Fluid-structure interactions are a widespread phenomenon in nature. Although their numerical modeling have come a long way, the application of numerical design tools to these multiphysics problems is still lagging behind. Gradient-based optimization is the most popular approach in topology optimization currently. Hence, it's a necessity to utilize mesh deformation techniques that have continuous, smooth derivatives. In this work, we address mesh deformation techniques for structured, quadrilateral meshes. We discuss and comment on two legacy mesh deformation techniques; namely the spring analogy model and the linear elasticity model. In addition, we propose a new technique based on the Yeoh hyperelasticity model. We focus on mesh quality as a gateway to mesh admissibility. We propose layered selective stiffening such that the elements adjacent to the fluid-structure interface - where the bulk of the mesh distortion occurs - are stiffened in consecutive layers. The legacy and the new models are able to sustain large deformations without deprecating the mesh quality, and the results are enhanced with using layered selective stiffening.
翻译:流体结构的相互作用是一个广泛的现象。 虽然数字模型已经取得了很大进展, 数字设计工具对这些多物理问题的应用仍然落后于以往。 以渐变为基础的优化是目前最流行的地形优化方法。 因此, 有必要使用具有连续、 顺流衍生物的网状变形技术。 在这项工作中, 我们处理结构化、 四边草裙的网状变形技术。 我们讨论并评论了两种遗留的网状变形技术, 即春季类比模型和线性弹性模型。 此外, 我们提出了一种基于 Yeoh 超弹性模型的新技术。 我们注重网状质量, 作为网状可接受性的通道。 我们建议分层加固, 使与流体结构界面相邻的元素( 大部分的网状变形) 在连续的层中变硬化。 遗产和新模型能够维持大型变形, 而不降低网状质量, 并且通过使用层层选择性变硬来强化结果。