Least weight cables: Optimal parameter selection approach

The least weight design of cables under selfweight and uniformly distributed load is considered. The set of necessary conditions for an optimal solution is obtained using a new optimization approach based on a Lagrange multiplier and the gradient expression of the cost functional for a general class of optimal parameter selection problems, The proposed approach is shown to be simple and efficient in solving this class of optimization problems involving ordinary differential equations with algebraic constraints at end points. interestingly, the selfweight does not appreciably affect the length and profile of the optimal cable under uniformly distributed load as it would for other loading conditions. The cost sensitivity of the design is also investigated.