Non-uniform rational Lagrange functions and its applications to isogeometric analysis of in-plane and flexural vibration of thin plates
Non-uniform rational Lagrange functions and its applications to isogeometric analysis of in-plane and flexural vibration of thin plates
复制标题
非均匀有理拉格朗日函数及其在薄板面内和弯曲振动等几何分析中的应用
DOI：
10.1016/j.cma.2017.04.007
复制
发表时间：
2017-07-01
影响因子：
7.2
通讯作者：
Sun, Hao
中科院分区：
文献类型：
--
作者：
Liu, Bo;Xing, Yufeng;Sun, Hao
为了克服NURBS(非均匀有理B-样条)等几何分析在处理Dirichlet边界条件方面的困难，提出了一种新的等距分析基函数。新的基函数是通过嵌套有理局部拉格朗日插值法来构造的，其计算过程与有限差分法类似。给出了新基函数的显式表达式。由于它们与NURBS的等价性，新的基函数被命名为非均匀有理拉格朗日(NURL)基。使用NURL的IGA将有限元方法作为特例包括在内，但使用NURL的IGA中的几何是精确的。使用NURL的免疫遗传算法可以进行具有NURBS k-精化嵌套特征的p-精化。Dirichlet边界条件可以使用NURL直接施加到IGA中，因为NURL是内插基函数。提出了一种将三角面片的张量积基直接转换为面积坐标的方法，解决了边界退化为单点的奇异性问题。将本文提出的方法应用于薄板的面内振动和弯曲振动。与文献结果的比较表明，NURL和三角面片变换法的IGA收敛速度快，精度高。文中还附上了一个MatLab工具箱的NURL。(C)2017爱思唯尔B.V.保留所有权利。
New basis functions were developed for isogeometric analysis (IGA) to overcome the difficulties of IGA using NURBS (Non-Uniform Rational B-Splines) on coping with Dirichlet boundary conditions. The new basis functions were constructed through nesting rational local Lagrange interpolations like the T-spline and were evaluated in similar procedure as the finite difference method. Explicit expressions for the new basis functions were presented. Due to their equivalence to the NURBS, the new basis functions were named as non-uniform rational Lagrange (NURL) basis. IGA using NURL includes the finite element method as a special case but the geometry in IGA using NURL is exact. IGA using NURL can carry out p-refinement that has the nesting feature of the k-refinement of NURBS. Dirichlet boundary conditions can be directly imposed in IGA using NURL because the NURL are interpolation basis functions. A method of directly transforming the tensor product basis of triangular patches to area coordinates was presented and the singularity problem at the edge degenerated to a single point was solved. The methods developed in this work were applied to in-plane and flexural vibration of thin plates. Comparisons with available results in literatures showed the fast convergence and high accuracy of IGA using NURL and the transformation method for triangular patches. Introduction of a MATLAB toolbox of the NURL was appended. (C) 2017 Elsevier B.V. All rights reserved.