| Course Unit Code | 330-0531/02 |
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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 | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | English |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| SOF007 | doc. Ing. Michal Šofer, Ph.D. |
| Summary |
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| The aim of the study course is to provide students with a deeper overview in the field of classical theory of elasticity, thanks to which the students will be able to solve complex problems in practice using analytical approach. The course is thematically divided into two parts. In the first part, students become familiar with the problematics of coordinate systems transformation, body deformation, stress and strain, and last but not least with the mathematical description of body compatibility or equilibrium equations in the case of elastostatics and elastodynamics. The second part of the course, on the other hand, deals with the theory of solving 2D problems using the stress function and also with the topic of torsion of arbitrary cross-sections. |
| 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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1. Orthogonal transformation. Transformation of coordinate system. Transformation properties of vectors and tensors. Physical components of vectors and tensors.
2. Analysis of strain at a point in a deformable body. Strain-displacement relations. Geometric meaning of individual components of Cauchy strain tensor.
3. 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.
4. Mohr´s representation of 3D stress state. Extreme shear stresses. Spherical and deviatoric stress tensor. Octahedral normal and shear strains.
5. Strain tensor invariants. Principal strains and directions. Maximum shear strains. Spherical and deviatoric strain tensor. Normal and shear stresses on the octahedral plane.
6. Compatibility and equilibrium equations.
7. Constitutive equations. Hook´s law for anisotropic, orthotropic, transversely isotropic and isotropic material. Pre-heating and initial deformation effect on constitutive equations.
8. Boundary conditions. Solution of the 2D elastic problem, formulation in terms of displacements - Lamé (Navier) equations, formulation in terms of stresses - Beltrami-Michell equations.
9. Two variants of the 2D elastic problem. Plane stress and plane strain problem. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates.
10. Expression of boundary conditions using Airy´s stress function. Biharmonic equation in polar coordinates.
11. 2D elastic problem with axially symmetric stress distribution. Pure bending of the circular curved bar.
12. Bending of the circular curved bar with the force acting at the free end. The effect of circular hole on the stress field in the plate.
13. The Flamant-Boussinesq problem.
14. Axially symmetric problem in cylindrical coordinates. Force acting in point of infinite isotropic elastic space (Kelvin problem).
15. Free torsion of arbitrary cross-section.
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| Recommended or Required Reading |
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| Required Reading: |
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| [1] 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.
[4] TIMOSHENKO, S. P.-GOODIER, J. N.: Theory of elasticity. New York-Toronto-London: Mc Graw-Hill, 1951, 3.ed.1970. |
| 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.
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[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.
[3] LEIPHOLZ, H.:Theory of elasticity. Noordhoff International Publishing Leyden, 1974. ISBN 90-286-0193-7 |
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Experimental work in labs, Project work |
| 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 | 25 |