An exact reanalysis method for structures with local modifications

An exact reanalysis method named Indirect Factorization Updating (IFU) is proposed for the structure with local modifications, including boundary modifications. The IFU method is developed from the Independent Coefficients (IC) and Sherman-Morrison-Woodbury (SMW) formula. Due to the local modifications, the modified equations are divided into two parts: balanced equations and unbalanced equations. Using the theory of the IC, extra constraints are enforced on the unbalanced Degree of Freedoms (DOFs), so that the fundamental solution system of the balanced equations can be obtained by using the SMW formula. Then, a unique solution is derived from the general solution of the balanced equations to satisfy the unbalanced equations. In order to use the SMW formula directly, the change of the stiffness matrix is converted to a low-rank form by using the Cholesky factorization of the initial stiffness matrix. The Cholesky factorization is indirectly updated according to the stiffness matrix of the balanced equations but not directly according to the modified equations. Three examples are presented to verify the performance of the suggested IFU method. The results show that the IFU can efficiently obtain the exact solution of the structures with boundary modifications.