Aims & Objectives

General Aims and Objectives

This study will begin with a single pinned support condition, and will perform a wide range of calculations on spherical shells of different geometry, focussing on the ratios R/t and the subtended angle ɸ. 

For each calculation, the buckling mode will be documented in terms of the number of waves occurring around the circumference of the shell and the approximate angular extent of the buckle up the meridian.  Once the relationships have been established for pinned supports between buckling pressure pcr and R/t for many different subtended angles ɸ, a first attempt will be made to approximate these relationships using empirical expressions, relating the buckling pressure to the theoretical critical pressure for a complete sphere.

R = radius of sphere (shell middle surface),
r = r(x) radius of shell middle surface perpendicular to axis of rotation
r0= radius of base circle of spherical cap,
t = thickness of shell,

ɸ = semi-angle of spherical cap.

The calculations will then be repeated for other boundary conditions and the same process explored.  The changing form of the buckling modes will also be related to the changing strengths.  If time permits, the calculations can be extended to deal with more realistic boundary conditions of an attached cylindrical shell or a stiffening ring of finite stiffness at the outer edge. However, no such existing calculations are known to exist at present and this may prove very challenging.

The final thesis will document all the findings of the project in terms of buckling pressures, buckling modes and prebuckling stress patterns, and it will discuss any unusual or unexpected findings, identifying why they may be important.

Specific Aims and Objectives

Aim: Gain knowledge in subject: Continuous


  • Meet with Professor Rotter and discuss the thesis project in general.
  • Begin reading of previous and relevant books, journals and documents.

2.       Aim: Familiarising ourselves with computer software: In Progress


  • Spend time learning how to run both the computer programmes by doing tutorials and any reading that may be required. 
  • Ensure that we are both capable of running the programmes correctly and efficiently.

3.       Aim: Analyse problem using software: To Begin


  • Enter all relevant data required to both computer programmes ensuring that it is correct.
  • Repeat to eliminate the chance of error occurring and to help find any mistakes when entering data.
  • Potentially run computer software for different boundary conditions if time allows.

4.        Aim: Interpret computer software results: To Begin


  • Compare the results of both computer software programmes highlighting any differences or unexpected findings.

5.       Aim: Thesis write up: To Begin


  • Gather all information collected from the beginning of the project
  • Select the sections of most significance and relevance to the thesis and conclude why they are of such importance.


(Courtesy of Prof. Ali Limam, Intstitut National des   
Scieanes Appliquees de Lyon, France)