A high performance flexibility-based GBT finite element. (1st October 2015) - de Miranda, Stefano; Madeo, Antonio; Melchionda, Domenico; Ubertini, Francesco
Highlights: A 2-node finite element for the Generalized Beam Theory is developed. Element formulation is based on the hybrid complementary energy functional. Equilibrated stress approximation is derived basing on analytical solutions. Displacements within the element are a posteriori recovered. Displacements and stresses are accurately predicted using very rough meshes. Abstract: A new 2-node finite element for the Generalized Beam Theory is developed based on the hybrid complementary energy functional, involving nodal displacements and equilibrating stresses within the element as independent variables. Assumed stresses are rationally derived basing on the stresses associated to analytical solutions of some particular cases. Displacements within the element are a posteriori recovered by shape functions based on the same solutions. Numerical results show the high performance of the proposed element: generalized displacements and stresses are accurately predicted with very rough meshes, often using only one or two finite elements.