330-3001/01 – Applied Mechanics (AM)

Gurantor departmentDepartment of Applied MechanicsCredits5
Subject guarantordoc. Ing. Leo Václavek, CSc.Subject version guarantordoc. Ing. Leo Václavek, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFMTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
SLA20 Dr. Ing. Ludmila Adámková
VAC10 doc. Ing. Leo Václavek, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Combined Credit and Examination 16+0

Subject aims expressed by acquired skills and competences

Educate students in basic procedures which are applied for a definition and solving of more exciting engineering technical problems in the sphere of mechanics of solid elastic deformable bodies. Ensure understanding of teaching problems. To learn the students apply gained theoretical peaces of knowledge in praxis.

Teaching methods

Lectures
Tutorials

Summary

Action of the forces on a body. Internal forces, method of sections, stress, deformation of the body. Normal stress, strain and deformation on terms of simple tension (compression). Hooke`s law for simple tension, Poisson`s ratio, Saint-Venant`s principle. Stress on an oblique plane under axial loading. Plane stress state. Stresses in an inclined plane. Mohr`s circle for stress. Principal stresses and principal planes. Application of Mohr`s circle to various types of stress analysis. Stresses and strains in pure shear. Extended Hooke`s law. Change in volume. Strain energy for a general state of stress. Volumetric and distortion strain energy density. Criteria of failure for ductile and brittle materials under three-dimensional state of stress, failure surface in Haigh-Westergard principal stress space. Maximum shear stress criterion (Guest`s or Tresca`s criterion), distortion energy criterion (von Mises or HMH criterion). Maximum normal stress fracture criterion (Rankine`s criterion), Coulomb-Mohr fracture criterion. Analysis of strain at a point in a deformable body. Strain-displacement relations. The Green-Lagrange strain tensor, Cauchy`s small (linear) strain tensor. Small strain tensor invariants. Principal strains. Principal axes of strain. Spherical tensor, strain deviator tensor. Octahedral normal and shear strains. Compatibility of strain conditions. The state of stress at a point in a body. Stress tensor. Invariants of the stress tensor. Principal stresses, principal planes, principal directions of the stress tensor at a point. Spherical tensor and stress deviator. Normal and shear stresses on the octahedral plane. The method of Mohr`s circles. Cauchy`s differential equations of equilibrium. Physical equations for anisotropic, orthotropic, transversely isotropic and isotropic, linearly elastic homogeneous solid. Boundary conditions. Planar problems of the theory of elasticity, plane stress and plane strain. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates. The planar problem in polar coordinates.

Compulsory literature:

FRYDRÝŠEK, K., ADÁMKOVÁ, L.: Mechanics of Materials 1 - Extended Edition (Introduction, Simple Stress and Strain, Basic of Bending), Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, Ostrava, Ostrava, 2008, Czech Republic, pp. 203. FRYDRÝŠEK, K., LENERT, J.: Mechanics of Materials, VŠB-TU Ostrava, 2005, ISBN 80-248-08006-4, pp. 63.

Recommended literature:

FRYDRÝŠEK, K., ADÁMKOVÁ, L.: Mechanics of Materials 1 (Introduction, Simple Stress and Strain, Basic of Bending), Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, Ostrava, ISBN 978-80-248-1550-3, Ostrava, 2007, Czech Republic, pp. 179.

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Splnění požadavků na cvičení a u zkoušky

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Action of the forces on a body. Internal forces, method of sections, stress, deformation of the body. Normal stress, strain and deformation on terms of simple tension (compression). Hooke`s law for simple tension, Poisson`s ratio, Saint-Venant`s principle. Stress on an oblique plane under axial loading. Plane stress state. Stresses in an inclined plane. Mohr`s circle for stress. Principal stresses and principal planes. Application of Mohr`s circle to various types of stress analysis. Stresses and strains in pure shear. Extended Hooke`s law. Change in volume. Strain energy for a general state of stress. Volumetric and distortion strain energy density. Criteria of failure for ductile and brittle materials under three-dimensional state of stress, failure surface in Haigh-Westergard principal stress space. Maximum shear stress criterion (Guest`s or Tresca`s criterion), distortion energy criterion (von Mises or HMH criterion). Maximum normal stress fracture criterion (Rankine`s criterion), Coulomb-Mohr fracture criterion. Analysis of strain at a point in a deformable body. Strain-displacement relations. The Green-Lagrange strain tensor, Cauchy`s small (linear) strain tensor. Small strain tensor invariants. Principal strains. Principal axes of strain. Spherical tensor, strain deviator tensor. Octahedral normal and shear strains. Compatibility of strain conditions. The state of stress at a point in a body. Stress tensor. Invariants of the stress tensor. Principal stresses, principal planes, principal directions of the stress tensor at a point. Spherical tensor and stress deviator. Normal and shear stresses on the octahedral plane. The method of Mohr`s circles. Cauchy`s differential equations of equilibrium. Physical equations for anisotropic, orthotropic, transversely isotropic and isotropic, linearly elastic homogeneous solid. Boundary conditions. Planar problems of the theory of elasticity, plane stress and plane strain. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates. The planar problem in polar coordinates.

Conditions for subject completion

Combined form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100  51
        Credit Credit  
        Examination Examination  
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials K Czech Ostrava 1 Choice-compulsory study plan
2019/2020 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P Czech Ostrava 1 Choice-compulsory study plan
2018/2019 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P Czech Ostrava 1 Choice-compulsory study plan
2018/2019 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials K Czech Ostrava 1 Choice-compulsory study plan
2017/2018 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P Czech Ostrava 1 Choice-compulsory study plan
2017/2018 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials K Czech Ostrava 1 Choice-compulsory study plan
2016/2017 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P Czech Ostrava 1 Choice-compulsory study plan
2016/2017 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials K Czech Ostrava 1 Choice-compulsory study plan
2015/2016 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P Czech Ostrava 1 Choice-compulsory study plan
2015/2016 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials K Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner