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A family of Craig-Bampton methods considering residual mode compensation. (English) Zbl 1433.74105
Summary: In this paper, we investigate the formulation of a family of Craig-Bampton (CB) methods considering residual modes by O’Callahan’s approximation and adding generalized coordinate vectors containing unknown eigenvalues. In addition, we propose an \(n\)th-order higher-order CB+ (HCBn+) method for compensating the \((n + 1)\)th residual flexibility in the \(n\)th-order HCB (HCBn) method by O’Callahan’s approach. Therefore, various CB methods with improved performance, such as the enhanced Craig-Bampton (ECB) method, which uses O’Callahan’s approximation, and the higher-order Craig-Bampton (HCB) method, which adds generalized coordinate vectors, and HCB+ are employed for the comparison of performance with the aid of multiprecision computing. Through three benchmark examples, it is revealed that the HCB1+ method, a modified version of the first-order HCB method (HCB1) with the aid of O’Callahan’s approximation proposed, shows better performance than HCB1 with the same number of retained modes. However, HCB2+ and HCB3+, modified versions of the second- and third-order HCB method, respectively, cannot be improved further. From the results, we concluded that this was due to the limitation of O’Callahan’s approach, which many researchers have fundamentally questioned.
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
ABAQUS; advanpix
Full Text: DOI
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