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A Virtual Element Method for elastic and inelastic problems on polytope meshes

机译:多面网格上弹性和非弹性问题的虚拟单元法

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摘要

We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as a suitable treatment of the displacement gradient. The proposed method allows for general polygonal and polyhedral meshes, it is efficient in terms of number of applications of the constitutive law, and it can make use of any standard black-box constitutive law algorithm. Some theoretical results have been developed for the elastic case. Several numerical results within the 2D setting are presented, and a brief discussion on the extension to large deformation problems is included. (C) 2015 Elsevier B.V. All rights reserved.
机译:我们针对可能的非线性弹性和非弹性问题提出了一种虚拟元素方法(VEM),主要集中在较小的变形区域。数值方案基于位移场的低阶近似以及位移梯度的适当处理。所提出的方法允许使用一般的多边形和多面体网格,在本构法的应用数量方面是有效的,并且可以利用任何标准的黑盒本构法。已经为弹性壳体开发了一些理论结果。给出了二维设置中的几个数值结果,并简要讨论了扩展到大变形问题。 (C)2015 Elsevier B.V.保留所有权利。

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