Level set methods for the fully-coupled topology optimization of flexible multibody systems

柔性多体系统全耦合拓扑优化的水平集方法

• 批准号: 421344187
• 负责人: Dr.-Ing. Alexander Held
• 金额: --
• 依托单位: Institut für Mechanik und Meerestechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/421344187?language=en
• 关键词: Level; set; methods; fully; coupled

The method of flexible multibody systems is used to model technical systems, whose components undergo both large rigid body motions and deformations. If the deformations are small and linear elastic, the floating frame of reference approach is often the most efficient way to model the flexible bodies. That is because the deformations are here approximated by a set of global shape functions. Next to the analysis of dynamical loads on the bodies, multibody simulations can also be used to develop control designs or perform simulation-based optimization, such as structural optimization. The latter is often applied to find optimal design of the flexible bodies with regard to the dynamical loads in order to prevent vibrations of undesired deformations. Topology optimization methods, such as the SIMP approach or level set methods, offer usually the biggest influence on the design. There are already some results for the optimization of flexible multibody systems using the SIMP approach. However, they confine to simple and mostly academic application examples, since the solution of these nonlinear large-scale optimization problems and, in particular, the gradient evaluation is highly complex and time consuming. The number of design variables is therefore limited. In this research project the potential of level set methods in the topology optimization of flexible multibody systems shall be used to solve more realistic and, thus, more complex optimization problems. In contrast to the SIMP approach using level set methods the design is described by an implicit level set function. Constructional details, which evolve along the optimization, can partially be described more efficiently using less design variables. At the same time the number of design variables in the topology optimization shall be significantly increased compared to the existing SIMP optimizations. In order to provide the gradient information for this high-dimensional optimization problem in reasonable times a parallelized adjoint variable method has to be developed. By combination of an efficient parameterization and a parallelized gradient computation the enormous computing and memory costs in the optimization can be managed and methods for the computer-aided design of dynamical loaded bodies with complex geometries can be provided.

采用柔性多体系统的方法对技术系统进行建模，其构件既经历大刚体运动又经历大变形。如果变形较小且具有线弹性，浮动坐标系方法往往是对柔性体进行建模的最有效方法。这是因为变形在这里是由一组全局形函数近似的。除了分析车身上的动态载荷外，多体仿真还可以用于开发控制设计或执行基于仿真的优化，如结构优化。后者经常被应用于寻找关于动力载荷的柔性体的最优设计，以防止不需要的变形的振动。拓扑优化方法，如SIMP方法或水平集方法，通常对设计产生最大的影响。利用SIMP方法对柔性多体系统进行优化已经取得了一些成果。然而，由于这些非线性大规模优化问题的求解，特别是梯度计算是非常复杂和耗时的，它们仅限于简单且大多是学术应用的例子。因此，设计变量的数量是有限的。在这个研究项目中，水平集方法在柔性多体系统拓扑优化中的潜力将被用来解决更现实的、因此更复杂的优化问题。与使用水平集方法的SIMP方法不同，该设计由隐式水平集函数来描述。随着优化的发展，结构细节可以使用更少的设计变量来部分地更有效地描述。同时，与现有的SIMP优化方案相比，拓扑优化中的设计变量数量应显着增加。为了在合理的时间内为这个高维优化问题提供梯度信息，必须开发一种并行伴随变量方法。通过将有效的参数化和并行的梯度计算相结合，可以管理优化过程中巨大的计算和存储成本，并为复杂几何形状的动态受载体的计算机辅助设计提供方法。