An analysis of composite beams by means of hierarchical finite elements and a variables separation method

Laminated composite three-dimensional beams are investigated by means of hierarchical one-dimensional finite elements and a space decomposition approach. The global three-dimensional problem is separated by a Proper Generalised Decomposition into two coupled ones over the cross-section approximation space and on the beam axis approximation space. The size of the resulting problem is smaller than that of a classical equivalent finite element solution. The approximation of the displacements versus the cross-section and along the axis are general regardless the kinematic expansion order and the number of nodes per element thanks to a Unified Formulation. Accurate yet computationally affordable solutions are obtained.