Spectral decomposition for graded multi-scale topology optimization

Multi-scale topology optimization (MTO) is exploited today in applications that require designs with large surface-to-volume ratio. Further, the advent of additive manufacturing, MTO has gained significant prominence. However, a major drawback it computationally expensive. As an alternate, graded been proposed where design features at smaller scale are variations single microstructure. This leads to reduction computational cost, while retaining many benefits MTO. Graded fundamentally rests on interpolation elasticity matrices. The direct method used unfortunately does not guarantee positive-definiteness resulting Consequently, during algorithm strain energy may become negative and non-physical. In this paper, we propose simple but effective spectral decomposition-based approach which guarantees positive-definite relies (eigen) decomposition instances matrices, followed by regression eigenvalues eigenvector orientations. matrix can then be for stable optimization. methods compared here robustness, accuracy speed, through several numerical experiments.