Isogeometric analysis using G-spline surfaces with arbitrary unstructured quadrilateral layout
Isogeometric analysis using G-spline surfaces with arbitrary unstructured quadrilateral layout
复制标题
DOI：
10.1016/j.cma.2023.115965
复制
发表时间：
2023-02
期刊：
影响因子：
--
通讯作者：
Zuowei Wen;Md Sadman Faruque;Xin Li;Xiaodong Wei;Hugo Casquero
中科院分区：
文献类型：
--
作者：
Zuowei Wen;Md Sadman Faruque;Xin Li;Xiaodong Wei;Hugo Casquero
G 样条曲线是 B 样条曲线的推广，通过在辐条边缘施加 G 1 约束来处理异常点，从而在整个表面上获得连续的切平面。使用等参概念和 Bubnov-Galerkin 方法求解具有 G 样条的偏微分方程，可在物理空间中实现具有全局 C 1 连续性的离散化。需要非常点（EP）来表示具有任意拓扑属的流形表面。在这项工作中，我们允许内部和边界 EP，并且 EP 彼此之间的距离没有限制。达到这种灵活性水平是必要的，这样带有 EP 的样条才能成为工程应用中出现的复杂薄壁结构的设计到分析周期的主流。据作者所知，本文提出的基于施加 G 1 约束的两种 EP 构造是等几何分析（IGA）中使用的前两种 EP 构造，它们结合了以下显着特征：（1）仅使用基于顶点的控制点，并且它们充当几何形状手柄，（2）控制网络的任何控制点都可能是 EP，（3）在不引入奇点的情况下获得物理空间中的全局 C 1 连续性，（4）EP 周围的面不被分割分解为多个单元，即得到单元尺寸均匀的贝塞尔网格，(5)获得良好的表面质量。本文进行的收敛性和表面质量研究表明，G 样条比基于 D 面片框架的 EP 结构更适合 IGA。最后，我们用 G 样条曲面表示 B 柱的加强筋、内部部分和外部部分，并使用 Kirchhoff–Love 和 Reissner–Mindlin 壳理论解决了特征值问题。将结果与双线性四边形网格进行比较，发现 G 样条与传统有限元之间具有极好的一致性。总之，G 样条是使用相同几何表示设计和分析薄壁结构的可行替代方案，从而简化从设计到分析的周期。
G-splines are a generalization of B-splines that deals with extraordinary points by imposing G 1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the Bubnov–Galerkin method to solve partial differential equations with G-splines results in discretizations with global C 1 continuity in physical space. Extraordinary points (EPs) are required to represent manifold surfaces with arbitrary topological genus. In this work, we allow both interior and boundary EPs and there are no limitations regarding how close EPs can be from each other. Reaching this level of flexibility is necessary so that splines with EPs can become mainstream in the design-through-analysis cycle of the complex thin-walled structures that appear in engineering applications. To the authors’ knowledge, the two EP constructions based on imposing G 1 constraints proposed in this work are the first two EP constructions used in isogeometric analysis (IGA) that combine the following distinctive characteristics:(1) Only vertex-based control points are used and they behave as geometric shape handles,(2) any control point of the control net can potentially be an EP,(3) global C 1 continuity in physical space is obtained without introducing singularities,(4) faces around EPs are not split into multiple elements, ie, Bézier meshes with uniform element size are obtained, and (5) good surface quality is attained. The studies of convergence and surface quality performed in this paper suggest that G-splines are more suitable for IGA than EP constructions based on the D-patch framework. Finally, we have represented the stiffener, the inner part, and the outer part of a B-pillar with G-spline surfaces and solved eigenvalue problems using both Kirchhoff–Love and Reissner–Mindlin shell theories. The results are compared with bilinear quadrilateral meshes and excellent agreement is found between G-splines and conventional finite elements. In summary, G-splines are a viable alternative to design and analyze thin-walled structures using the same geometric representation so as to streamline the design-through-analysis cycle.