Elasticity 2

Course guarantor:

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& 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 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed	roomTR:341 Oliva V. Materna A. 14:00–15:50 (lecture parallel1) Trojanova 13
Thu
Fri	roomTR:308a Oliva V. Materna A. 09:00–10:50 (parallel nr.101) Trojanova 13

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství materiálů (compulsory course in the program)