shear , bending stress plates, twisting
prismatic rods of non-circular cross-section , membrane analogy , voltage,
stress distribution in the rotationally symmetrical bodies , the circular cylinder, rotating
ring strain of rotationally symmetric plates , thermal stresses. basics
komozitních mechanics of materials. Types of material, homogeneous, heterogeneous ,
inhomogeneous isotropic , anisotropic , orthotropic material , material response .
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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