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:

Credit will be awarded after successful completion of a written test including several simple examples from plane elasticity.

The exam is oral. The student should demonstrate an understanding of the basic assumptions, procedures, and general results of solving individual classes of problems and knowledge of basic relationships and their connections. Detailed derivation of these relationships will not be required.

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 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství materiálů (compulsory course in the program)