Fixing the problem of pseudo buckling modes in optimizing elastic structures with the aim of maximizing the smallest buckling load factor

In the topology and support optimization of continues structures, stability and buckling issues due to computational complexities are not usually considered, therefore in some cases, long and thin members are obtained in optimized configuration that can lead to the instability of structure. One of the major problems during the implementation of conventional buckling optimization processes that are based on changing the density or removing and replacing the material is the creation of pseudo buckling modes that lead to the divergence of the optimization problem, decreasing the rate of solving process or producing non-optimal shapes. In this article level set method with incorporating a fictitious interface energy is applied to find optimal configuration. The level set method is based on the movement of the structural boundaries and it has a high ability to control the complexity of the topology, so the idea of using this method has led to the elimination of pseudo buckling modes and the solving of this problem. Derivation of the required speed term in the level set method for buckling load factor is complicated and this derivation is another innovation of this research. Numerical examples are illustrated to prove the effectiveness of this method.