The enhanced assumed strain method for the isogeometric analysis of nearly incompressible deformation of solids
The enhanced assumed strain method for the isogeometric analysis of nearly incompressible deformation of solids
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DOI：
10.1002/nme.4328
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发表时间：
2012-10
影响因子：
2.9
通讯作者：
R. Cardoso;J. C. D. César de Sá
中科院分区：
文献类型：
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作者：
R. Cardoso;J. C. D. César de Sá
近几年来，等轴测分析在构造和流体数值模拟中变得非常流行。与传统的有限元方法相比，基于非均匀有理B-Splines(NURBS)的等距分析的优点包括可以使用高次多项式作为近似空间的基函数，这可以很容易地以递归(分层)的方式建立以及更高的收敛比。然而，基于NURBS的等距分析在再现等容形变时遇到了其他方法所描述的相同问题，即它表现出体积锁定，特别是对于低阶基函数。在基于NURBS的等距分析中，与有限元方法所建议的类似的补救措施可能是适当的，其中一些已经被成功地尝试。在这项工作中，对基于NURBS的等距近似的不可压缩变形的基本空间进行了分析，主要目的是了解体积锁定的可能性。作为补救措施，改进的假设应变方法与基于NURBS的等几何分析相结合，以缓解与不可压缩变形相关的体积锁定。该解包括一个稳定项，它直接从经典的Veubeke-Hu-Ouizu三场变分原理的惩罚形式中得到。版权所有©2012 John Wiley&Sons，Ltd.
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. Copyright © 2012 John Wiley & Sons, Ltd.