The space elevator system is a space tether system used to solve low-cost space transportation. Its high efficiency, large load, reusability and other characteristics have broad application prospects in the aerospace field. Most of the existing mechanical models are based on “chain-bar” and a lumped mass tether model, which cannot effectively reflect the flexible behaviour of the rope of space elevator system. To establish an accurate mechanical model, the gradient deficient beam elements of the absolute nodal coordinate formulation (ANCF) are used to build the mechanical model of the space elevator system. The universal gravitation and centrifugal force in the model are derived. The calculation results of the ANCF model are compared with the results of the finite element method (FEM) and lumped mass (LM) models. The results show that the calculation results of the ANCF method are not very different from the results of the FEM and LM models in the case of axial loading. In the case of lateral loading, the calculation results of the ANCF method are basically the same as the results of the FEM and LM models, but can better reflect the local flexible deformation of the space elevator rope, and have a better calculation stability than FEM. Under the same calculation accuracy, the ANCF method can use fewer elements, and the speed of convergence is faster than the FEM and LM models.

In order to improve the shortcomings of the traditional constant section and gradual section space elevator system, combined with the advantages of constant section and gradual section space elevator system, a model of segmented space elevator system is designed. This model has the characteristics of easier construction, more practical functions, and easier maintenance. The cyclic iterative method is proposed to calculate the stress distribution of the space elevator system. The maximum stress variation and system scale variation of segmented space elevator system with different segment numbers is analyzed and compared with the system scale of constant section and gradual section space elevator system. The results show that the segmented space elevator model can significantly reduce the peak stress of the space elevator system under the condition of limited increase in the system scale, and the peak stress is 56% lower than that of the constant section space elevator model. Considering the number of segments, peak stress, and system scale, the calculation results show that the optimal number of segments is 5 or 6.

The space elevator system is a space tether system used to solve low-cost space transportation. Its high efficiency, large load and other characteristics have broad application prospects in the aerospace field. The stability analysis is the foundation of the space elevator system research. Based on the new segment space elevator system model, in this paper, the stability of the system at the equilibrium point is analyzed by Lyapunov stability theory; And based on the criterion that the change rate of the system restoring torque and the anchor point tension are greater than 0, the maximum offset angle of the system inside and outside the equatorial plane is analyzed. The results show that the segment space elevator is stable near the equilibrium point; The maximum deflection angle of the space elevator inside and outside the equatorial plane is related to the design stress of the anchor point; When the space elevator is offset outside the equatorial plane, it will only lose stability because the restoring torque reaches the maximum value; When the space elevator is offset in the equatorial plane, and due to the design stress of the anchor point is small, it will lose stability because the tensile force of the anchor point is reduced to 0, and when the design stress of the anchor point is large, it will lose stability because the recovery torque reaches the maximum value; The stability of the space elevator outside the equatorial plane is better than that in the equatorial plane.