Abstract:
A study of bending of plates for small
deformations by applying the finite element method
is presented in this thesis.
This thesis is mainly concerned with the
development of new displacement functions for
rectangular and triangular elements. For reotangular
elements, a method has been proposed for selecting
displacement funotions in which trigonometric
expression that had apparently failed to give
satisfactory results in earlier attempts, can be
used along with polynomial terms. The method leads
to conforming displacement functions which satisfy
the oonvergenoe criteria. Not many suitable
conforming functions have been reported so far.
But, the method developed here for rectangular
elements shows how many more new displacement functions
can be found, all of them satisfying the convergence
oriteria. In fact, the number of such functions
is almost unlimited.
A conforming displacement function has been
suggested for triangular elements by .using simple
polynomial expressions. Continuity of normal
slopes have been achieved by forcing them to vary
linearly along the element boundaries. To accomplish
this, additional correction functions have been used.
Several plate bending problems have been
solved using an IBM 1620 Model I computer. Results
are presented for four different displacement
functions; three are for rectangular elements and
one for triangular elements.
All the functions converge towards the
true answers with successive refinements in the
sub-division analysis. The convergence is
mo no tonic in all Cases.
