Singular Optima in Geometrical Optimization of Structures

摘要

APOINT is said to be a local (relative) minimum if it has the least function value in its neighborhood but not necessarily the least function value for all the feasible region. In this Note, a point is said to be a singular optimum if it has the least function value in its neighborhood, but this neighborhood is a reduced (degenerate) feasible region, formed by assuming certain variables as zero. Singular optima are usually associated with changes in the topology of the structure. If the optimal solution is a singular point in the design space, it might be difficult or even impossible to arrive at the true optimum by numerical search algorithms. The singularity of the optimal topology in cross-sectional optimization of truss structures was first shown by Sved and Ginos.1 Singular optima of grillages213 and some properties of singular optimal topologies4'5 were studied later, In particular, problems of continuous constraint functions have been discussed, and limiting stresses obtained in cases of elimination of members have been defined.