Non-linear stability analysis of laminated composite plates on one-sided foundation by hierarchical Rayleigh–Ritz and finite elements

Abstract In this paper, the influence of one-sided foundation on the unilateral buckling behavior of laminated composite orthotropic plates is investigated under compressive load. Derivation of governing equations is based on Kirchhoff's hypotheses and the principle of minimum total potential energy. The solutions are performed by the hierarchical Rayleigh–Ritz (HRRM) and finite element methods (HFEM) and are compared. Most of previous research studies on the unilateral buckling of plates are limited to single-layer plates. The results show that unsymmetric lamination experiences lower critical loads than those of symmetric lamination due to the existence of extensional–bending coupling in unsymmetric laminated sequencing schemes. Influences of aspect ratio, fiber orientation, the number of plies, Young's modulus ratio, and different boundary conditions on the unilateral buckling load are examined. The numerical results are validated with previous works studying unilateral buckling of single-layer plates resting on one-sided foundation.

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