3D Structures

Topology optimization of a satellite support structure

Skilled engineers may be able to come up with efficient designs for geometrically simple structures. An example of a geometrical complexity that goes beyond the abilities of engineers is the design of a small satellite structure.

The Danish government is sponsoring a small satellite program with the aim of launching a satellite with scientific mission goals every fifth year. One of the proposals (BALLERINA)  for the next launch is a small satellite that can investigate the physics behind Gamma-ray bursts appearing in distant galaxies. Physicists and astronomers are disagreeing on the source of the Gamma-ray bursts, but there is agreement that the Gamma-ray bursts release energies which are bigger than any previously known energy releases. An average of one burst can be detected per day with the strongest signal appearing in the first few minutes after the burst. The release of Gamma-rays decays to a non-detectable signal in approximately 24 hours. The satellite should therefore be able to detect the burst and turn its telescope towards the source as fast as possible.

To solve its mission, the satellite will be equipped with four wide-angle cameras that can search the whole space for Gamma-ray bursts. Once one of the cameras detects a burst, the satellite will orient its telescope toward the source and record the signal. In addition to the four cameras and the telescope, the satellite will be equipped with electronic instruments for controls and communication, batteries and solar panels. The size of the satellite is limited to 60x60x80 centimetres and the weight is limited to 80 kilograms. The small size of the satellite makes it possible to launch it as a `secondary' payload which is economically favourable.

A way to mount the cameras, telescope and electronic boxes in the satellite is shown in figure 1a. The problem is how to design a support structure that weighs less that 12 kilograms, yet is strong enough to carry the instruments during launch. Furthermore, it should be possible to attach two hooks to the top of the structure for ground handling.

The design problem is very well suited for topology optimization. The design domain is a box-like structure where material can be distributed everywhere, except for the space taken up by the instruments. The structure is supported by a circular ring attached to the launch-rocket and the main load case comes from the 15 g acceleration force experienced during launch. Two other load cases simulate the side-way vibrations and a fourth load case simulates the ground handling. Finally, the resonance frequency of the whole satellite should be higher than 35 Hz.

The design domain is discretized using 288000 cubic finite elements. The optimal design is shown in 1b. The computation took two days on a powerful workstation. It is evident that the structure is truss-like and supports all the instruments. Another view of the satellite structure with instruments is shown in 1c. The structure requires some post-processing.

  Ballerina's design
Figure 1: Design of a small satellite. a) Design domain and instrumentation, b) topology optimized support structure and c) support structure with instrumentation.