A Small Strain Tensor for the Geometrically Exact Thin-Walled Composite Beam

Abstract

This work presents the derivation of a small strain tensor compatible with the geometrically exact kinematics of the thin walled composite beam theory. The formulation is based on the expression of the Green strain tensor in terms of a pure linear strain plus a pure nonlinear strain measure obtained through the decomposition of the deformation gradient. The discrete small strain measures are expressed in terms of the current director and displacement fields and its derivatives in terms of very simple relations; they result to be objective under rigid body motion and independent of the integration path. The formulation is consistent in the sense that both the strain measures and the constitutive relations are valid for small strains.