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Precise integration methods based on the Chebyshev polynomial of the first kind

Earthquake Engineering and Engineering Vibration 2008年第2期7卷 207-216页

作者： Wang Mengfu F. T. K. Au Department of Civil Engineering Hunan University Changsha 410082 China Department of Civil Engineering The University of Hong Kong China

This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homogenized initial system method （HISM）. In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.

关键词： structural dynamics Chebyshev polynomial of the first kind the crout decomposed method integral formula method homogenized initial system method

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