Static deformation of space elevator tether due to climber

• We model the deformation of the space elevator tether due to a static climber.
• We use the assumed modes method and compute numerical solutions.
• We generate strain, stress, and tension profiles.
• We compute the displacement of the counterweight.

As higher strength to density ratio materials become available, the construction of a space elevator on Earth becomes more plausible. Though many fundamental aspects of the mechanical behaviour of a space elevator have been previously analysed, several details have not been rigorously explored. This paper examines the deformation of the tether from its nominal state when it is loaded with a climber at any altitude.Using an assumed modes numerical approach, the equilibrium conditions governing the static deformation of the elevator tether are derived, taking into account the presence of a climber. These discretised equations are solved numerically to determine the static deformation of the tether. A spectrum of statically deformed tether profiles is presented. Strain, stress and tension profiles are also computed and discussed. In general, when a climber is present below GEO, the extension (and stress) of the portion of tether below it is reduced and that above it is largely unaffected. When a climber is present above GEO, the extension (and stress) of the portion of tether below it is increased (that above it remains largely unaffected). Finally, the absolute displacement of the apex anchor (counterweight) is plotted against climber locations.