Structural reanalysis method for local modifications based on system reduction and iterative solution. (15th December 2022) - Li, Wenxiong; Chen, Suiyin
Highlights: A novel structural static reanalysis method is proposed for both low-rank and high-rank local modifications. The reanalysis method realizes the integration of system reduction and iterative solution algorithm. The iterative solution algorithm with simplified pre-conditioning method is developed for solution of the reduced system. The reanalysis method is introduced to the solution algorithm for static nonlinear analysis of the structures with material nonlinearity. Abstract: In this paper, a novel static reanalysis method based on system reduction and iterative solution is proposed for structures with local modifications of physical properties. In this approach, the equilibrium equations of a modified structure is expressed by the original stiffness matrix and the pseudo forces introduced under the consideration of the effects of structural modifications. Based on the relationship between the element deformation displacements and element nodal displacements, the reduced equation system of the modified structure is reconstructed according to the distribution of modified elements. The iterative solution algorithm is employed to solve the reduced equation system of the modified structure, and the simplified pre-conditioning operation is proposed to significantly improve the solution efficiency. In addition, the structural nonlinear analysis method based on the proposed reanalysis method is developed for static nonlinear analysis of the structures with material nonlinearity. As indicated by the numerical investigation, the proposed method realizes the integration of system reduction and iterative solution algorithm, achieving high computational efficiency and satisfactory solution accuracy in the cases of both high-rank and low-rank local modifications of physical properties. Furthermore, the introduction of the proposed reanalysis method significantly improves the performance of solution algorithms for structural static nonlinear analysis.