Abstract: Currently， suitable bedrock sites are becoming increasingly scarce， and the development of nuclear engineering has been constrained by site selection. The transition from bedrock sites to complex non-bedrock sites has become a prevailing trend in the field. To ensure the sustainable development of nuclear engineering， numerous theoretical and technical challenges in soil-structure dynamic interaction within complex heterogeneous non-layered foundations must be addressed. One of the core challenges is the seismic wave input.The classical seismic wave input method requires the incident free-field waves at the bottom boundary， combining upward and downward wave propagation. This approach is applicable to homogeneous layered foundations but struggles to address seismic input challenges in complex heterogeneous non-layered foundations. To tackle the difficulty in determining downgoing waves in heterogeneous non-layered foundations， an improved dynamic artificial boundary combined with an upgoing-wave input method is adopted. The classical viscoelastic artificial boundary and the corresponding seismic input scheme are further developed， and an analytical method for soil-structure dynamic interaction in non-horizontally layered foundations is proposed. When the upgoing wave is used as the input at the bottom boundary instead of the free-field input for external source problems （e.g.， earthquakes）， the model does not suffer from low-frequency instability； it is recommended to use the viscous boundary for computation， which can yield accurate solutions. For internal source problems in which low-frequency instability occurs， it is recommended to conduct sensitivity analyses to determine a reasonable scattering radius.