材料二维微结构仿真随机概率圆优化填充算法

Random Circles Optimization Filling Algorithm of Material Two Dimensional Microstructures Simulation

几何建模是影响有限元法计算材料性能精确性的主要因素之一。利用圆等简单的几何实体近似模拟离散化实体效果良好,不仅能大量简化几何计算,还能构造出误差在可接受范围内的近似模型。材料特性不仅取决于平均颗粒尺寸,受颗粒尺寸分布的影响也十分显著。本文设计的随机圆填充算法保证了填充圆半径服从某一概率分布,重点分析了常规圆产生方法和依据干涉圆的干涉类型生成新圆。该算法不仅完全杜绝了圆的干涉还极大的减小了圆的相离,相对于现有的填充算法,填充度有了显著提升。

Geometric modeling is one of the main factors affecting the accuracy of material properties calculation by finite element method. Using simple geometric entities, such as circles, to simulate discrete objects is demonstrated well. Beyond the great simplifications in the geometrical calculation, it can provide an approximate model within acceptable error. Material properties not only depend on the average grain size, but also are influenced by the grain size distribution significantly. Random circles packing algorithm designed in this paper ensured these circles＇ radius following a certain probability distribution. Normal circles generation method and generating new circle based on the interference types were analyzed. This algorithm not only avoided the interference completely, but reduced the separation greatly. Compared with existing filling algorithms, the filling density of this algorithm was improved obviously.