A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM
A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM
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DOI：
10.1002/nme.2864
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发表时间：
2010-08-06
影响因子：
2.9
通讯作者：
Belytschko, T.
中科院分区：
文献类型：
--
作者：
Benson, D. J.;Bazilevs, Y.;Belytschko, T.
许多公式的厘米租金的研究兴趣，包括等几何方法和扩展的有限元方法，使用非传统的基函数。某些曲面（如细分曲面）可能没有方便的分析表达。要素的概念，如果确实适当的话，也不再与传统的定义相一致。为每一类新的基函数开发一个新的软件是一个很大的研究负担，特别是当问题涉及大变形、非线性材料和接触时。本文的目的是提出一种方法，分离尽可能多的生成和评估的基础功能的分析，从而在制定，可以在传统的结构内实现的一个有限的编程，但允许使用任意组的基础功能，仅通过输入文件定义。从传统的线性四节点四面体到结合XFEM和等几何分析的高阶元素，可以完全通过输入文件指定元素，而无需任何额外的编程。这个框架的应用程序与拉格朗日元素，等几何元素，和XFEM断裂基函数的例子。版权所有（C）2010约翰威利父子有限公司
Many of the formulations of cm-rent research interest, including iosogeometric methods and the extended finite element method, use nontraditional basis functions. Some, such as subdivision surfaces, may not have convenient analytical representations. The concept of an element, if appropriate at all, no longer coincides with the traditional definition. Developing a new software for each new class of basis functions is a large research burden, especially, if the problems involve large deformations, non-linear materials, and contact. The objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file. Elements ranging from a traditional linear four-node tetrahedron through a higher-order element combining XFEM and isogeometric analysis may be specified entirely through an input file without any additional programming. Examples of this framework to applications with Lagrange elements, isogeometric elements, and XFEM basis functions for fracture are presented. Copyright (C) 2010 John Wiley & Sons, Ltd.