Fail-safe optimization concerning partial damage—a comparison of rigid plastic and linear elastic material models

Existing studies on stress-constrained fail-safe optimization concerning partial damage with elastic material models have shown that the partial degradation of a member may cause a worse objective function than complete removal. This brief note compares the results of a simple formulation using a rigid plastic material with those of the existing elastic problem, using a three-bar example as an illustration. It is demonstrated that the plastic formulation resolves the singularity issues, and the underlying characteristics of both formulations can be understood from both a mathematical and an intuitive engineering perspective. As well as remaining continuous at complete damage, plastic load redistribution enables optimum volumes to be 80% lower than the elastic optimum in cases approaching complete damage. Investigations into the workings of the problems unveil their inherent strengths and weaknesses, and thus areas for future improvement.