Elasticity 2

Lecturer:

Aleš Materna (gar.), Vladislav Oliva (gar.)

Tutor:

Aleš Materna (gar.), Vladislav Oliva (gar.)

Supervisor:

Department of Materials

Synopsis:

The course deals with an advanced theory of elasticity - buckling of long straight collumns, torsion of non-circular shafts, various plane stress and plane strain problems, Kirhoff's plates, shells. The emphasis is made on methods and results relevant to general solid mechanics and materials science applications.

Requirements:

Elasticity 1 (14EME1)

Fourier series and integrals.

Complex functions.

Syllabus of lectures:

1. Elastic stability - buckling of long straight collumns. 2. Torsion of non-circular shaft, Prandtl's membrane analogy, eliptical 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

Syllabus of tutorials:

Analysis of bars under torsional and combined loading, buckling of bars, bending of plates.

Study Objective:

Knowledge: Stress function in the theory of elasticity. 2D elasticity - different state of stress under plane stress and plane strain conditions, the state of stress around notches, cracks and concentrated loads. Character of stress and strain fields in plates and differences between plates and beams. Stresses and strains in shells; assumptions, advantages and imperfections of the membrane state

Skills: Solution of simple problems of 2D elasticity, plates and membrane shells. Understanding of elastic models of such bodies and their applications in material sciences.

Study materials:

Key references:

[1] Šubrt L.: Teorie desek a skořepin. [University textbook FSI] Vydavatelství ČVUT 2007.

Recommended references:

[1] Servít, R. - Drahonovský, Z. - Šejnoha, J. - Kufner, V.: Teorie pružnosti a plasticity II. SNTL-ALFA 1984.

[2] Brdička, M. - Samek, L. - Sopko, B.: Mechanika kontinua. Academia 2005, ISBN: 80-200-1344-X.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: