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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >3D volumetric isotopological meshing for finite element and isogeometric based reduced order modeling
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3D volumetric isotopological meshing for finite element and isogeometric based reduced order modeling

机译：基于有限元和等几何面的降阶建模的3D立体等体积网格

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This paper presents a generic framework to construct 3D structured volumetric meshes of complicated geometry and arbitrary topology. Structured meshes are well-suited for reduced order model applications with geometric parameters. For that purpose, we use the triangulated solid 3D model's boundary provided from B-Rep CAD (Boundary-Representation in Computer Aided Design) models. The input triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. Both segmentations understand the geometry and features of meshes. Cuboid decomposition splits a surface into a set of quadrilateral patches which can define a volumetric layout of the associated boundary surface. Using aligned global parameterization, patches of the cuboid decomposition are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. The optimization process is thought to design cross fields with topological and geometrical constraints. Using the optimized cuboid decomposition, a volumetric layout is extracted. Based on the global parameterization and the structured volumetric layout previously computed, a 3D volumetric parameterization is deducted. For different geometrical instances with the same topology but different geometries, the proposed method allows to have the same representation: 3D volumetric isotopological meshes holding the same connectivity. MEG-IsoHex method is introduced to compare fields on 3D hexahedral meshes. The efficiency and the robustness of the proposed approach are illustrated through a remeshing case for large deformations and reduced order models using isogeometric analysis. (C) 2020 ElsevierB.V. All rights reserved.
机译：本文提出了一个通用框架来构造具有复杂几何形状和任意拓扑的3D结构体网格。结构化网格非常适合具有几何参数的降阶模型应用。为此，我们使用从B-Rep CAD（计算机辅助设计中的边界表示）模型提供的三角实体3D模型边界。通过两个步骤将输入的三角网格分解为一组长方体：裤子分解和长方体分解。两种分割都了解网格的几何形状和特征。长方体分解将一个表面分成一组四边形斑块，这些块可以定义相关边界表面的体积布局。使用对齐的全局参数化，将长方体分解的补丁重新放置在表面上，以实现较低的总体失真以及与主曲率方向和锋利特征对齐的方式。优化过程被认为是设计具有拓扑和几何约束的交叉场。使用优化的长方体分解，可以提取体积布局。基于先前计算的全局参数化和结构化的体积布局，可以推导出3D体积参数化。对于具有相同拓扑但具有不同几何形状的不同几何实例，所提出的方法允许具有相同的表示形式：具有相同连通性的3D体积等值网格。引入了MEG-IsoHex方法来比较3D六面体网格上的字段。通过使用等几何分析的大变形和降阶模型的重划案例，说明了所提出方法的效率和鲁棒性。 （C）2020爱思唯尔版权所有。

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