Hexagonal Geodesic Domes - Dome Optimisation

Optimisation

Because of this optimality, it makes some sense to try designing domes by building a model of the dome in a virutal world - and then using classical optimisation techniques to iteratively adjust the model until it maximises some specified "dome desirability" function.

This approach seems likely to lead to domes which depart from the classical polyhedral regularity of many geodesic domes.

Several factors seem likely to lead real domes away from classical polyhedra:

• Domes cope well with irregular ground:
  • Deviations here can impact the shape, strut sizes and topology of the dome.

• Struts in domes have to support more weight at the bottom:
  • The increased number of struts towards the base of domes is no match for the increased weight they have to support. Adjustment in strut diameter is one possibility, but there may be constraints on the available materials which make this challenging. However, strut lengths could be varied - so structural material became more concentrated lower in the dome.

• Struts in domes have to support more weight at the bottom:
  • The increased number of struts towards the base of domes is no match for the increased weight they have to support. Adjustment in strut diameter is one possibility, but there may be constraints on the available materials which make this challenging. However, strut lengths could be varied - so structural material became more concentrated lower in the dome.

• Domes are not full spheres - instead they meet the ground:
  • One classical approach to this is simply truncating the dome at ground level - and achoring it in place.

    This is a crude approach - which can be improved upon a great deal.

• Domes need entrances, fire escapes, and ventilation:
  • The need for entrances and exits of particular sizes can naturally deform the desired shape of the resulting dome.

Building a realistic model

Real world domes need to resist impact forces, withstand high winds, endure adverse weather conditions - while remaining cost effective.

Optimisation techniques

• Genetic algorithms;

• Simulated annealing;

While - in principle - genetic algorithms are much more flexible, initially, we expect to be exploring simulated annealing as a method of generating optimal domes.

Annealing domes

By a process of automated gradual "chilling" of the system, we hope that this approch will be capable of doing a good job of avoiding getting stuck in local minima.