Lumped-parameter models for foundations base on Chevshev complex polynomials-fraction

This paper puts its attention on the application of Chebyshev complex polynomials in the development of an extensible lumped-parameter model of unbounded soil. The normalized flexibility function of foundations is adopted to improve the accuracy of the model and to reduce the parameters in modeling. A ratio of two Chebyshev complex polynomials is adopted to represent the normalized flexibility function of foundations. Through performing a partial-fraction expansion on this Chebyshev complex polynomial-fraction, a Chebyshev complex polynomial-fraction is designed as two basic discrete-element models. The accuracy and validity of the lumped-parameter model are extensively investigated for the case of foundations. Subsequently, these models are applied for representing the dynamic stiffness functions of foundations. The proposed method may be easily applied to analyze various practical problems in soil-structure interactions in a time domain and nonlinear analyses.