| Citation: | GAO Xiang, WANG Linjun, DU Yixian, et al. Gray element filtering technology of topology structure based on improved guide-weight method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(6): 1106-1114. doi: 10.13700/j.bh.1001-5965.2020.0728(in Chinese)
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Aiming at the problem of slow convergence speed when calculating Lagrange multiplier by bisection method, the proposed Lagrange multiplier calculation method is applied to the optimal criteria (OC) method and the guide-weight (GW) method to update the density, and the results of the proposed method are compared with the bisection method. The topology optimization model with the smallest compliance under the volume constraint is established. The elastic modulus of element density is calculated by the solid isotropic material with penalization (SIMP) or rational approximation of material properties (RAMP) method. The multiplier is calculated by the proposed method in this paper, and the element density is updated by the GW method. The number of gray element is reduced by the Heaviside projection function. The computational results show that: the proposed method does not significantly reduce the number of finite element analysis, but the CPU time used by the proposed method to calculate the Lagrange multiplier is less than that of the bisection method, and the number of density updates is reduced to less than 50% than before. In addition, in the two numerical examples, when SIMP model is adopted, the structure obtained by the GW method has smaller compliance than the OC method.
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