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Yang, Qiu Wei; Peng, Xi

A highly efficient method for structural model reduction. (English) Zbl 07769217

Int. J. Numer. Methods Eng. 124, No. 2, 513-533 (2023).
Summary: Model reduction is a commonly used method for quickly computing the lower-order eigenvalues and eigenvectors of a structure. This article proposed a direct model reduction method without any iterations. Compared with the existing methods, the proposed technique has two main advantages. The first one is that the explicit expression of the transformation matrix can be directly obtained using a recurrence formula. The second one is that the calculation efficiency of the proposed method is very high because there is no need for iterative calculation. Three types of structure are used as examples to verify the proposed method. It is found that the lower-frequency eigenpairs calculated by the reduced model are very close to the exact ones obtained by the full model. Moreover, the calculation time of the proposed method is much less than that of the existing methods. It has been shown that the proposed method is reliable and effective.
{© 2022 John Wiley & Sons Ltd.}

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K99 Thin bodies, structures

Keywords:

eigensolution; transformation matrix; matrix inversion; Neumann series; recurrence formula; beam element discretization; plane truss structure; hollow I-beam; 50-story frame structure
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References:

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