In-Plane Shear-Axial Strain Coupling Formulation for Shear-Deformable Composite Thin-Walled Beams

Abstract

This paper presents an improved description of the in-plane strain coupling in Librescu-type shear-deformable composite thin-walled beams (CTWB). Based on existing descriptions for Euler-type CTWB, an analogous formulation for shear-deformable CTWB is here developed by building, via the Mindlin–Reissner theory and an orthotropic constitutive law of the shell wall, an alternate equation for the in-plane shear force which effectively couples the axial and shear in-plane strains. It is observed that this strain coupling formulation includes some of the transversal (out-of-plane) shear strain terms, thus also functioning as a path for transferring transversal shear energy to the in-plane strain field and therefore improving shear-deformability. The performance of the new CTWB model is compared against that of previously available CWTB (i.e. Euler-type with strain coupling and Timoshenko-type without strain coupling) for several aspect ratios, fibre-orientations and laminate types. Error measures are calculated by comparing several relevant stiffness coefficients and displacement shapes to reference results provided by corresponding 3D shell-based ANSYS finite-element models. Results indicate that for cases involving significant shear energy (i.e. short aspect ratios) and/or in-plane shear-axial strain coupling (i.e. off-axis or asymmetric/unbalanced laminates), the new CTWB model proposed in this work can attain an accuracy level comparable to that associated to more sophisticated models, two to three orders of magnitude larger, at a fraction of the computational cost.