On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

authored by: P. Wriggers, B. Hudobivnik, O. Allix
Abstract: The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the C¹-continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of C¹-continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for C-continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these C¹-continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.
Organisation(s): Institute of Continuum Mechanics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
External Organisation(s): École normale supérieure Paris-Saclay (ENS Paris-Saclay)
Type: Article
Journal: Computational mechanics
Volume: 69
Pages: 615-637
No. of pages: 23
ISSN: 0178-7675
Publication date: 02.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-021-02106-1 (Access: Open)