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This paper focuses on the fast highly approximate modal analysis and its applications in topology optimization design based on the triangle finite element. The proposed modal analysis methods are based on the initialized pseudo-random number vectors with the Rayleigh-Ritz analysis, which is very simple to implement and can easily be extended for structural dynamic topology optimization design. The numerical examples show that the proposed method is very effective with small computational cost and high efficiency which can effectively reduce huge computational cost without affecting the outcome of the optimization process. Meanwhile, the introduction of pseudo-random approximate modal analysis leads to the randomness and sub-optimal multiplicity of topology optimization results. Numerical examples show that the approximate pseudo-random modal analysis could also enlarge the search ability of the Optimality Criterion Method (OCM).

Quick pseudo-random topology optimization design based on triangle element