Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation

The buckling and large deflection postbuckling behavior of plates laterally constrained by a tensionless foundation and subjected to in-plane compressive forces are investigated. A nonlinear finite-element formulation based on Marguerre’s nonlinear shallow shell theory, modified by Mindlin’s hypothesis, is employed to model the plate response. To overcome difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the unilateral contact condition, two different approaches are used: (1) the unilateral constraint is accounted for indirectly by a bilinear constitutive law and (2) the problem is formulated as a mathematical programming problem with inequality constraints from which a linear complementarity problem is derived and solved by the Lemke algorithm. To obtain the nonlinear equilibrium paths, the Newton–Raphson algorithm is used together with path-following strategies. Plate–foundation interaction leads to interesting deformation sequences, chara...

[1]  A. A. Khathlan.  Large‐Deformation Analysis of Plates on Unilateral Elastic Foundation , 1994 .

[2]  Claude Do,et al.  Bifurcation theory for elastic plates subjected to unilateral conditions , 1977 .

[3]  Hui-Shen Shen.  Postbuckling analysis of orthotropic rectangular plates on nonlinear elastic foundations , 1995 .

[4]  Noboru Kikuchi,et al.  Analysis of Certain Unilateral Problems in von Karman Plate Theory by a Penalty Method-part 1 , 1980 .

[5]  Anthony M. Waas,et al.  DELAMINATION BUCKLING ; EXPERIMENT AND ANALYSIS , 1995 .

[6]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[7]  M. Crisfield.  Non-Linear Finite Element Analysis of Solids and Structures, Essentials , 1997 .

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

[9]  Koji Uetani,et al.  The secondary buckling and post-secondary-buckling behaviours of rectangular plates , 1979 .

[10]  J. Oden,et al.  Nonlinear eigenvalue problems characterized by variational inequalities with applications to the postbuckling analysis of unilaterally-supported plates , 1981 .

[11]  G. Onu.  Equivalences in the soil-structure interaction , 1996 .

[12]  Scott T Smith,et al.  Semi-compact steel plates with unilateral restraint subjected to bending, compression and shear , 1999 .

[13]  K.Kanaka Raju,et al.  Post-buckling of a square plate resting on an elastic foundation under biaxial compression , 1990 .

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

[15]  Z. Celep,et al.  Rectangular Plates Resting on Tensionless Elastic Foundation , 1988 .

[16]  P. Gonçalves,et al.  Numerical methods for analysis of plates on tensionless elastic foundations , 2001 .

[17]  Herzl Chai,et al.  Buckling and Post-Buckling Behavior of Elliptical Plates: Part I—Analysis , 1990 .

[19]  Y. Shimizu,et al.  Buckling Strength of Lining Shells of Pressure Vessels , 1992 .

[20]  H. D. Wright,et al.  Local Stability of Filled and Encased Steel Sections , 1995 .

[21]  Jin-Guang Teng,et al.  Axisymmetric shells and plates on tensionless elastic foundations , 1999 .

[22]  Y. Weitsman,et al.  On Foundations That React in Compression Only , 1970 .

[23]  Anthony M. Waas,et al.  Buckling of unilaterally constrained plates: Applications to the study of delaminations in layered structures , 1998 .

[24]  Leif Asp,et al.  Delamination buckling and growth for delaminations at different depths in a slender composite panel , 2001 .

[25]  Surkay D. Akbarov,et al.  On the bending problems of anisotropic (orthotropic) plates resting on elastic foundations that react in compression only , 1997 .

[26]  J. Hutchinson,et al.  Buckling of Bars, Plates and Shells , 1975 .

[27]  Paulo B. Gonçalves,et al.  Analysis of slender structural elements under unilateral contact constraints , 2001 .