Virtual element for the buckling problem of Kirchhoff–Love plates

By David Mora, Iv'an Vel'asquez. Computer Methods in Applied Mechanics and Engineering, 2019

56 citations recorded by the source corpus.

Abstract In this paper, we develop a virtual element method (VEM) of high order to solve the fourth order plate buckling eigenvalue problem on polygonal meshes. We write a variational formulation based on the Kirchhoff–Love model depending on the transverse displacement of the plate. We propose a C 1 conforming virtual element discretization of arbitrary order k ≥ 2 and we use the so-called Babuska–Osborn abstract spectral approximation theory to show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates for the buckling modes (eigenfunctions) and a double order for the buckling coefficients (eigenvalues). Finally, we report some numerical experiments illustrating the behavior of the proposed scheme and confirming our theoretical results on different families of meshes.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ba43f828075b0fbf86d3abfaa2605bee9f3c93af