基于Bézier提取的三维等几何分析

等几何分析(IGA)将非均匀有理B样条(NURBS)函数作为有限元形函数,具有几何精确、高阶连续和精度高等优点。与常规有限元法C0连续的形函数不同,高阶IGA基函数不是定义在一个单元上,而是跨越由几个单元组成的参数空间,因而编程复杂且无法嵌入现有的有限元法计算框架及相应算法。本文建立了基于Bézier提取的三维IGA,将NURBS函数分解成伯恩斯坦多项式的线性组合,从而实现把NURBS单元分解为C0连续Bézier单元,这些单元与Lagrange单元相似,使IGA的实现和常规有限元一样,以便将IGA分析嵌入现有的有限元软件中。两个三维算例结果表明,基于Bézier提取的IGA和传统IGA的收敛性和精度相同。

Three-dimensional isogeometric analysis based on Bézier extraction

Isogeometric analysis (IGA) uses non-uniform rational B-splines (NURBS) functions as shape functions of finite element method (FEM),so that IGA has some advantages such as exact geometrical representation,high-order continuity and high accuracy.Unlike shape functions in FEM is C⁰-continuity,in high-order IGA,the basis functions are not confined to one element,but span a global domain,so the programming is complicated and which cannot be embedded into existing FEM framework.In this paper,a three-dimensional IGA based on Bézier extraction is developed,which decomposes NURBS functions to a set of Bernstein polynomials,thus C⁰ continuous Bézier elements,which are similar to Lagrange elements,can be obtained.Hence,the implementation of IGA is similar to that of conventional FEM,so that IGA can be embedded in existing FEM software easily.Two examples are given to illustrate the IGA based on Bézier extraction has the same convergence rate and accuracy as those in the conventional IGA.