使用等几何分析与模型降阶的拉胀超材料三维拓扑优化
Three-dimensional topology optimization of auxetic metamaterial using isogeometric analysis and model order reduction
AI总结：
本文提出一种将等几何分析、参数化水平集与模型降阶相结合的拓扑优化方法，用于高效设计拉胀超材料微结构，并通过二维和三维数值实验验证其有效性。
摘要：
在这项工作中，我们提出了一种通过拓扑优化设计材料微结构的高效计算方法。核心思想在于将等几何分析与参数化水平集函数相结合，用于数值均匀化、灵敏度计算以及有效弹性能的优化。设计变量是与控制点相关联的水平集值，由优化器更新并表征单胞的几何形状。我们进一步通过在每个迭代中采用降阶建模来求解平衡方程的线性系统，从而提高计算效率。我们通过重用先前优化步骤中已计算出的解来构造降阶基，并在该降阶基上求解一个规模小得多的线性方程组。二维和三维数值结果表明，该拓扑优化算法与降阶基方法相结合在超材料设计中的有效性。
英文摘要：
In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set function for numerical homogenization, sensitivity calculation and optimization of the effective elastic properties. Design variables, which are level set values associated with control points, are updated from the optimizer and represent the geometry of the unit cell. We further improve the computational efficiency in each iteration by employing reduced order modeling when solving linear systems of the equilibrium equations. We construct a reduced basis by reusing computed solutions from previous optimization steps, and a much smaller linear system of equations is solved on the reduced basis. Two- and three-dimensional numerical results show the effectiveness of the topology optimization algorithm coupled with the reduced basis approach in designing metamaterials.
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