非线性边界条件下的汽车不确定性拓扑优化方法

The study and application of Topology Optimization to automotive light-weighting is the focus of automotive engineering. To improve the self-development ability, management of uncertainty and nonlinear during vehicle design is one of the bottlenecks and key technologies..In this study, the Partial Differential Equations (PDE) will be built for Topology Optimization problem. The integration will be realized between Topology Optimization and PDE, according to the mechanism of the built PDE. The study of Topology Optimization filtering and boundary improving which is based on PDE will be carried out and make a good compromise between the numerical instability suppressing and the topology and geometric boundary enhancement. Sparse grid numerical integration and sparse grid interpolation will be extended to the probabilistic domain for uncertainty propagation. The two techniques will be respectively used for moment and reliability estimation. Robust reliability design based on Topology Optimization under nonlinear boundary condition and uncertainties will be studied, and be demonstrated with the light weighting design of some automotive development problem. The influence of nonlinear boundary condition and uncertainties to structure design will be improved, and the the robust and reliability of the light-weighting design will be realized. The study is aimed to the key theoretical issues in the vehicle development and dedicated to applied basic research, which would provide the theoretical basis for further study and technical support to independent development of automobile industry.

拓扑优化理论与方法应用于汽车轻量化设计，是目前汽车工程领域的研究热点；解决含不确定性及非线性因素的汽车设计问题，是当前我国汽车自主开发的技术难点。.本项目构建面向拓扑优化方法的偏微分方程；根据所构建偏微分方程的作用机理，实现拓扑优化架构下的偏微分方程融合；进行基于偏微分方程的拓扑优化过滤及边界增强方法研究，实现数值不稳定抑制与边界轮廓增强的协调。将稀疏网格数值积分和插值扩展到概率空间的不确定性传播问题，实现基于稀疏网格技术的矩估计和可靠性估计。开展不确定性条件下基于可靠性稳健设计的拓扑优化方法研究，并针对某型自主知识产权汽车的轻量化设计开发问题进行实证分析，改善结构边界条件非线性、载荷随机性及设计参数随机性对结构设计的影响，实现轻量化设计方案的稳健性与可靠性。项目研究内容针对汽车开发中关键科学问题，致力于应用基础研究，可望为我国汽车自主开发提供良好的理论研究基础和技术支撑。

本项目建立了基于线性扩散偏微分方程的过滤方法和基于各向异性扩散偏微分方程的过滤方法，有效改善了棋盘格格式、网格依赖性以及灰度单元等问题的出现，并通过构建适宜的边缘函数，实现了拓扑构型边界轮廓增强。建立了基于稀疏网格技术的不确定性传播方法，高效、高精度地实现稳健设计的矩估计和可靠性设计的失效概率估计。提出基于可靠性分析前置-单层解耦格式的可靠性拓扑优化设计方法，建立了可靠性拓扑优化设计数学模型的一般性表述，归纳总结双层嵌套格式、单层融合格式与单层解耦格式的优缺点和适用范围。解决了结构拓扑优化中载荷工况与材料属性不确定性问题，实现了可靠性分析与轻量化设计的有机结合，解决了拓扑优化过程中繁琐的可靠性分析，具有良好的计算效率和精度。提出基于稀疏网格技术的稳健拓扑优化设计方法，依据积分法则，构建三类典型的稀疏网格模型,较好地解决了结构拓扑优化设计中所面临的载荷工况不确定性问题，实现了稳健设计中的统计矩精确估计，有效缓解了积分点数目对随机变量维数的依赖性，解决了不确定性分析中高维变量所引起的“维数灾难”和计算误差。通过悬架控制臂、副车架、动力电池箱、变速器壳体等大量的汽车典型结构轻量化实际工程问题对所研究的方法进行应用技术研究，对相关研究成果在生产实际中的普及和应用奠定了良好的基础，项目研究基本达到了预期的目标。