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

结构优化代表了一种经济有效的轻量化设计方法，特别是当要求在强度和刚度方面充分利用材料时。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方法是研究的重点。因此，主要是3D模拟数据和3D拓扑优化结果将作为改进一维理想化的预测行为的训练基础。总共将调查三个不同的PINN。第一个Pinn有望改进对一维模型的形变和应变等物理量的预测。第二个Pinn用于根据给定的一维框架结构导出最优横截面参数。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优设计方案，这样，例如，具有多轴状态的区域可以被直接优化并作为参数模型导出，而不需要复杂的拓扑优化。除了PINN的训练外，还研究了一种基于所谓的骨架化的方法，用于将三维模拟的结果完全自动地传输到一维模型。这种全自动传输对于为各个PINN生成合成数据集是必要的。最后，将训练好的PINN结合起来，以实现实时(几秒钟)自行车车架的自动评估、截面尺寸确定和局部优化区域。

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.