Instability of a Transversely Isotropic Elastic Slab Subjected to Axial Loads

Abstract

After obtaining the relations between incremental stresses and incremental strains, we analyzed the instability problem stated in the title on the basis of Biot’s mechanics of incremental deformations. The slab, made of a hypothetical transversely isotropic compressible elastic material, is assumed to be stronger in its transverse direction than in its axial direction. The analysis shows that, no matter what the anisotropy strength of the slab is or its thickness is, it can become unstable under tension as well as under compression. The critical load is higher for the stronger anisotropy in the compressive case, while it is lower for the stronger anisotropy in the tensile case. In other words, the reinforcement in the “wrong” direction weakens the slab under tension with respect to its stability. Furthermore, the weakly anisotropic slab can become unstable only after the axial resultant force reaches its maximum, while the strongly anisotropic slab can lose its stability before the force reaches its maximum.