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 |
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:
Recommended literature:
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:
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.