APPLICATION OF KRONECKER PRODUCT TO THE ANALYSIS OF MODIFIED REGULAR STRUCTURES

In this paper, structures transformable to regular forms are studied. Here, two cases are
investigated. In the first case, the effect of different boundary conditions on these structures are
explored, and in the second case the effect of adding or removing members and nodes are studied.
In some structures the graph model is regular and different boundary conditions change the
corresponding block matrices into non-regular ones. In some other structures the addition or
removal of nodes and/or members changes the structure into a regular one. Here an efficient
method is presented for dealing with the above-mentioned irregularities.
The main idea steams from the fact that on the one hand there exist simple relationships for
finding the inverse of some block matrices related to regular structures, and on the other hand we
want to find out how to obtain the inverse of matrices corresponding to structures which become
regular by the addition or removal of some members and/or nodes.
One of the applications of the present method is related to the finite difference (FD) method
for the analysis of plates with some irregularities in their boundary or having different support
conditions.