A new approximation of the constraints in truss sizing problems: An explicit second order approximation which is exact for statically determinate truss structures

A new explicit approximation of the constraint functions (displacements and stresses) in truss sizing problems is presented and shown to have the following properties:

—it is a second order approximation;

—it is exact if at most two variables (cross-sectional areas) are varied simultaneously;

—it is exact when applied on statically determinate structures.

The approximation is included in an optimization scheme for truss sizing and applied on several test problems. The optimal solution is always obtained, with a very high accuracy, after less than 5 global iterations, even on problems where traditional first order methods require up to 40 global iterations.