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Lecturer(s)
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Hokr Milan, doc. Ing. Ph.D.
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Hančilová Ilona, Ing. Ph.D.
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Course content
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Lectures: 1. description of forces in continuum - traction vector and stress tensor 2. tensor properties, force equilibrium equation 3. small and large strain tensors, equation of compatibility 4. principal values/directions of stress and strain 5. generalized Hooke's law (triaxial) 6. component transformation in coordinate systems, equation for 2D case 7. special cases - plane stress and strain 8. Lame and Michel Beltrami equations 9. formulation of boundary-value problems 10-11. energetic/variational methods - virtual work principle, minimum of energy 12. strength conditions in triaxial stress 13. introduction to nonlinear problem, plasticity and discontinuity mechanics 14. practical illustration of numerical simulation application (spare time) Tutorials: 1. practice with the mathematical apparatus - vector algebra, Einstein summation 2. calculation of triaxial stress problems from the equilibrium equation and surface force 3. derivation of torsion and bending stresses/strains from general equations 4. problems on plane strain and plane stress 5. calculations of coordinate system transformation and principal directions 6. demonstration of boundary conditions definition from real-cases of support and load 7. examples of numerical simulation results interpretation with stress and strain components
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Contacts hours
- 42 hours per semester
- Preparation for credit
- 20 hours per semester
- Preparation for exam
- 29 hours per semester
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Learning outcomes
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The aim is to complete the knowledge of engineering elasticity and strength, with a general description of quantities and governing equation of stress and deformation and with its solution methods. The theory is a necessary basis for numerical simulations and result evaluation, which are included in other courses of the programme. It also supports a context for coupled phenomena like the piezoelectricity and for the fluid mechanics.
The graduate will understand a general distribution of stress and deformation in bodies and interpret the engineering cases of e.g. tension, torsion and bending as special cases. The knowledge of tensor form of stress and deformation and of mathematical properties of the equations will allow correct input of real-world problem data into numerical simulation software and to interpret the results.
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Prerequisites
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Unspecified
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Assessment methods and criteria
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Combined examination
Requirements for getting a credit are activity at the tutorials. Examination is in written form.
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Recommended literature
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Brdička M.,Samek L., Sopko B. Mechanika kontinua. Academia, 2000. ISBN 80-200-0772-5.
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Hokr M. Mechanika kontinua a termodynamika, učební text FM TUL [online]. [cit. 2016-01-08]. Dostupné z: http://www.nti.tul.cz/cz/Vyuka/MKT. 2013.
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Nečas, Hlaváček. Úvod do matematické teorie pružných a pružně plastických těles. SNTL, Praha 1983. &, &.
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Sadd M.H. Elasticity: Theory, Application, and Numerics. 2005. ISBN 0-12-605811-3.
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