구조물의 토폴로지 최적화에 관한 연구

Abstract

The problem of structural topology optimization can be relaxed and converted into the optimal density distribution problem. The optimal density distribution must be post-processed to get the real shape of the structure. The extracted shape can then be used for the next process, which is usually shape optmization based on the boundary movement method. In the practical point of view, it is very important to get the optimal density distribution from which the corresponding shape can easily be extracted. Among many other factors, the presence of checker-board patterns is a powerful barrier for the shape extraction job. The nature of checker-board patterns seems to be a numerical locking. In this paper, an efficient algorithm is presented to suppress the checker-board patterns. At each iteration, density is re-distributed after it is updated according to the optimization rule. The algorithm also results in the optimal density distribution whose corresponding shape has smooth boundary. Some examples are presented to show the performance of the density re-distribution algorithm. Checker-board patterns are successfully suppressed and the resulting shapes are considered very satisfactory.