Application of Kronecker Product to the Analysis of Modified Regular Structures

Abstract– 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.