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An efficient multiscale concurrent design method using fitting function

In this paper, a multiscale concurrent optimisation method is presented for the design of cellular structures. The purpose is to search the configurations and layouts of microstructures simultaneously. At the microscale, a family of graded microstructures (GMs) is obtained via reconstructing the level set function (LSF) and parallelly moving the cutting plane. Based on the gradient-varying mechanical properties, the fitting functions of elasticity tensors with respect to relative densities are established. The numerical homogenisation method is utilised to calculate the mechanical properties of sample points which are regarded as fitting parameters. For the multiscale scheme, the allocation of GMs is optimised by a material distribution method, while the configurations of microstructures are designed by an extended parameterised level set method (PLSM) which is inspired from the design thinking of the bi-directional evolutionary structural optimisation (BESO). Numerical examples demonstrate the effectiveness of the proposed method.