System reduction-based approximate reanalysis method for statically indeterminate structures with high-rank modification

Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To improve the efficiency of engineering computations, a novel approximate static reanalysis method based on system reduction and iterative solution is proposed for statically indeterminate structures with highrank modification. In this approach, a statically indeterminate structure is divided into the basis system and the additional components. Subsequently, the structural equilibrium equations are rewritten as an equation system with the stiffness matrix of the basis system and the pseudo forces derived from the additional elements. With the introduction of the spectral decomposition, a reduced equation system with the element forces of the additional elements as unknowns is established. The approximate solutions of the modified structure can then be obtained by solving the reduced equation system through a pre-conditioned iterative solution algorithm. The computational costs of the proposed method are compared with those of two other reanalysis methods, and numerical examples including static reanalysis and static nonlinear analysis are presented. The results demonstrate that the proposed method has excellent computational performance for both structures with homogeneous material and structures composed of functionally graded beams. Furthermore, the superiority of the proposed method suggests that the combination of system reduction and pre-conditioned iterative solution technology is an effective approach to develop high-performance reanalysis methods.