Hierarchical beam finite elements based upon a variables separation method

Authors

G. Giunta, S. Belouettar, O. Polit, L. Gallimard, P. Vidal, and M. D'Ottavio

Reference

International Journal of Applied Mechanics, vol. 08, no. 02, art. no. 1650026, 2016

Description

A family of hierarchical one-dimensional beam finite elements developed within a variables separation framework is presented. A Proper Generalized Decomposition (PGD) is used to divide the global three-dimensional problem into two coupled ones: one defined on the cross-section space (beam modeling kinematic approximation) and one belonging to the axis space (finite element solution). The displacements over the cross-section are approximated via a Unified Formulation (UF). A Lagrangian approximation is used along the beam axis. The resulting problems size is smaller than that of the classical equivalent finite element solution. The approach is, then, particularly attractive for higher-order beam models and refined axial meshes. The numerical investigations show that the proposed method yields accurate yet computationally affordable three-dimensional displacement and stress fields solutions.

Link

DOI: 10.1142/S1758825116500265