Abstract:
A numerical method of determining displace
ments and stresses in a uniformly thin shallow
spherical shell with general shape of the boun
dary and boundary conditions of practical impor
tance is studied. The partial differential equa
tions for the shell are derived from the varia
tional principle in a form so as to yield a real
symmetric matrix on discretisation. The use of
the variational principle also leads to a better
insight into the boundary conditions which are
discussed in detail.
The matrix of finite difference equations
derived as approximations of the partial differen
tial equations has been proved to be symmetric
and positive definite in some of the physically
significant cases of boundary conditions. This
ensures the success of successive over-relaxation
iterative methods of solution of the finite
difference equations on a high speed digital
computer.
The method is illustrated by solving a few
problems of shallow spherical shells with circular
and rectangular boundaries, for in these cases the
results could be compared with known analytical
solutions.
A chapter-wise summary of the thesis is
given in section 1.4 of Chapter I (Introduction).
