Application of the Radial Integration Method for the Buckling Analysis of Plates with Shear Deformation R.A. Soares Jr. 1 , L. Palermo Jr. 1 , L.C. Wrobel 2 1 School of Civil Engineering, Architecture and Urban Design, State University of Campinas, Caixa Postal 6143, CEP 13083-889, Campinas, Brazil 2 Brunel University London, Department of Mechanical Engineering, Uxbridge UB8 3PH, UK; also, at Department of Civil and Environmental Engineering, PUC-Rio - Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil Abstract This work presents a novel formulation of the Boundary Element Method (BEM) with the Radial Integration Method (RIM) to calculate the critical loads of the plate buckling problem with shear deformation. An alternative formulation is adopted where the effect of the geometric non-linearity is described by using the first derivative of the function for the out-of-plane displacements. The RIM is developed for this problem and used to convert the resulting domain integrals into equivalent boundary integrals. The results are compared with other results available in the literature and with the results obtained with the Dual Reciprocity Method (DRM). The advantages of using the RIM are discussed at the end of this work. Keywords: radial integration method, plate buckling, shear deformation, Reissner plates, boundary elements. Introduction The present work develops an alternative formulation of the Radial Integration Method (RIM) within a Boundary Element Method (BEM) formulation for calculating the critical load in plate buckling problems. The bending model takes into account the effect of shear deformation as the classical plate bending theory [1] presents difficulties in the modelling of the plate borders and/or in the representation of the stresses around holes with diameter lower than or equal to the plate thickness. The formulation employed in this work assumes that the effect of shear deformation is constant along the plate thickness, as considered by Reissner [2] and Mindlin [3]. The relations between the Reissner model and the classical bending theory are discussed by Timoshenko and Woinowsky-Krieger [4]. The effect of shear deformation has an influence on the value of critical loads in plates, besides the flexural rigidity, as can be explicitly demonstrated in the analytical solution of the plate buckling problem [5], or through the use of numerical analysis. The numerical treatment of the
Application of the Radial Integration Method for the Buckling Analysis of Plates with Shear Deformation
Jun 14, 2023
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