Unified theory for curved composite thin-walled beams and its isogeometrical analysis

Abstract

This paper presents a unified theory for modelling composite thin-walled beams (TWB) of arbitrary planar axial curvature, variable cross-section and general material layup, complemented by the development of an Isogeometric Analysis (IGA) formulation for the discretization and solution of the equilibrium equations. To this end, the standard formulation of composite TWB with rectilinear axes is combined with a general framework for describing the kinematics of arbitrary three-dimensional curves based on the Frenet-Serret frame field. The theory includes explicit terms accounting for curvature gradients within the IGA stiffness matrix, allowing for the treatment of cases with highly curved geometry. Also included is an advanced shear-modification adjustment previously derived for rectilinear TWB, here reformulated for the case of curved TWB, improving the description of the in-plane shear-strain coupling and thus increasing the accuracy for cases with axial-bending-torsional structural coupling. Results from three numerical test cases indicate that this unified formulation effectively transfers all the advantages associated with rectilinear TWB to curved TWB models, yielding an accuracy comparable to more complex models while maintaining a competitive computational economy.