Search Results (2)

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses. Full article

The sensitivity reanalysis technique is an important tool for selecting the search direction in structural optimization design. Based on the decomposition perturbation of the flexibility matrix, a fast and exact structural displacement sensitivity reanalysis method is proposed in this work. For this purpose, the direct formulas for computing the first-order and second-order sensitivities of structural displacements are derived. The algorithm can be applied to a variety of the modifications in optimal design, including the low-rank modifications, high-rank modifications, small modifications and large modifications. Two numerical examples are given to verify the effectiveness of the proposed approach. The results show that the presented algorithm is exact and effective. Compared with the existing two reanalysis methods, this method has obvious advantages in calculation accuracy and efficiency. This new algorithm is very useful for calculating displacement sensitivity in engineering problems such as structure optimization, model correction and defect detection. Full article