David Mora, Iván Velásquez:
Virtual element for the buckling problem of Kirchhoff-Love plates
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 $kge2$ and we use the so-called Babuv ska--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 behaviour of the proposed scheme and confirming our theoretical results on different families of meshes.
This preprint gave rise to the following definitive publication(s):
David MORA, Iván VELáSQUEZ: Virtual element for the buckling problem of Kirchhoff-Love plates. Computer Methods in Applied Mechanics and Engineering, vol. 360, Art. Num. 112687, (2020).