Fine Properties and Applications of Thin-Sheet Folding

薄板折叠的优良特性及应用

• 批准号: 441528968
• 负责人: Professor Dr. Sören Bartels
• 金额: --
• 依托单位: Abteilung für Angewandte Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/441528968?language=en
• 关键词: Fine; Properties; Applications; Thin; Sheet

In the first funding period of the research project, the analytical understanding and the reliable numerical approximation of thin-sheet folding processes have been addressed. In particular, a two-dimensional bending-folding model has been derived from a three-dimensional hyper-elastic material description of a pre-damaged plate, a discontinuous Galerkin method has been devised, quasi-optimal error estimates for a corresponding small deflection interface problem have been established, and a precise characterization of the relation of folding angles and curvature quantities along creases has been identified. Further results are subject of ongoing research. In a second funding period specific analytical questions such as the optimality of scaling relations leading to other interface conditions, the understanding of piecewise smooth folding line systems, and the characterization of folding angle discontinuities will be addressed. Besides this, the improvement of the efficiency of basic numerical schemes via acceleration procedures and adaptive local mesh refinement based on a posteriori error estimates will be analyzed. Using the analytical results and new computational methodology, application-related questions including the leverage effect of different folding constructions, the development of new mechanisms based on singular flapping effects, and the determination of unstable critical configurations arising in switching processes of bistable devices will be investigated.

在研究项目的第一个资助期间，薄板折叠过程的分析理解和可靠的数值近似已经解决。特别是，二维弯曲折叠模型已从三维超弹性材料描述的预损伤板，一个不连续的Galerkin方法已被设计出来，准最优误差估计相应的小挠度界面问题已被建立，和一个精确的表征的折叠角和曲率量的关系沿着折痕已被确定。进一步的结果是正在进行的研究的主题。在第二个资金周期的具体分析问题，如最优的缩放关系，导致其他接口条件，分段光滑折叠线系统的理解，和折叠角度不连续的特性将得到解决。除此之外，通过加速程序和基于后验误差估计的自适应局部网格细化，将分析基本数值格式的效率的提高。使用的分析结果和新的计算方法，应用相关的问题，包括不同的折叠结构的杠杆效应，基于奇异扑翼效应的新机制的发展，并确定不稳定的临界配置中出现的开关过程中的MEMS器件将进行调查。