Integrated form finding, simulation and optimization using the generalized force density method based on mixed functionals

使用基于混合泛函的广义​​力密度方法集成找形、仿真和优化

• 批准号: 434336509
• 负责人: Professor Dr.-Ing. Kai-Uwe Bletzinger
• 金额: --
• 依托单位: Lehrstuhl für Statik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/434336509?language=en
• 关键词: Integrated; form; finding; simulation; optimization

The proposed project sets itself the goal of expanding the force density method (KDM) into a universally applicable tool for solving mixed problems of form finding, optimization, structural simulation and cutting pattern analysis. The KDM is to be developed into a further, thorough tool of structural analysis, which allows to handle not only completely novel but also conventional tasks of form finding with significantly better accuracy. The methodically new aspect is to treat the force densities as equivalent variables in addition to the deformations. The classical understanding of energetically conjugated forces and displacements is complemented by the special formulation of the force density as moderator between force and geometry. As a result of the reparameterization by means of force densities, the mathematical properties of known (nonlinear) questions change significantly; simulation, form finding and cutting pattern analysis can be smart and efficiently dealt with together. It opens up new perspectives along the force densities into standard statics, including direct and adjoint simulation and sensitivity analysis. Because of its consistent integration into continuum mechanics, the method will be mathematically and numerically sound. The force densities as scalar quantities can also be easily and clearly visualized for 3D structures, which should be used for the development of interactive methods and practice-relevant implementations. Last but not least, the goal is to demonstrate the practical relevance of large, impressive examples together with cooperation partners from the relevant engineering sector, which significantly advance the current state of the art and open up new fields of application. Methods and models are implemented in own or open source software (KRATOS, Carat ++, TeDA, kiwi!3d).

提议的项目本身设定了将力密度方法（KDM）扩展到普遍适用的工具，以解决形式查找，优化，结构模拟和切割模式分析的混合问题。 KDM将被发展为一个结构分析的进一步，详尽的工具，该工具不仅可以完全新颖，而且可以以更高的精度处理形式查找的常规任务。有条不紊的新方面是将力密度视为等效变量，除了变形。对力量密度的特殊表述作为力量和几何形状之间的主持人，对能量共轭力和位移的经典理解得到了补充。由于力密度重新聚集，已知（非线性）问题的数学特性发生了很大变化。模拟，形式查找和切割模式分析可以是聪明，有效地处理的。它将沿力密度的新观点打开到标准静态，包括直接和伴随的模拟和灵敏度分析。由于它始终如一地集成了连续力学，因此该方法在数学上和数值上都将是合理的。用于3D结构的力密度作为标量数量也可以轻松明显地可视化，该结构应用于开发交互式方法和与实践相关的实现。最后但并非最不重要的一点是，目的是证明大型，令人印象深刻的例子与相关工程领域的合作合作伙伴的实际相关性，这大大推动了当前的艺术状态并开放了新的应用领域。方法和模型是用自己或开源软件（Kratos，Carat ++，Teda，Kiwi！3D）实现的。