Gurantor department | Department of Applied Mechanics | Credits | 6 |

Subject guarantor | doc. Ing. Michal Šofer, Ph.D. | Subject version guarantor | doc. Ing. Michal Šofer, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | FS | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

SLA20 | Dr. Ing. Ludmila Adámková | ||

SOF007 | doc. Ing. Michal Šofer, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 3+2 |

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

Transformation properties of vectors and tensors. 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. Solution of the elastic problem, formulation in terms of displacements - Lamé (Navier) equations, formulation in terms of stresses - Beltrami-Michell equations. 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. Planar axial-symmetric problem. The stress concentration due to a circular hole in an infinite plate of constant thickness. Pure bending of the circular curved bar. Bending of the circular curved bar with the force at the free end. The stress field around an edge dislocation. Line uniform continuous traction on the boundary of the elastic half-space – Flamant`s problem.

[1] TIMOSHENKO, S. P.-GOODIER, J. N.: Theory of elasticity. New York-Toronto-
London: Mc Graw-Hill, 1951, 3.ed.1970.
[2] LEIPHOLZ, H.:Theory of elasticity. Noordhoff International Publishing Leyden, 1974. ISBN 90 286 0193 7

[1] TIMOSHENKO, S. P.-GOODIER, J. N.: Theory of elasticity. New York-Toronto-
London: Mc Graw-Hill, 1951, 3.ed.1970.
[2] LEIPHOLZ, H.:Theory of elasticity. Noordhoff International Publishing Leyden, 1974. ISBN 90 286 0193 7

Test, example solutions

no

Requirements to the students are solved in exercise

Subject has no prerequisities.

Subject has no co-requisities.

Transformation properties of vectors and tensors. 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. Solution of the elastic problem, formulation in terms of displacements - Lamé (Navier) equations, formulation in terms of stresses - Beltrami-Michell equations. 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. Planar axial-symmetric problem. The stress concentration due to a circular hole in an infinite plate of constant thickness. Pure bending of the circular curved bar. Bending of the circular curved bar with the force at the free end. The stress field around an edge dislocation. Line uniform continuous traction on the boundary of the elastic half-space – Flamant`s problem.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 | |

Credit | Credit | 35 | 20 | |

Examination | Examination | 65 | 16 | 3 |

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

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Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2022/2023 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2017/2018 Winter |