The enhanced assumed strain method for the isogeometric analysis of nearly incompressible deformation of solids

Cardoso, Rui P.R.; Cesar de Sa, J. M.A.

Abstract

Isogeometric analysis has recently become very popular for the numerical modeling of structures and fluids. Among other potential features, advantages of using a non-uniform rational B-splines (NURBS)-based isogeometric analysis over the traditional finite element method include the possibility of using higher-order polynomials for the basis functions of the approximation space, which may be easily built on a recursive (hierarchical) fashion as well as higher convergence ratio. Nevertheless, NURBS-based isogeometric analysis suffers from the same problems depicted by other methods when it comes to reproduce isochoric deformations, that is, it shows volumetric locking, especially for low-order basis functions. Similar remedies as those that have been proposed for the finite element method may be appropriate for integration in the NURBS-based isogeometric analysis and some have already been tried with success. In this work, the analysis of the underlying space of incompressible deformations of a NURBS-based isogeometric approximation is performed with the main objective of understanding the likelihood of volumetric locking. As a remedy, the enhanced assumed strain methodology is blended with the NURBS-based isogeometric analysis to alleviate the volumetric locking associated with incompressible deformations. The solution includes a stabilization term derived directly from a penalized form of the classical Veubeke-Hu-Washizu three-field variational principle. © 2012 John Wiley & Sons, Ltd.

Citation

Cardoso, R. P., & Cesar de Sa, J. M. (2012). The enhanced assumed strain method for the isogeometric analysis of nearly incompressible deformation of solids. International Journal for Numerical Methods in Engineering, 92(1), 56-78. https://doi.org/10.1002/nme.4328

• Journal Article Type: Article
• Publication Date: Oct 5, 2012
• Deposit Date: Oct 1, 2012
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Electronic ISSN: 1097-0207
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 92
• Issue: 1
• Pages: 56-78
• DOI: https://doi.org/10.1002/nme.4328
• Keywords: NURBS, isogeometric analysis, enhanced assumed strain, volumetric locking
• Public URL: https://uwe-repository.worktribe.com/output/943931
• Publisher URL: http://dx.doi.org/10.1002/nme.4328