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 p_{cr} 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 = r(x) radius of shell middle surface perpendicular to axis of rotation r_{0}= 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
2.
Aim: Familiarising
ourselves with computer software: In Progress
3.
Aim:
Analyse problem using software: To Begin
4.
Aim: Interpret computer software results: To
Begin
5.
Aim:
Thesis write up: To Begin
(Courtesy of Prof. Ali Limam, Intstitut National des Scieanes Appliquees de Lyon, France) |