| Course Unit Code | 330-0501/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| SLA20 | Dr. Ing. Ludmila Adámková |
| SOF007 | doc. Ing. Michal Šofer, Ph.D. |
| Summary |
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| 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. |
| Learning Outcomes of the Course Unit |
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| 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. |
| Course Contents |
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| 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. |
| Recommended or Required Reading |
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| Required Reading: |
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[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] LENERT,J. Základy matematické teorie pružnosti. 1. vyd. Ostrava : VŠB-TU,
1997. 96 s. ISBN 80-7078-437-7.
[2] SERVÍT, R.–DOLEŽALOVÁ, E.–CRHA, M.: Teorie pružnosti a plasticity I. Praha: SNTL, 1981. 456 s.
[3] SERVÍT, R.-DRAHOŇOVSKÝ, Z.-ŠEJNOHA, J.-KUFNER, V.: Teorie pružnosti a plasticity II. Praha: SNTL, 1984. 424 s.
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| Recommended Reading: |
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[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] KAISER, J.-SLOŽKA, V.-DICKÝ, J.-JURASOV, V.: Pružnosť a plasticita.
Bratislava: Alfa,1990. 584s. ISBN 80-05-00579-2.
[2] NĚMEC, J.-DVOŘÁK, J.-HÖSCHL, C.: Pružnost a pevnost ve strojírenství.
Praha : SNTL 1989. 600 s. ISBN 80-03-00193-5.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 35 | 20 |
| Examination | Examination | 65 | 16 |