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

采用柔性多体系统的方法对技术系统进行建模，该系统的部件既要经历较大的刚体运动，又要经历较大的变形。如果变形较小且为线弹性，则浮动参考框架法通常是对柔性体建模最有效的方法。这是因为这里的变形是由一组全局形状函数近似的。除了分析物体上的动力载荷外，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，例如结构优化。后者通常用于寻找柔性体在动力载荷下的最佳设计，以防止非期望变形的振动。拓扑优化方法，如SIMP方法或水平集方法，通常对设计的影响最大。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，特别是梯度评估是非常复杂和耗时的，因此它们仅限于简单且主要是学术应用实例。因此设计变量的数量是有限的。在本研究项目中，水平集方法在柔性多体系统拓扑优化中的潜力，可以解决更现实、更复杂的优化问题。与使用水平集方法的SIMP方法相反，该设计由隐式水平集函数描述。随着优化而演变的结构细节，可以使用更少的设计变量更有效地部分描述。同时，与现有的SIMP优化相比，拓扑优化中的设计变量数量需要显著增加。为了在合理的时间内为这种高维优化问题提供梯度信息，必须发展并行化伴随变量法。通过有效的参数化和并行梯度计算的结合，可以控制优化过程中巨大的计算量和存储量，为复杂几何形状动载体的计算机辅助设计提供方法。

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.