Maximizing natural frequencies of inhomogeneous cellular structures by Kriging-assisted multiscale topology optimization

Abstract This paper proposes a Kriging-assisted multiscale topology optimization method for maximizing natural frequencies of inhomogeneous cellular structures, where spatially-varying microstructural configurations and their macroscopic distribution are simultaneously optimized. At the beginning, under macroscopic boundary conditions for a cellular structure, the configurations of multiple prototype microstructures are topologically optimized by the parametric level set method (PLSM) combined with the numerical homogenization approach. A kinematical connective constraint is considered to ensure the connectivity between adjacent prototype microstructures. Then, a shape interpolation method is adopted to interpolate shapes of the prototype microstructures, so as to generate a series of sample microstructures. Based on these samples, Kriging metamodels are constructed to predict the effective property of each microstructure within the macrostructure. Finally, the variable thickness sheet (VTS) method is applied to optimize the material distribution pattern at macroscale for maximizing the natural frequency of the cellular structure, where an efficient mode-tracking strategy based on modal assurance criterion (MAC) is employed to track the target mode accurately. Numerical examples are provided to test the performance of the proposed method in natural frequency optimization of cellular structures. The results indicate that the multiscale cellular structures obtained by the proposed method show higher natural frequency compared with the monoscale macrostructural and microstructural designs.

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