Optimization of singular problems
Alan Scott Hoback Structural and Multidisciplinary Optimization, vol. 12(2), 2020, pp. 93-97.
A new optimization method is presented that optimizes singular structures. An example of a singular problem is deleting an inefficient member from a structure. As the member is deleted, the stresses in the member may increase above the allowables. When a member is deleted the nature of the analysis changes because the member stiffness becomes zero. This causes a local optima because stress constraints prevent inefficient members from zeroing. The problem is reformulated using the percent method so that the appropriate stress constraints are deleted as the member is deleted. Several examples show that the global optimal design is reached. Other methods to reach the global optima are appropriate only if the optimal structure is statically determinate. The percent optimization is also useful for optimization of discrete problems.
Link to full paper
1. The minimum weight of certain redundant structures, Article, Jan 1954, G. Sved
2. A new method for finding the global and discrete optima of structural systems, Article, Jul 1994, COMPUT STRUCT, Alan Scott Hoback, Kevin Z. Truman
3. Structural optimization under multiple loading, Article, Oct 1968, INT J MECH SCI, G SVED, Z GINOS
4. On singular topologies in structural design, Article, Sep 1990, STRUCT MULTIDISCIP O, U. Kirsch
5. On singular topologies in exact layout optimization, Article, Jan 1994, STRUCT MULTIDISCIP O, G. I. N. Rozvany, T. Birker
6. Difficulties in truss topology optimization with stress, local buckling and system stability constraints, Article, Jun 1996, STRUCT MULTIDISCIP O, G. I. N. Rozvany
7. Optimal Topologies of Structures, Article, Aug 1989, COMPUT METHOD APPL M, U. Kirsch