Finite deformation of a multi-layered strong anisotropic bar

Abstract

Deformations, stresses and potential energy in a bar were examined in accordance with the Theory of Ideal Fibre-Reinforced Composites. The cross section of the bar consisted of several fibrereinforced inextensible layer bonded together. A concentrated external force in an axial or transverse direction caused finite deformation. For plane deformation and a general constitutive law relating shearing stress to the shearing modulus and the shear in the material, S = Gγ ^⩼a. The potential energy was examined as a variational problem. The results were discussed and compared with the results obtained by the Euler-buckling and the bending analysis. It was found for the axially loaded bar that only values a = 1 possibly lead to a critical buckling force. For a > 1 every value of the external force causes buckling and ∑a _i < 1 in S = ∑ G _i γ^a _i entails buckling angles larger than π/2. A criterion for deciding which theory yields the minimum load for collapse, is presented.