Hierarchical p-version C-1 finite elements on quadrilateral and triangular domains with curved boundaries and their applications to Kirchhoff plates
Hierarchical p-version C-1 finite elements on quadrilateral and triangular domains with curved boundaries and their applications to Kirchhoff plates
复制标题
具有弯曲边界的四边形和三角形域上的分层 p 版本 C-1 有限元及其在基尔霍夫板中的应用
DOI：
10.1002/nme.6046
复制
发表时间：
2019
影响因子：
2.9
通讯作者：
Liu Bo
中科院分区：
文献类型：
--
作者：
Wu Yang;Xing Yufeng;Liu Bo
本文主要研究具有曲线边界的p型有限元的构造问题。三角形和四边形元素都是基于在本工作和文献中开发的c1 -版本混合函数插值方法构建的。构建正交层次基并将其转化为插值节点基，以方便边界条件的施加和曲线域上c1一致性的实现。为了提高数值性能，研究了节点的配置策略，提出了一种新的非均匀分布节点，即高斯-雅可比（GJ）点。对于平行四边形和直边三角形单元，相邻单元之间完全满足c1连续性。通过在Gauss - Lobatto节点上插值法向导数，避免了具有弯曲边界的元素c1一致性的困难。此外，在混合函数插值方法的帮助下，边缘基和内部模态的近似阶数可以不同。因此，局部细化可以很容易地由这些元素执行。数值结果表明，对于规则域和不规则域的问题，这些单元计算成本低，收敛速度快。
This work focuses on the construction ofp‐version finite elementsthat have curve boundariesforC1problems. Both triangular and quadrilateral elements are constructed based on theC1‐version blending function interpolation methods that are developed in this work and in the literature. Orthogonal hierarchical bases are constructed and subsequently transformed into interpolative nodal bases to facilitate the imposition of boundary conditions and the implementation ofC1conformity on curvilinear domains. Nodal collocation strategies are also studied for improving the numerical performance, and novel nonuniformly distributed nodes, namely, Gauss‐Jacobi (GJ) points, are proposed. For parallelograms and straight‐sided triangular elements,C1continuity is exactly satisfied between neighboring elements. The difficulty ofC1conformity for elements that have curved boundaries is circumvented by interpolating the normal derivatives at Gauss‐Lobatto nodes. Moreover, with the help of the blending function interpolation method, the bases on edges and the internal modes can differ in terms of approximation order. Therefore, localp‐refinements can be easily performed by these elements. Numerical results demonstrated that these elements are computationally inexpensive and converge fast for problems with regular and irregular domains.