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Abstract This work combines flexibility disassembly perturbation (FDP) and preconditioned conjugate gradient (PCG) methods to propose a new FDP-PCG static reanalysis method, which is then integrated with the Monte Carlo (MC) method for random finite element analysis of large-scale structures. The proposed method enables rapid computation of static responses for each random sampling of the structure, facilitating statistical analysis of response parameters and calculation of failure probabilities. Compared with traditional MC algorithms, the proposed method maintains similar computational accuracy while significantly improving computational efficiency. Results from two numerical cases demonstrate that the FDP-PCG method outperforms both traditional MC methods and the original PCG method. Taking a large-span cable-stayed bridge structure as an example, the computational time of the FDP-PCG method is only about 20% of that of the traditional MC method, and even in cases with high randomness in material properties, the calculation errors for various indicators are all less than 0.5%. The proposed method provides a new, fast, and reliable approach for random finite element analysis of large-scale structures.
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Received: 14 July 2025
Published: 27 December 2025
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2025, Vol. 46 
