An analytical model for the buckling of plates under mixed boundary conditions

An analytical approach for the buckling analysis of rectangular plates under mixed boundary conditions is presented. In order to solve the partial differential equation governing the problem at hand a method of separation of variables is here adopted, by introducing the displacement field as a result of the scalar product of two vectors which combine prescribed and unknown scalar functions. By following this strategy, exact buckling solutions for a wide class of problems, in which mixed boundary conditions can be assigned relaxing some usual constraints, are determined, and buckling load of plates, where biaxial tensile and compressive loads are applied in presence of piecewise clamped and partially supported sides, obtained analytically. Several cases of engineering interest are finally analyzed, and comparisons of the theoretical outcomes with literature data and Finite Element-based numerical results are also shown, in order to highlight the effectiveness of the proposed strategy.

[1]  Y. Liu,et al.  A generalized analytical approach to the buckling of simply-supported rectangular plates under arbitrary loads , 2008 .

[2]  M. Aliabadi,et al.  Buckling analysis of shear deformable plates by boundary element method , 2005 .

[3]  Julio F. Davalos,et al.  LOCAL BUCKLING OF COMPOSITE FRP SHAPES BY DISCRETE PLATE ANALYSIS , 2001 .

[4]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[5]  Qiusheng Li,et al.  Concise formula for the critical buckling stresses of an elastic plate under biaxial compression and shear , 2009 .

[6]  M. Aliabadi,et al.  Local buckling of thin-walled structures by the boundary element method , 2009 .

[7]  J. Reddy,et al.  Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory , 1985 .

[8]  Jae-Hoon Kang,et al.  VIBRATION AND BUCKLING OF SS-F-SS-F RECTANGULAR PLATES LOADED BY IN-PLANE MOMENTS , 2001 .

[9]  Jae-Hoon Kang,et al.  Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses , 2002 .

[10]  Eugenio Ruocco,et al.  A GENERALIZED ANALYTICAL APPROACH FOR THE BUCKLING ANALYSIS OF THIN RECTANGULAR PLATES WITH ARBITRARY BOUNDARY CONDITIONS , 2011 .

[11]  R. Szilard,et al.  Theory and Analysis of Plates, Classical and Numberical Methods , 1974 .

[12]  M. Aliabadi,et al.  Post buckling analysis of shear deformable shallow shells by the boundary element method , 2010 .

[13]  L. Kollár,et al.  Buckling of Rectangular Orthotropic Plates Subjected to Biaxial Normal Forces , 2001 .

[14]  P. Qiao,et al.  Explicit local buckling analysis of rotationally restrained composite plates under uniaxial compression , 2008 .

[15]  Eugenio Ruocco,et al.  Optimum topological design of simply supported composite stiffened panels via genetic algorithms , 2008 .

[16]  C. Wang,et al.  Buckling load relationship between Reddy and Kirchhoff plates of polygonal shape with simply supported edges , 1997 .

[17]  Raffaele Casciaro,et al.  Asymptotic post-buckling FEM analysis using corotational formulation , 2009 .

[18]  Marco Amabili,et al.  Exact solution for linear buckling of rectangular Mindlin plates , 2008 .