A finite element method for the buckling problem of simply supported Kirchhoff plates
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Felipe Millar [1] ; David Mora [1]
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[1] Universidad del Bío-Bío
Universidad del Bío-Bío
Comuna de Concepción, Chile
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 286, Nº 1 (1 October 2015), 2015, págs. 68-78
- Idioma: inglés
- DOI: 10.1016/j.cam.2015.02.018
- Enlaces
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Resumen
The aim of this paper is to develop a finite element method to approximate the buckling problem of simply supported Kirchhoff plates subjected to general plane stress tensor. We introduce an auxiliary variable w:=Δu (with uu representing the displacement of the plate) to write a variational formulation of the spectral problem. We propose a conforming discretization of the problem, where the unknowns are approximated by piecewise linear and continuous finite elements. We show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we present some numerical experiments supporting our theoretical results.
