Non-Linear Elastic Beam Deformations with Four-Parameter Timoshenko Beam Element Considering Through-the-Thickness Stretch Parameter and Reduced Integration

Abstract

In this work, non-linear elastic deformations of beams are investigated. The kinematics of the beam is derived based on an element with four-parameter containing a through-the-thickness stretch parameter to avoid Poisson locking. Moreover, the Kirchhoff-Saint Venant model is used to derive kinetic quantities. Next, a non-linear FE formula in Total Lagrangian form is obtained, and three-node beam element with two-node reduced integration is employed to avoid shear locking. Finally, to evaluate the performance of the derived formulations, some examples are provided. The results prove that the current formulation is in very good agreement with those available in the literature. More importantly, the formulation is capable of predicting the experimental results with high accuracy.