Structural reanalysis via force method. (April 2018) - Koohestani, K.
Highlights: A new framework for structural reanalysis has been developed. The approach is iterative and formulated based on the method of forces. Structural reanalysis is carried out using iterative matrix to vector multiplications. A rigorous study of the convergence for the iterative process is provided. The method requires only O ( m 2 ) flops in order to form accurate solutions. Abstract: We propose a novel approach for predicting forces in a structure after altering physical properties of some of its elements (new structure) using the solution of the structure before any change (parent structure). The force method for structural analysis is adopted throughout the paper. In order to obtain the forces in the new structure the method merely utilizes forces in the parent structure, diagonal/block diagonal flexibility matrix of the new structure and null space of the rectangular equilibrium matrix, which the latter only depends on structural topology and geometry. The forces in the new structure are obtained using an O ( m 2 ) scheme which performs iterative matrix to vector multiplications. A rigorous study of the convergence criterion and rate is also presented for our method. We comprehensively describe our method through three numerical examples to clarify the major steps of the process and to demonstrate its efficiency and viability.