Postbuckling of shear deformable laminated plates resting on a tensionless elastic foundation subjected to mechanical or thermal loading

Postbuckling responses of shear deformable laminated plates supported by a tensionless elastic foundation and subjected to in-plane compressive edge loads or a uniform temperature rise are investigated. The formulations are based on the higher order shear deformation plate theory with a von Karman-type of kinematic non-linearity and include the plate-foundation interaction, for which the foundation reacts in compression only. The thermal effects are also included and the material properties are assumed to be independent of temperature. The initial geometric imperfection of the plate is taken into account. The analysis uses a two step perturbation technique to determine the postbuckling response of the plate. An iterative scheme is developed to obtain numerical results without using any prior assumption for the shape of the contact region. The numerical illustrations concern the postbuckling behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates resting on tensionless elastic foundations of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of the plate subjected to either mechanical or thermal loading when the foundation stiffness is sufficiently large.

[1]  Mark A. Bradford,et al.  Elastic buckling of unilaterally constrained rectangular plates in pure shear , 1999 .

[2]  Noboru Kikuchi,et al.  Analysis of certain unilateral problems in von karman plate theory by a penalty method-part 2. Approximation and numerical analysis , 1980 .

[3]  In Lee,et al.  Vibration behaviors of thermally postbuckled anisotropic plates using first-order shear deformable plate theory , 1997 .

[4]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[5]  G. Bezine,et al.  Unilateral buckling of thin elastic plates by the boundary integral equation method , 1985 .

[6]  Herzl Chai,et al.  Contact buckling and postbuckling of thin rectangular plates , 2001 .

[7]  Mark A. Bradford,et al.  Numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the Rayleigh-Ritz method , 1999 .

[8]  Hui-Shen Shen.  THERMAL POSTBUCKLING OF PRELOADED SHEAR DEFORMABLE LAMINATED PLATES , 2000 .

[9]  Anthony M. Waas,et al.  Buckling of Unilaterally Constrained Infinite Plates , 1998 .

[10]  Clive L. Dym,et al.  STABILITY THEORY AND ITS APPLICATIONS TO STRUCTURAL MECHANICS , 1974 .

[11]  G. Venkateswara Rao,et al.  Thermal post-buckling behaviour of laminated plates using a shear-flexible element based on coupled-displacement field , 2003 .

[12]  Hui-Shen Shen,et al.  Thermal Postbuckling of Imperfect Shear-Deformable Laminated Plates on Two-Parameter Elastic Foundations , 1999 .

[13]  Hui-Shen Shen.  Postbuckling Analysis of Shear-Deformable Composite Laminated Plates on Two-Parameter Elastic Foundations , 2000 .

[14]  H D Wright,et al.  BUCKLING OF PLATES IN CONTACT WITH A RIGID MEDIUM , 1993 .

[15]  J. N. Reddy,et al.  A refined nonlinear theory of plates with transverse shear deformation , 1984 .

[16]  Hui‐Shen Shen.  Postbuckling of shear deformable laminated plates under biaxial compression and lateral pressure and resting on elastic foundations , 2000 .

[17]  Paul Seide,et al.  Compressive Buckling of a Long Simply Supported Plate on an Elastic Foundation , 1958 .

[18]  Hui-Shen Shen,et al.  Thermal postbuckling behavior of imperfect shear deformable laminated plates with temperature-dependent properties , 2001 .

[19]  Anthony M. Waas,et al.  A mechanical model for the buckling of unilaterally constrained rectangular plates , 1994 .

[20]  G. Venkateswara Rao,et al.  Buckling and post-buckling analysis of moderately thick laminated rectangular plates , 1996 .

[21]  Paulo B. Gonçalves,et al.  Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation , 2003 .