Finite difference integration for the computation of force-based beam transverse displacements

Numerous engineering problems require the mechanical simulation of framed structures, which can easily undergo significant deformation. Neuenhofer and Filippou introduced an improved force-based beam model that addresses geometric nonlinearities by expressing the element equilibrium in the deformed state. To this end, transverse displacements are determined through a numerical technique based on the interpolation of bending curvatures and shear deformations, which, however, proves numerically unstable and leads to substantial errors in certain simulations. This work investigates the use of a new technique based on a finite difference approximation of the second-order derivative of the displacement fields. The technique offers equivalent accuracy and computational cost, but greater robustness compared to the original approach.