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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.
MSC:
 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