Stiffness optimisation of graded microstructal configurations using asymptotic analysis and machine learning

The article is aimed to address a combinative use of asymptotic analysis and machine learning, for fast stiffness design of configurations infilled with smoothly-varying graded microstructures. The discussion is conducted in the context of an improved asymptotic-homogenisation topology optimisation (AHTO plus) framework (Zhu et al., 2019). It is demonstrated that machine learning can be employed to represent the key but implicit inter-relationships between formulations obtained at different orders from asymptotic analysis. Moreover, in the context of microstructural homogenisation, asymptotic analysis helps offer a platform for machine learning to release its full potentials in function representation. Firstly, asymptotic analysis identifies a computational routine for data acquisition, thus the training data are sufficient in theory. Secondly, the number of input arguments for machine learning can be minimised based on the explicit results by asymptotic analysis, and the scale of the machine learning model in use is kept small. Thirdly, the input arguments for machine learning are shown to be complete. Then the situation where certain factors affecting the function relationship represented by machine learning is avoided. Other issues on incorporating machine learning into the AHTO plus framework, such as ensuring the positive definiteness of the homogenised elasticity tensor and the speeding-up of the associated sensitivity analysis, are also discussed here. Numerical examples show that the use of machine learning in the AHTO plus scheme can bring about an acceleration by two orders of magnitude, if compared with the existing treatments of using a zoning strategy.