关键词: 结构-地基动力相互作用, 比例边界有限元法, 连分式法, 量纲分析, 数值稳定性

Abstract: In the scaled boundary finite element method (SBFEM) for solving the fundamental dynamic stiffness of an unbounded domain, the continued fraction solution that takes the mixing variables of the stiffness and flexibility matrices as the basic model is becoming popular increasingly. However, for the parameters of practical ground site, the enormous difference of the elements magnitudes of the stiffness matrix or flexibility matrix leads to the unstable solution of the dynamic stiffness of the unbounded domain. Aiming at the problem above, firstly, we verifies the rationality of the calculation result of a numerical example by improved continued fraction solution and then the influence of dimensionless degree of parameters on calculation accuracy is analyzed by the improved continued fraction, so the SBFEM dynamic stiffness numerical model is established based on dimensional transformation. In the new model, the real parameters of the site are converted to dimensionless form, with the converted parameters, the dynamic stiffness matrix is calculated and then the computational results are reduced to the real dimension. Finally, through the parameter sensitivity analysis and the dynamic stiffness analysis of the unbounded domain of different weathering degrees, numerical results are given to validate the accuracy and applicability of the presented model.

Key words: structure-ground dynamic interaction, scaled boundary finite element method, continued fraction, dimension analysis, numerical stability