Physics-Inspired Neural Networks in the Evaluation, Generation and Design of Frame Structures

结构优化是一种经济有效的轻量化设计方法，特别是在强度和刚度要求充分利用材料的情况下。桁架结构的设计和评估是实践中最常见的任务之一，通常采用梁或桁架单元的数值模拟。在这项工作中，基于所谓的物理启发神经网络（PINN）的这种一维理想化的替代设计和评估程序是研究的重点。因此，主要以三维仿真数据和三维拓扑优化结果作为训练基础，提高一维理想化的预测行为。总共将调查三种不同的pin码。第一个PINN有望改善对一维模型的变形和应变等物理量的预测。第二个PINN旨在基于给定的一维框架结构推导出最佳截面参数。第三个PINN将使用来自3D优化的训练数据来预测框架结构的最佳设计方案，例如，具有多轴状态的区域可以直接优化并导出为参数化模型，而无需进行复杂的拓扑优化。除了pinn的训练之外，还研究了一种基于所谓的骨架化的方法，用于将结果从3D模拟完全自动转移到1D模型。这种完全自动的传输对于为各自的pin生成合成数据集是必要的。最后，结合训练好的pin，以自行车车架为例，实现实时（几秒）的自动评估、横截面尺寸标注和局部优化区域。

Structural optimization represents an economical and effective lightweight design method, especially when full material utilization in terms of strength and stiffness is desired. The design and evaluation of truss structures is one of the most common tasks in practice, often by using numerical simulation with beam or truss elements. In this work, alternative design and evaluation procedures of such 1D idealizations based on so-called physical-inspired neural networks (PINN) are the focus of research. Thereby, mainly 3D simulation data and 3D topology optimization results shall serve as a training basis to improve the predictive behaviour of the 1D idealizations. In total, three different PINNs will be investigated. The first PINN is expected to lead to improved prediction of physical quantities such as deformation and strain of 1D models. The second PINN is intended to derive optimal cross-section parameters based on a given 1D frame structure. The third PINN will use training data from 3D optimizations to predict optimal design proposals for frame structures so that, for example, regions with multi-axial states can be directly optimized and derived as a parametric model without the need for complex topology optimization. In addition to the training of PINNs, a method based on the so-called skeletonization for the fully automatic transfer of results from a 3D simulation to a 1D model is also investigated. This fully automatic transfer is necessary to generate the synthetic data sets for the respective PINNs. Finally, the trained PINNs are combined to realize an automated evaluation, cross-section dimensioning and locally optimized regions in real time (a few seconds) for a bicycle frame, for example.