From a quasi-static fluid-based evolutionary topology optimization to a generalization of BESO

A new algorithm is proposed for topology optimization based on a fluid dynamics analogy. It possesses characteristics similar to most well-known methods, such as the Evolutionary Structural Optimization (ESO)/Bidirectional Evolutionary Structural Optimization (BESO) method due to Xie and Steven (1993 Xie, Y. M., and G.P. Steven. 1993. “A Simple Evolutionary Procedure for Structural Optimisation.” Computers and Structures 49 (5): 885–896. doi: 10.1016/0045-7949(93)90035-C[Crossref], [Web of Science ®] , [Google Scholar], “A Simple Evolutionary Procedure for Structural Optimisation.” Computers and Structures 49 (5): 885–896.), which works with discrete values, and the Solid Isotropic Material with Penalization (SIMP) method due to Bendsøe (1989 Bendsøe, M.P. 1989. “Optimal Shape Design as a Material Distribution Problem.” Structural Optimization 1 (4): 193–202. doi: 10.1007/BF01650949[Crossref] , [Google Scholar], “Optimal Shape Design as aMaterial Distribution Problem.” Structural Optimization 1 (4): 193–202.) and Zhou and Rozvany (1991 Zhou, M., and G.I.N. Rozvany. 1991. “The COC Algorithm—Part II: Topological, Geometry and Generalized Shape Optimization.” Computer Methods in Applied Mechanics and Engineering 89 (1–3): 309–336. doi: 10.1016/0045-7825(91)90046-9[Crossref], [Web of Science ®] , [Google Scholar], “The COCAlgorithm–Part II: Topological, Geometry and Generalized Shape Optimization.” Computer Methods in Applied Mechanics and Engineering 89 (1–3): 309–336.) (using Optimality Criterion (OC) or Method of Moving Asymptotes (MMA)), which works with intermediate values, as it is able to work both with discrete and intermediate densities, but always yields a solution with discrete densities. It can be proven mathematically that the new method is a generalization of the BESO method and using appropriate parameters it will operate exactly as the BESO method. The new method is less sensitive to rounding errors of the matrix solver as compared to the BESO method and is able to give alternative topologies to well-known problems. The article presents the basic idea and the optimization algorithm, and compares the results of three cantilever optimizations to the results of the SIMP and BESO methods.