トポロジー最適化の剛性最大化問題において密度のランダムな変動が最適形状に与える影響について

抄録

The present study proposes a computational method with random noise of material density in the stiffness maximization problem of topology optimization. To give random fluctuations to material density, noise with normal distribution is introduced to the density when updating the design variables. To change the influence of the random numbers, a coefficient from 0 to 0.1 is given to the density. By changing the calculation conditions and boundary conditions, we investigated the effects of density fluctuations on the optimal shape. In addition, to investigate the effects of random numbers on the stiffness and morphology of the optimal shape, we performed 50 simulations on each condition to obtain the variance of mean compliance and the variance of average thickness of the beam. As a result, when random fluctuations were given to the material density, the mean compliance gradually decreased compared to deterministic case, and an optimal structure with a finer beams and higher stiffness were obtained.