Optimal Design of Helical Springs of Power Law Materials
  In this paper the geometric dimensions of a compressive helical spring made of power law materials are optimized to reduce the amount of material. The mechanical constraints are derived to form the geometric programming problem. Both the prime and the dual problem are examined and solved semi-analytically for a range of spring index. A numerical example is provided to validate the solutions. 
Dongming Wei, Marios Fyrillas, Adilet Otemissov, Rustam Bekishev
math.OC