|
|
||
|
|
|
|
This and the next 2 images are from:
D.J. Benson (1), Y. Bazilevs (1), E. De Luycker (1), M.-C. Hsu (1), M. Scott (2), T.J.R. Hughes (2) and T. Belytschko (3)
(1) Department of Structural Engineering, University of California, San Diego 9500 Gilman Drive, La Jolla, CA 92093, USA
(2) Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX 78712, USA
(3) Department of Mechanical Engineering, 2145 North Sheridan Road, Northwestern University, Evanston, IL 60208-3111
“A generalized finite element formjulation for arbitrary basis functions: from isogeometric analysis to XFEM”, Int. J. Numer. Meth. Engng, 2009 (no volume number given in the pdf file)
ABSTRACT: Many of the formulations of current research interest, including iosogeometric methods, the extended finite element method, and meshless methods, 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 new software for each new class of basis functions is a large research burden, especially if the problems involve large deformations, nonlinear materials, and contact. The objective of the current research is to separate 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 element program but that permits the use of reasonably arbitrary sets of basis functions that are defined only through the input file. Examples of this framework to applications with Lagrange elements, isogeometric elements and XFEM basis functions for fracture are presented.
Page 198 / 410