Finite difference technique for the evaluation of the transverse displacements in force-based beam finite elements

In force-based beam finite elements, cross-section transverse displacements are often needed for post-processing purposes and for geometrically nonlinear structural analysis. This involves the complex integration of the cross-section strains along the beam axis, typically done by the Curvature and Shear Based Displacement Interpolation (CSBDI) technique. Although, the CSBDI is sufficiently accurate for standard applications, this may cause numerical issues when many quadrature cross-sections are placed along the element length. This work presents a novel technique for computing the transverse displacements of a 3D Timoshenko beam, based on a finite difference approximation of the bending and shear compatibility conditions, which avoids the issues of the CSBDI. The proposed technique is introduced in a force-based finite element formulation with moderately large deformations, endowed with a corotational approach, suitable for analyzing geometrically nonlinear framed structures. Detailed investigation of the accuracy and efficiency of the proposed technique is conducted comparing its performance with that of the CSBDI approach.