1. Problem position

In the field of modeling of beam elements, there are a large number of theories to describe kinematics (Euler-Bernoulli, Timoshenko, Vlassov,…) and Code_Aster naturally includes a declination of these theories into as many finite element models (POU_D_E, POU_D_T, POU_D_TG).

In addition to the hypotheses on which they are based, these models can be enriched with non-linear behavior whether of material origin (plasticity criterion for beams, 1D behavior based on a fiber description) or geometric (large displacements and large three-dimensional rotations).

This document describes element POU_D_TGM, which is based on a Timoshenko model with Vlasov’s awkward twist. This element combines a fiber description of the section to benefit from a non-linear 1D behavior in traction-compression/flexure and second-order kinematics to allow a description in large displacements and large rotations.

The focus will be on the geometric aspect, with multi-fiber behavior being addressed in detail in.