The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.

Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.

This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency, the maximum stress, and a loading condition.

The design variables are the diameter of the wire, the outside diameter of the spring, and the number of coils.