General Treatment of Structural Modifications

In order to perform modifications of structures analyzed by the Matrix Displacement Method, a direct computer-oriented approach is presented enabling the treatment of coupled combinations of three possible types of modifications, namely, removal of freedoms, addition of freedoms, and modification of elements. The formulation is extended to cover modifications of elements in substructures together with the corresponding modification to the main structure. The method is derived from the laws of partitioned matrices and Boolean transformation of freedoms within the structural stiffness matrix, and fully exploits symmetry and positive-definiteness. The presented form of the modification equations allows the use of an alternative existing approach of updating the triangularized factor of the structural stiffness matrix due to the modification of elements. The method is extended to provide a recursive hypermatrix Cholesky algorithm. All formulations are accompanied by operation counts to enable rapid determination of break-even points for reanalysis or possible iterative solutions.