Course detail

Thin-walled Structures

FSI-RTKAcad. year: 2017/2018

Thin-walled structures represent a specific type of problem, which cannot be fully explained in the basic course Strength of Materials II.
This course deals with these specifics in detail for individual types of thin-walled structures: membranes, plates, membrane and bending theory of shells and thin-walled beams. Basic equations describing the
above problems are formulated, the possibility of their analytical solution is discussed and numerical solution by the FEM is realised in seminars. Attention is also paid to the stability and vibration of thin-walled structures. In vibration, besides the numerical analysis of modal characteristics, students gain the experience in experimental modal analysis, which is a part of practical training.

Learning outcomes of the course unit

Students will be able to classify correctly individual practical problems in the context of theory of thin-walled bodies. They will discern relevant and irrelevant input parameters from the point of view of structural response and possible failure modes such as large displacements, structural instability or load-bearing capacity. They will be able to select an effective solution algorithm for each problem.


Mathematics: linear algebra, matrix notation, functions of one and more variables, calculus, ordinary and partial differential equations. Others: basic theory of elasticity, dynamics, theory and practical knowledge of the FEM, including nonlinear problems solution.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

J.F.Doyle: Nonlinear Analysis of Thin-Walled Structures, Springer, 2001
Hodnocení pevnosti zařízení a potrubí jaderných elektráren typu VVER, Normativně technická dokumentace A.S.I., Praha-Brno, 2001
V.Křupka, P.Schneider: Skořepiny tlakových nádob a nádrží, VUT v Brně, 1986 (skriptum)
S.Timoshenko, J.M.Gere: Theory of Elastic Stability, McGraw-Hill, 1963
P.Puchmajer: Stabilita pružných soustav, ČVUT Praha, 1989 (skriptum)
Z.Waszczyszyn et al.: Stability of Structures by Finite Element Method, Elsevier, 1994
I.E.Mileikovskij, S.I.Trushin: Analysis of Thin-Walled Structures, A.A.Balkema, 1993
Š.Markuš: Mechanika kmitania valcových škrupín, Veda, vyd.SAV, Bratislava, 1982

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

The course-unit credit for seminars is granted under the condition of:
- active participation in seminars,
- individual preparation and presentation of a seminar project.
Final evaluation is based on the result of examination, which has a form of a written test of gained knowledge.

Language of instruction


Work placements

Not applicable.


The course objective is for students to get a complete view of the possibility of computational and experimental solution of individual classes of thin-walled problems.

Specification of controlled education, way of implementation and compensation for absences

Attendance at practical training is obligatory. One absence can be compensated by working out an additional assignment. Longer absence is compensated by special tasks assigned by the tutor.

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-IMB , 2. year of study, winter semester, 5 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Introduction, classification of thin-walled structures, internal forces, shear effects
2. Membranes - basic equations, Airy stress function, numerical solution
3. Plates cartesian coordinates, possibility of analytical solution
4. Plates in polar coordinates
5. Vibration of plates
6. Axisymmetrical shells, membrane theory
7. Axisymmetrical shells, bending theory, local effects in contact between bottom and wall of cylindrical vessel
8. Basic principles of normative standards for boilers, pressure vessels and pipes
9. Vibration of axisymmetrical shells
10. Thin-walled beams - coupled bending and torsion, shear centre, deplanation
11. Stability and load-carrying capacity - introduction, stability of struts and strut systems
12. Stability of membranes, plates and cylindrical shells
13. Numerical solution of stability problems - linear and nonlinear stability

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer


1. Overview of thin-walled finite elements, characteristics, limitations
2. Example of analytical solution of membrane and comparison with FEM solution
3. Solution of rectangular plate by infinite series
4. Numerical solution of plates by FEM
5. Consultation of semester projects
6. Modal analysis of rectangular plate by FEM
7. Experimental modal analysis of rectangular plate, influence of boundary conditions on frequency, comparison with FEM
8. Modal analysis of axisymmetrical shell by FEM
9. Experimental modal analysis of axisymmetrical shell, comparison with FEM
10. Consultation of semester projects
11. Influence of shear stress on deformation and stress state of thin-walled beam
12. Numerical solution of stability of cylindrical shell
13. Presentation of seminar projects