This work proposes a nodal-based evolutionary design optimization algorithm to design frame structures whose edges are the Delaunay triangulation of homogeneously distributed nodes in the design domain. The remaining nodes can freely sway in the design domain except for the loading nodes and boundary nodes. As a result, it can extend the space of admissible solutions to this optimization problem and reduce the number of design variables. Then, the sensitivity of the objective function, namely, the sum of compliance and its volume, is input into the method of moving asymptotes to update the nodal coordinates and member thickness. The most inefficient node is deleted in each iteration based on the average nodal strain energy until its number reaches a prescribed limit. 2D numerical examples for the Michell arch, L-shaped bracket, and Messerschmidt–Bölkow–Blohm beam show that the proposed algorithm can get the optimal structure within a few iterations. Compared with initial configurations in 3D, the optimal crane arm, transmission tower, and aquatic dome have less strain energy and fewer materials, showing a great potential of the proposed method to design actual space frames.

中文翻译：

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一种基于节点的框架结构进化优化算法

这项工作提出了一种基于节点的进化设计优化算法来设计框架结构，其边缘是设计域中均匀分布节点的 Delaunay 三角剖分。除加载节点和边界节点外，其余节点可在设计域内自由摆动。结果，它可以扩展该优化问题的可接受解的空间并减少设计变量的数量。然后，将目标函数的灵敏度，即柔量之和及其体积输入到移动渐近线的方法中，以更新节点坐标和杆件厚度。根据平均节点应变能在每次迭代中删除效率最低的节点，直到其数量达到规定的限制。Michell 拱、L 形支架的二维数值示例，和 Messerschmidt–Bölkow–Blohm 梁表明，所提出的算法可以在几次迭代内获得最佳结构。与 3D 中的初始配置相比，优化的起重机臂、输电塔和水上穹顶具有更少的应变能和更少的材料，显示了所提出的方法设计实际空间框架的巨大潜力。