Geometrically nonlinear hierarchical finite elements via a unified formulation

This paper presents the formulation of advanced one-dimensional finite elements for the geometrically non-linear static analysis of beams. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation. The approximation order of the displacement field along the thickness is a free parameter that leads to the formulation of a family of several beam elements. The tangent stiffness matrix of the element is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used. Newton-Raphson method is employed in order to solve the non-linear governing equations. Numerical investigations in terms of displacements and stresses are validated towards two-dimensional FEM solutions in order to show the correctness and the advantages of the proposed modelling approach.