自适应四叉树结构的连续Optimization
Continuous Optimization of Adaptive Quadtree Structures
摘要：
针对离散四叉树优化问题，提出了一种新的连续最优化方法。优化的目的是实现具有最高机械刚度的四叉树结构，其中四叉树中的边缘被解释为承载机械载荷的结构元件。我们制定四叉树优化作为一个连续的材料分配问题。离散设计变量（即，细化或不细化）被四叉树层次结构中的多个级别上的连续变量替换。在离散四叉树优化中，仅当其父单元已被细化时，单元才有资格进行细化。我们提出了一个连续的模拟连续多级设计变量的依赖关系，并将其集成在迭代优化过程中。我们的研究结果表明，不断优化的四叉树结构执行更严格的比均匀的模式和并行优化的同行。我们展示了自适应结构作为3D打印部件的轻质填充物的使用，其中统一的几何图案通常在实践中使用。
英文摘要：
We present a novel continuous optimization method to the discrete problem of quadtree optimization. The optimization aims at achieving a quadtree structure with the highest mechanical stiffness, where the edges in the quadtree are interpreted as structural elements carrying mechanical loads. We formulate quadtree optimization as a continuous material distribution problem. The discrete design variables (i.e., to refine or not to refine) are replaced by continuous variables on multiple levels in the quadtree hierarchy. In discrete quadtree optimization, a cell is only eligible for refinement if its parent cell has been refined. We propose a continuous analogue to this dependency for continuous multi-level design variables, and integrate it in the iterative optimization process. Our results show that the continuously optimized quadtree structures perform much stiffer than uniform patterns and the heuristically optimized counterparts. We demonstrate the use of adaptive structures as lightweight infill for 3D printed parts, where uniform geometric patterns have been typically used in practice.
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