# 330-3001/02 – Applied Mechanics (AM)

 Gurantor department Department of Applied Mechanics Credits 5 Subject guarantor Dr. Ing. Ludmila Adámková Subject version guarantor doc. Ing. Leo Václavek, CSc. Study level undergraduate or graduate Requirement Choice-compulsory Year 1 Semester winter Study language English Year of introduction 2015/2016 Year of cancellation 2019/2020 Intended for the faculties FMT Intended for study types Follow-up Master
Instruction secured by
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Part-time 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.

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.

### Other requirements

Meet the requirements of exercises and exam

### 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

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2019/2020 Summer semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 35  20
Examination Examination 65  16 3
Mandatory attendence participation:

Show history

Conditions for subject completion and attendance at the exercises within ISP:

Show history

### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2018/2019 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2017/2018 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2016/2017 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2015/2016 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

### Assessment of instruction

Předmět neobsahuje žádné hodnocení.