Global convergence of the stress ratio method for truss sizing

It is proved that if the well-known stress ratio method is applied to a “perturbed” stress-constrained minimum weight problem for truss structures, then the generated sequence of iteration points always converges to a global optimum.The most interesting step in the proof is a transformation of the stress-constrained problem to an equivalent unconstrained problem in which a combination of weight and compliance should be minimized. After the transformation, the stress ratio method becomes in fact a “successive linearization” method for solving this unconstrained problem.