【作者】 李威；

【导师】 刘利刚；

【作者基本信息】 中国科学技术大学 ， 计算数学， 2018， 硕士

【摘要】 结构优化设计在建筑几何、机械工程、计算机图形学等众多学科领域中都是一个极其重要的问题,一般是指为了满足预定目标(如重量最轻、造价最小、强度最高等),在某些约束条件下(如体积、重量、几何约束等),对结构进行的优化设计。结构优化设计的常见目标之一便是如何设计并优化结构以在尽可能节省材料的基础上满足特定的结构强度要求,文章通过优化筋肋结构来达到这一目的。筋肋结构具有很好的抗弯性,而且不会占用太多的空间,因而一般用来给壳结构做应力加强。虽然该结构在建筑工程中已有大量应用,但对于一个任意的曲面如何生成合理的筋肋网络来达到较好的应力加强效果,仍然是一个较难的问题,文章提出了一个算法来自动生成筋肋网络以加强任意的壳结构。文章的基本思路是沿着曲面的主应力线布置肋条,主应力线反映了物体内部应力的走向,自然地反映了任何结构在给定外力情况下的最佳拓扑结构。给定一个曲面并将其看作一个有厚度的壳结构,在指定外力后对壳进行有限元分析计算其表面的主应力方向,借助这一正交向量场计算一个场方向对齐的全局参数化,并提取一个四边形网格,这样四边形网格的边都沿着曲面的主应力方向,然后通过追踪连续的网格边得到初始的筋肋网络。接下来再对该筋肋结构进行拓扑和几何优化。考虑到初始筋肋网络中可能存在大量冗余的肋条,拓扑优化首先删除对壳贡献度较低的肋条,然后优化余下肋条的位置。几何优化进一步对每根肋条的截面形状进行优化,以用较少的材料达到最好的结构强度,对壳起到最佳的加强效果。文章通过理论分析和物理实验验证了算法的有效性。文章最后对全文进行了总结,并对结构优化设计问题进行了展望。更多还原

【Abstract】 Optimal structure design is a very important problem in architecture geometry,mechanical engineering,computer graphics and many other fields.Usually,it means designing and optimizing a structure to satisfy certain goals like minimal weight or cost,maximal stiffness and so on,under some practical constraints,like volume,weight,geometry constraints,etc..A common goal of optimal structure design is to design and optimize a structure to save more material while meeting certain strength requirement.This paper proposes to achieve this goal by optimizing rib structure.Rib has an excellent capability to resist bending and doesn’t occupy too much space.And it’s usually used to reinforce a shell.Although ribs are widely used in architecture engineering,it still remains a challenge to generate a reasonable rib layout on an arbitrary surface while achieving good strengthen-ing performance.To address this problem,this paper proposes a computational method to generate such a rib layout.The essential of our method is to place ribs along the principal stress lines,which indicate the trajectories of internal force and naturally encode the optimal topology for any structure under a given set of boundary conditions.Given a surface,we assign it a thickness and regard it as a shell.After imposing the external loads,we perform a Finite Element Analysis and compute the principal stress field.With this cross field we calcu-late a field-aligned global parametrization and further extract a quad-mesh whose edges align with the principal stress directions.By tracing consecutive quad-mesh edges we obtain an initial rib network.Then a topology and geometry optimizations are applied to this rib network.Considering the differences of contribution from each rib,we simplify the rib network by dropping ribs with little contribution.And a further position opti-mization is applied to the remaining ribs.When the topology is determined,geometry optimization is carried out to optimize the cross-sectional shape of ribs,to further reduce the material usage while striving to achieve better reinforcement effect.Stress analysis and physical experiment validate the effectiveness and performance of our method.The final chapter makes a conclusion of this paper and prospects a further research on optimal structure design in the near future.更多还原