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首页> 外文期刊>International Journal for Numerical Methods in Engineering >Hierarchical p-version C-1 finite elements on quadrilateral and triangular domains with curved boundaries and their applications to Kirchhoff plates
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Hierarchical p-version C-1 finite elements on quadrilateral and triangular domains with curved boundaries and their applications to Kirchhoff plates

机译：在四边形和三角形域上的分层P-version C-1有限元，曲线边界及其应用于Kirchhoff Plates

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摘要

This work focuses on the construction of p-version finite elements that have curve boundaries for C-1 problems. Both triangular and quadrilateral elements are constructed based on the C-1-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 of C-1 conformity 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, C-1 continuity is exactly satisfied between neighboring elements. The difficulty of C-1 conformity 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, local p-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.
机译：这项工作侧重于构建具有C-1问题的曲线边界的P-Version有限元。三角形和四边形元素都是基于在本工作和文献中开发的C-1版本混合功能插值方法构建。构建正交层基碱基，随后转化为内插核心基础，以促进边界条件和C-1在曲线域的实施方式的实施。还研究了节点搭配策略来改善数值性能，提出了新的非均匀分布节点，即高斯-Jacobi（GJ）点。对于平行四边形和直侧三角形元件，在相邻元件之间完全满足C-1连续性。通过在高斯-Lobatto节点处插入正常衍生物来规避具有弯曲边界的元素的C-1符合性的难度。此外，在混合功能插值方法的帮助下，边缘上的基础和内部模式可以在近似顺序的方面不同。因此，可以通过这些元件容易地执行局部p细化。数值结果表明，这些元素是计算地廉价的，并且在常规和不规则域的问题上快速收敛。

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