Topological derivatives for layout generation of crash-loaded structures

机械零部件的布局(拓扑和形状)对其功能和质量有很大影响。在线性静态中，存在用于生成良好布局的有效算法。一方面，有一些方法将设计领域细分为许多小部分(通常超过1000万。体素)，并决定每个部件是否需要材料。基于该布局方案，在后处理过程中推导出部件结构。另一方面，在CAD中也有直接描述构件结构和拓扑变化的方法。在这里，不需要任何后处理活动。将这些拓扑优化方法推广到非线性任务是一个很大的挑战。尤其是碰撞载荷结构布局的生成需要广泛的研究。需要考虑材料模型的非线性、大位移和大变形以及接触现象。本DFG研究项目涉及拓扑导数方法的可能扩展，该方法对于线性静态应用中的版图生成具有强大的功能。其目的是确定预测结构域移除所产生的影响的可能性。碰撞加载结构中断口的整合。科学问题如下：1)是否有可能推广碰撞吸收结构的拓扑导数方法？2)可以考虑哪些非线性现象？3)新方法如何执行自包含的布局生成？本研究项目细分为7个工作包。前三个工作包生成开发框架，以便集成以下工作包。基于拓扑导数的算法将为版图生成而开发。它是关于在碰撞结构发展过程中使用拓扑导数作为部件中敏感位置的指示器，以及体素方法和气泡方法的扩展。这些第一批工作包在整个研究期间都参与了研究项目。以下工作包处理与碰撞相关的行为，如材料非线性(塑性和应变率相关性)、屈曲现象、时间相关性和接触(自身接触和与相邻组件的接触)。每个工作包都从功能分析开始。表面上的重点是对拓扑导数的完全解析描述的发展。如果这是不可能的，则研究适用于数值解的概念。这个想法是基于实验设计驱动的碰撞模拟来生成元模型。

The layout (topology and shape) of mechanical components has a very large influence on their functionality and quality. In the linear static, effective algorithms for the generation of good layouts exist. On the one hand, there are methods, which subdivide the design domain in many small parts (often over 10 Mio. Voxel) and decide for every part, is there material required or not. Based on this layout proposal, a component structure is derived in a post processing procedure. On the other hand, there are methods, which describe the component structure and the topology changes directly in CAD. Here, no post-processing activities are necessary. The extension of these topology optimization methods for non-linear tasks is a big challenge. Especially, the generation of layouts for crash-loaded structures needs extensive researches. It is necessary to consider non-linear material models, large displacements and deformations as well as contact phenomena. This DFG research project deals with the possible extensions of the method of topological derivatives, which is powerful for the layout generations in linear static applications. The objective is to determine the possibility to predict the effects which result from the removal of structural domains resp. the integration of cut-outs in crash-loaded structures. The scientific issues are the following: 1) Is it possible to extend the method of topological derivatives for crash-absorbing structures? 2) Which non-linear phenomena can be considered? 3) How can the new method execute a self-contained layout generation?The research project is subdivided in 7 work packages. The first three work packages generate the development frame, in order to integrate the following work packages. Algorithms, based on the topology derivatives, will developed for layout generations. It is about the use of the topological derivatives as an indicator for sensitive positions in the component during the crash structure development and the extension of the voxel method and the bubble method. These first work packages attend the research project over the whole period. The following work packages deal with the crash relevant behaviors like material non-linearity (plasticity and strain rate dependency), buckling phenomena, time dependency and contact (self contact and contact to neighbor components). Each work package starts with a functional analysis. The superficial focus is on the development of completely analytical description for the topological derivatives. If this is not possible, research is carried out on suitable concepts for a numerical solutions. The idea is the generation of meta-models based on a design-of-experiment driven crash simulations.