Elastic Buckling of Infinitely Long Specially Orthotropic Plates on Tensionless Foundations

The results of an analytical study on the elastic buckling of long narrow orthotropic plates resting on a tensionless foundation are reported. The motivation for the present study stems from the importance of delamination buckling as a viable mode of failure in fibrous laminated composites. When near surface delaminations undergo buckling, the buckled displacements are of one sign, because the remainder of the laminate (parent sublaminate) essentially acts like a rigid foundation. The results of the present study can be incorporated into developing delamination growth models for various loading conditions. Example results are presented for five different types of plates where one is of the isotropic type and the remaining four are of the laminated orthotropic type. Example results for two types of Graphite/Epoxy material systems (IM7/8551-7 and T300/BP907) are reported. In the laminates considered, the stacking is sequenced so that the bending constitutive constants D₁₆ and D₂₆ vanish. Extensive parametric analysis was performed and it was found that for the case of a simply supported plate and in the limiting case of a rigid foundation, conforming to buckled displacements of one sign, the increase in the buckling load over that of a simply supported plate but with no foundation varies between 22 and 33 percent, depending on the plate stacking sequence. On the other hand, for the clamped-free case this number was found to vary between 24 and 36 percent for all types of materials used in this study. Previous studies that addressed similar issues did not pay particular attention to the one sided buckling constraint that is placed due to physical considerations.