Reanalysis for Limited Structural Design Modifications

This study presents ways to implement the algorithm of Sherman and Morrison when modifications occur in a small part of the structure. For such limited modifications, a corresponding small number of elements in the original stiffness matrix are affected, and the inverse of the new stiffness matrix can be computed efficiently by this method. However, for matrices of high order, this method also becomes time consuming. Therefore, two new procedures for a direct solution without generating the inverse are developed. The first procedure is based on the Sherman and Morris algorithm and the second on a solution of a reduced set of equations in which the independent unknowns are computed directly. Numerical difficulties due to matrix singularity and ways to overcome them are analyzed. A comparative study demonstrates the efficiency of the proposed methods in terms of the number of arithmetic operations in reanalysis of limited structural design.