Stress based topology optimization of reinforcement structure under in-plane load

As the static safety of mechanical structure is one of important criteria in engineering design process, it has been one of important topics to consider the static failure of a structure in topology optimization (TO). With the help of some recent relevant researches, some difficult issues in considering static failure are solved. However, this research found that the singularity issue which refers the difficulty of obtaining global optima with the KKT condition is not serious and mathematically relaxed for reinforcement TO design. And it is found that the existing qp-relaxation stress interpolation scheme to resolve the singularity issue in TO just shows the local optima issue in reinforcement TO design with different penalization factors in Solid Isotropic Material with Penalization (SIMP). In order to explain this feature, the TO problems for simple benchmark truss structures are revisited. Several two-dimensional examples only with in-plane load are solved to confirm the validity of the present study.