The chapter presents Virtual Element Methods for linear elasticity. In particular, displacement based methods stemming from the principle of virtual works for 2D problems, and mixed methods based on the Hellinger-Reissner variational principle for 2D and 3D problems are discussed and detailed. A series of numerical examples for each set of methods are given in order to show the characteristic features of the newly developed methods and to assess their accuracy and convergence properties.
Some Virtual Element Methods for Infinitesimal Elasticity Problems / E. Artioli, S. de Miranda, C. Lovadina, L. Patruno, M. Visinoni (SEMA SIMAI SPRINGER SERIES). - In: The Virtual Element Method and its Applications / [a cura di] P.F. Antonietti, L. Beirão da Veiga, G. Manzini. - [s.l] : Springer Science and Business Media, 2022. - ISBN 978-3-030-95318-8. - pp. 137-183 [10.1007/978-3-030-95319-5_4]
Some Virtual Element Methods for Infinitesimal Elasticity Problems
C. Lovadina;M. VisinoniUltimo
2022
Abstract
The chapter presents Virtual Element Methods for linear elasticity. In particular, displacement based methods stemming from the principle of virtual works for 2D problems, and mixed methods based on the Hellinger-Reissner variational principle for 2D and 3D problems are discussed and detailed. A series of numerical examples for each set of methods are given in order to show the characteristic features of the newly developed methods and to assess their accuracy and convergence properties.
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