## Theory of Shells (CI3-337)

### Module aims

• To introduce the students to the fundamental concepts and principles of the analysis and design of thin-walled shelled structures.
• The module begins with an introduction to membrane theory for common shapes of axisymmetric structural shells, followed by an overview of axisymmetric bending theory for cylindrical shells and an introduction to the phenomenon of shell buckling.
• The module introduces the students to the analysis of shells using commercial finite element software including linear elastic, linear plastic, nonlinear elastic and linear buckling analyses. An introduction to the design of shells using EN 1993-1-6 is also given.

### Learning outcomes

On successfully completing this course unit, students will be able to:

• Understand what is meant by a 'thin' walled assumption for axisymmetric shell structures.
• Apply shell membrane theory to analyse cylindrical, conical and spherical shells under varying load cases.
• Apply axisymmetric bending theory to perform stress analyses of isotropic and orthotropic cylindrical shells.
• Use numerical analysis to perform a series of increasingly sophisticated analyses on different types of shell structures, and to compare the outcomes to previously calculated membrane theory solutions.
• Become familiar with the design philosophy in EN 1993-1-6.

### Module syllabus

• Membrane theory of thin shells: Cylindrical, conical and spherical shells; Generalisation to other axisymmetric shells.
• Axisymmetric bending theory for cylindrical shells.
• Introduction to buckling of cylindrical shells.
• Introduction to the analysis of shell structures using finite element software and overview of linear elastic, linear plastic, linear buckling and nonlinear buckling analyses.
• Overview of structural design according to EN 1993-1-6.
• Overview of advanced research topics in shells.
 No. Topic Staff 01 Introduction – Membrane theory of cylindrical shells AJS 02 Membrane theory and deformations of cylindrical shells AJS 03 Membrane theory of general shells of revolution – cylindrical shells AJS 04 Membrane theory of spherical shells AJS 05 Bending theory of cylindrical shells AJS 06 Buckling of cylindrical shells and computational analyses AJS 07 ABAQUS project AJS 08 ABAQUS project AJS 09 ABAQUS project AJS

### Teaching methods

The course has lectures and supporting tutorials.

### Assessments

The final three weeks of the project consist of an advanced ABAQUS project, carried out in the computer lab. The exam consists of two questions, both mandatory and both carrying equal marks. The split between examination and coursework is 70% / 30%.

### Supplementary

• #### Theory of plates and shells

Timoshenko, Stephen

2nd, McGraw Hill

• #### Stresses in shells

Flu¨gge, Wilhelm

2nd, Springer-Verlag Berlin

• #### Equilibrium of shell structures

Heyman, Jacques

Clarendon Press