Elasticity 1
Code  Completion  Credits  Range  Language 

14EM1  Z,ZK  5  2P+2C  Czech 
 Garant předmětu:
 Vladislav Oliva
 Lecturer:
 Aleš Materna, Vladislav Oliva
 Tutor:
 Aleš Materna, Vladislav Oliva
 Supervisor:
 Department of Materials
 Synopsis:

Abstract:
The course represents an introduction for several another lectures on continuum mechanics and the strength of materials. The first part contains a detailed theory of stress, small strains and linear elasticity. The second one represents a logical descent from the continuum mechanics to the practical engineering solution of simple problems on tension, bending, shearing and torsion in the cross section of bars and beams.
 Requirements:
 Syllabus of lectures:

Outline:
1. Tensors 2. Strain: Lagrangian and Eulerian coordinates, finite strain tensor, small strain tensor, rotation tensor, compatibility equations 3. Stress: internal forces, stress vector, Cauchy's stress tensor, equilibrium equations, principal stresses, octahedral shear stress, Mohr's circles. 4. Basic of elasticity theory: generalized Hook's law, linear equations of mathematical theory of elasticity and boundary conditions, SaintVenant’s principle, superposition principle, BeltramiMichell equations, Lame's equations, potential and complementary strain energy of internal and external forces, variational principles of elasticity, Castigliano’s theorems, principle of finite element method, elasticity equations in polar coordinates 5. Mathematical vs. engineering solutions of elasticity problems, plasticity conditions, fatigue fracture, brittle and ductile fracture.
6. Bars and beams: geometric characteristics of the cross section, forces and moments in the cross section, load and supports and fixations, statically determinate and indeterminate problems. 7. Tension and compression: statically indeterminate cases, thinwalled pressure vessel, sudden changes in geometry and in the load. 8. Flexural loading of straight beams  stress: pure bending, transverse loading, load and shear and moment relationship, stresses in symmetrical and thinwalled cross sections under the shear force. 9. Flexural loading of straight beams  deflections: curvature of neutral axis, differential equation of the elastic curve, energy methods. 10. Statically indeterminate straight beams, theorem of three moments. 11. Curved beams: flexural stresses and changes in curvature, thin curved beams, frames. 12. Torsion of circular shaft: shear stress distribution, geometry of deformation.
Keywords:
Tensors, Analysis of stress, Small strain theory, Theory of linear elasticity, Axially loaded bars, Bending of straight bars and beams, Curved beams and frames, Torsion of circular shaft
 Syllabus of tutorials:
 Study Objective:
 Study materials:

Key references:
[1]Gross, D., Hauger W., Schröder, J., Wall W. A., Bonet J.: Engineering Mechanics 2: Mechanics of Materials,
2nd ed., 2018, ISBN 9783662562710
Recommended references:
[2]Boresi, A. P., Schmidt, R. J..: Advanced mechanics of materials. John Wiley& Sons, 2003,
ISBN 9780471 438816
[3]Atkin, R. J., Fox, N.: An Introduction to the Theory of Elasticity, Dover Publications, 2005, 9780486442419
 Note:
 Timetable for winter semester 2023/2024:
 Timetable is not available yet
 Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans: