NURBS-based modeling of laminated composite beams with isogeometric displacement-only theory

This paper develops a formulation for displacement-only beam elements based on isogeometric analysis, with intended application to laminated composite members. The main purpose of the current study was to overcome some deficiencies of commonly used beam theories, such as shear-locking, the lacking relevance of isotropic materials for multi-layer composites, the incompatibility with other continuum elements, and the limited continuity in interpolation. A bi-variable non-uniform rational B-spline (NURBS) beam element with complete plane-stress elasticity terms and geometrical expressions was developed. Shear-locking, interlaminar stresses, the deep-beam situation, and vibration features were evaluated for several aspect ratios, ply orientations, and NURBS degrees, in order to verify the efficiency and accuracy. h-, p- and k-refinements were used to improve the displacement field. The validity of the solutions was measured based on results from plane-stress finite element analysis, and compared to the alternative Carrera unified formulation. Results show that the isogeometric displacement-only beam theory can provide the interlaminar stress distribution, gives high accuracy for mid and high-range eigen-frequencies, and avoids the shear-locking phenomenon.