Elasticity 2
Code  Completion  Credits  Range  Language 

14EM2  Z,ZK  4  2P+2C  Czech 
 Lecturer:
 Vladislav Oliva (guarantor), Aleš Materna
 Tutor:
 Vladislav Oliva (guarantor), Aleš Materna
 Supervisor:
 Department of Materials
 Synopsis:

Abstract:
The course deals with an advanced theory of elasticity  buckling of long straight columns, torsion of noncircular 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 noncircular shaft, Prandtl's membrane analogy, elliptical and narrowrectangular 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 halfplane 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 thinshells 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 9783540245568
Recommended references:
[3]Boresi, A. P., Schmidt, R. J.:Advanced mechanics of materials. John Wiley& Sons, 2003, ISBN 9780471 438816
[4]Ugural, A. C.: Plates and Shells: Theory and Analysis, CRC Press, 2017, 592 p.
 Note:
 Timetable for winter semester 2021/2022:
 Timetable is not available yet
 Timetable for summer semester 2021/2022:
 Timetable is not available yet
 The course is a part of the following study plans: