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经典的模型简化技术必须同时考虑仿真精度和交互速度,而且难以实现这一目标。本文旨在采用参数化设计方式,以任意精度实时预测蜂窝结构的应力分布,包括蜂窝的几何形状和分布,或外部载荷的大小。我们将应力分布表示为蜂窝设计参数的显式函数,通过离线计算这一从设计到应力的映射来实现这一点。该映射可通过解一个高维空间中扩展有限元分析问题予以确定,映射函数中包括了空间坐标和设计参数。


高维问题固有的维数灾难(部分)通过空间分离得以解决,其中采用了两种主要技术


  • 目标映射采取分离的单变量函数乘积之和的简化形式,从而扩展了适当广义分解技术。


  • 将不同计算域的仿真问题转化为固定域的仿真问题,结合高阶奇异值分解,将积分函数表达为分离的单变量函数的乘积之和。


本文提供了大量的2D和3D示例证明了该方法的性能。


关键词: 即时模拟,参数解,蜂窝结构,适当广义分解(PGD),模型简化


Fig. 1A direct design-to-stress mapping for cellular structures was built. The design choices include changing the shapes or distributions of the microstructures, or the magnitude of the external loadings. 


Fig. 2. Orthotropic microstructures from Materialise Magics.


Fig. 3. Different types of microstructure distributions can be dealt with using our approach, which covers various design cases.


Fig. 4. Numerical approach to computing PGD.


S2(software: Freecol).Fig. 8. Illustration for the usage scenario S3 (software: Carol).Fig. 7. Hair modeling results using our Hair-GAN with single-view images as input

 Design to stress mapping of the cellular offset link structure


全文信息

Direct design to stress mapping for cellular structures

BY:Liangchao Zhu, Ming Li, Weiwei Xu


Abstract: 

This paper aims to instantly predict within any accuracy the stress distribution of cellular structures under parametric design, including the shapes or distributions of the cell geometries, or the magnitudes of external loadings. A classical model reduction technique has to balance the simulation accuracy and interaction speed, and has difficulty achieving this goal. We achieve this by computing offline a design-to-stress mapping that ultimately expresses the stress distribution as an explicit function in terms of its design parameters. The mapping is determined as a solution to an extended finite element analysis problem in a high-dimension space, including both the spatial coordinates and the design parameters. The well-known curse of dimensionality intrinsic to the high-dimension problem is (partly) resolved through a spatial separation using two main techniques. First, the target mapping takes a reduced form as a sum of the products of separated one-variable functions, extending the proper generalized decomposition technique. Second, the simulation problem in a varied computation domain is reformulated as that in a fixed-domain, taking an integration function as the sum of the products of separated one-variable functions, in combination with high-order singular value decomposition. Extensive 2D and 3D examples are shown to demonstrate the approach’s performance.


Keywords: 

Instant simulation, Parametric solution, Cellular structures, Proper generalized decomposition (PGD), Model reduction


Link: https://www.sciencedirect.com/science/article/pii/S2468502X19300348





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