On the treatments of heterogeneities and periodic boundary conditions for isogeometric homogenization analysis
On the treatments of heterogeneities and periodic boundary conditions for isogeometric homogenization analysis
复制标题
等几何均匀化分析中异质性和周期性边界条件的处理
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
K. Terada
中科院分区：
文献类型：
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作者：
S. Matsubara;S. Nishi;K. Terada
探索了异质性和周期性边界条件的处理，以正确执行基于 NURBS 基函数的等几何分析（IGA），以解决具有全向周期性的异质介质和具有面内周期性的复合板的均质化问题。由于 IGA 模型中不同材料组合的处理并非微不足道，尤其是对于周期性约束而言，因此首要任务是在 IG 均质化分析 (IGHA) 的数值建模或等效网格生成中明确指定问题点。最尴尬但最重要的问题是如何为长方体晶胞的几何形状的 NURBS 表示生成补丁，以在考虑到 IGA 的凸包特性的情况下实现适当的变形。该问题是由于引入了位于异构晶胞中角点的重叠控制点而引起的，这些控制点必须满足与周期性边界条件 (PBC) 相关的多点约束 (MPC) 条件。尽管可以设想两种措施，但我们建议使用多个补丁以及双 MPC，同时施加 PBC 和不同补丁之间的连续性条件。提出了几个数值材料和平板试验的数值例子，以证明所提出的 IGHA IG 建模策略的有效性。版权所有 © 2016 约翰·威利父子有限公司
The treatments of heterogeneities and periodic boundary conditions are explored to properly perform isogeometric analysis (IGA) based on NURBS basis functions in solving homogenization problems for heterogeneous media with omni‐directional periodicity and composite plates with in‐plane periodicity. Because the treatment of the combination of different materials in IGA models is not trivial especially for periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most awkward, but important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex‐hull property of IGA. The issue arises from the introduction of overlapped control points located at angular points in the heterogeneous unit cell, which must satisfy multiple point constraint (MPC) conditions associated with periodic boundary conditions (PBCs). Although two measures may be conceivable, we suggest the use of multiple patches along with double MPC that imposes PBCs and the continuity conditions between different patches simultaneously. Several numerical examples of numerical material and plate tests are presented to demonstrate the validity of the proposed strategy of IG modeling for IGHA. Copyright © 2016 John Wiley & Sons, Ltd.