Elastic and inelastic local buckling of stiffened plates subjected to non-uniform compression using the Galerkin method

A solution for the elastic and inelastic local buckling of flat rectangular plates with centerline boundary conditions subjected to non-uniform in-plane compression and shear stress is presented. The loaded edges are simply supported, the longitudinal edges may have any boundary conditions and the centerline is simply supported with a variable rotational stiffness. The Galerkin method, an effective method for solving differential equations, is applied to establish an eigenvalue problem. In order to obtain plate buckling coefficients, combined trigonometric and polynomial functions that satisfy the boundary conditions are used. The method is programmed, and several numerical examples including elastic and inelastic local buckling, are presented to illustrate the scope and efficacy of the procedure. The variation of buckling coefficients with aspect ratio is presented for various stress gradient ratios. The solution is applicable to stiffened plates and the flange of the I-shaped beams that are subjected to biaxial bending or combined flexure and torsion and shear stresses, and is important to estimate the reduction in elastic buckling capacity due to stress gradient.

[1]  Gregory J. Hancock,et al.  Buckling of thin flat-walled structures by a spline finite strip method , 1986 .

[2]  Alastair C. Walker.  Local Instability in Plates and Channel Struts , 1966 .

[3]  Critical Bending Stress for Flat Rectangular Plates Supported Along All Edges and Elastically Restrained Against Rotation Along the Unloaded Compression Edge , 1953 .

[4]  A. A. Ilyushin.  The Elasto-Plastic Stability of Plates , 1947 .

[5]  Archibald N. Sherbourne,et al.  Plate/Stiffener Assemblies under Nonuniform Edge Compression , 1995 .

[6]  J. Rhodes,et al.  Effects of eccentricity of load or compression on the buckling and post-buckling behaviour of flat plates , 1971 .

[7]  R. J. Plank,et al.  Buckling under combined loading of thin, flat‐walled structures by a complex finite strip method , 1974 .

[8]  Mark A. Bradford,et al.  Buckling of arbitrary quadrilateral plates with intermediate supports using the Galerkin method , 1998 .

[9]  Mark A. Bradford,et al.  Buckling of plates with different end conditions using the finite strip method , 1995 .

[10]  James S. Davidson,et al.  Buckling of centerline-stiffened plates subjected to uniaxial eccentric compression , 2005 .

[11]  Mark A. Bradford.  Buckling of longitudinally stiffened plates in bending and compression , 1989 .

[12]  S. Shrivastava.  Inelastic buckling of plates including shear effects , 1979 .

[13]  Elbridge Z Stowell,et al.  A unified theory of plastic buckling of columns and plates , 1948 .

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

[15]  Mark A. Bradford,et al.  Inelastic initial local buckling of plates with and without residual stresses , 1993 .