Vol. 6, No. 9-10, 2011

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ISSN: 1559-3959
Linear buckling analysis of cracked plates by SFEM and XFEM

Pedro M. Baiz, Sundararajan Natarajan, Stéphane P. A. Bordas, Pierre Kerfriden and Timon Rabczuk

Vol. 6 (2011), No. 9-10, 1213–1238
Abstract
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In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify the simulation of cracks. The proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. The buckling coefficient and mode shapes of square and rectangular plates are computed as functions of crack length, crack location, and plate thickness. The effects of different boundary conditions are also studied.

Keywords
Mindlin, Reissner, shear deformable plate theory, buckling, partition of unity methods (PUM), extended finite element method (XFEM), fracture
Milestones
Received: 28 April 2010
Revised: 28 September 2010
Accepted: 30 November 2010
Published: 15 January 2012
Authors
Pedro M. Baiz
Department of Aeronautics
Imperial College London
Prince Consort Road
London  SW7 2AZ
United Kingdom
Sundararajan Natarajan
School of Engineering
Cardiff University
Cardiff  CF24 3AA
United Kingdom
Stéphane P. A. Bordas
School of Engineering
Cardiff University
Cardiff  CF24 3AA
United Kingdom
Pierre Kerfriden
School of Engineering
Cardiff University
Cardiff  CF24 3AA
United Kingdom
Timon Rabczuk
Department of Civil Engineering
Bauhaus-Universität Weimar
99421 Weimar
Germany