CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Elasticity 2

Code Completion Credits Range Language
14EM2 Z,ZK 4 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 deals with an advanced theory of elasticity - buckling of long straight columns, torsion of non-circular shafts, various plane stress and plane strain problems, Kirchhoff's plates, shells. The emphasis is made on methods and results relevant to general solid mechanics and materials science applications.

Requirements:
Syllabus of lectures:

Outline:

1. Elastic stability - buckling of long straight columns. 2. Torsion of non-circular shaft, Prandtl's membrane analogy, elliptical and narrow-rectangular cross section, combination of torsion, bending, tension and shear. 3. 2D problem: plane stress and plane strain, Airy's stress function, method of Fourier series and integrals, complex potentials (Muschelishvili), state of stress around the point force on a half-plane or plane, state of stress around holes (Kirsch, Inglis) and cracks (Westergaard), stress intensity factor. 4. Flat plates: classification, Kirchhoff's theory, plate differential equation, boundary conditions, basic solutions in rectangular and circular coordinate system, energetic methods - principle of virtual work, Ritz's and Galerkin's methods.

5. Shells: conditions of the membrane state, axisymmetric thin-shells under axisymmetric loading, rotational ellipsoid under internal pressure, circular cylindrical pressure vessel with ellipsoidal bottom

Keywords:

Buckling of columns, torsion of bars, plane stress, plane strain, plane problem of elasticity, stress concentration around holes and cracks, Kirchhoff's plates, axisymmetric shells

Syllabus of tutorials:
Study Objective:
Study materials:

Key references:

[1]Reddy J.N.: Theory and Analysis of Elastic Plates and Shells, CRC Press, 2006, 568 p.

[2]Lurie A.I., Belyaev A. The plane problem of the theory of elasticity. In: Theory of Elasticity. Foundations of Engineering Mechanics. Springer, Berlin, Heidelberg, 2005, ISBN 978-3-540-24556-8

Recommended references:

[3]Boresi, A. P., Schmidt, R. J.:Advanced mechanics of materials. John Wiley&amp; Sons, 2003, ISBN 978-0-471- 43881-6

[4]Ugural, A. C.: Plates and Shells: Theory and Analysis, CRC Press, 2017, 592 p.

Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-08-15
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