连续体结构拓扑优化敏度过滤研究

Research on Sensitivity Filtering of Continuum Topology Optimization

变密度法作为处理连续体结构拓扑优化问题的一种有效方法,在优化过程中常出现如棋盘格现象等数值不稳定现象,使得优化模型提取较为困难。针对这一问题,提出了一种改进的敏度过滤方法,该方法通过引入新的卷积因子,结合原有卷积因子建立三者在一定权重比分配下的数值关系,并采用一种带有预设修正权值的方法,弱化边界扩散问题。以柔度最小化为优化目标,采用多个二维数值算例研究改进敏度过滤方法在拓扑优化中的可行性及有效性。实验表明,该方法能有效消除棋盘格现象和网格依赖性,且大幅度提高了优化速度,优化结构的柔度收敛值小,取得了更好的优化结果。

SIMP method is an effective method to deal with topology optimization of continuum structure,but in the process of optimization,there are often numerical instability phenomena such as chessboard phenomenon,which makes it difficult to extract the optimization model.Aiming at this problem,this paper proposes an improved sensitivity filtering method.By introducing a new convolution factor and combining with the original convolution factor,the numerical relationship of the three under a certain weight ratio distribution is established,and a method with preset modified weights is adopted to weaken the boundary diffusion problem.Taking the flexibility minimization as the optimization objective,the feasibility and effectiveness of the improved sensitivity filtering method in topology optimization are studied by several two-dimensional numerical examples.The experimental show that this method can effectively eliminate the chessboard phenomenon and grid dependence,and greatly improve the optimization speed.The flexibility convergence value of the optimized structure is small,and better optimization results are obtained.