Assessment of a simplified computational model for axial-lateral displacement of buckled beams

Source abstract

The paper presents an investigation of the relation between the axial and lateral displacement for an axially loaded beam under four different boundary conditions based on the infinitesimal strain theory. The mathematical model is developed by solving the buckling governing differential equation, where the use of geometric rules leads to a formula containing the axial and lateral displacement variables. For the purpose of practical use, the model is further simplified, and the solution of a radical equation is performed. The obtained results are compared with the finite-element simulation, where good agreement is achieved in the region of the infinitesimal strain theory validity, whereas significant discrepancies appear in the region of the finite-strain theory. The paper shows a limitation of the infinitesimal strain theory to derive a relation between the axial and lateral displacement and provides the displacement range where the mentioned theory may be used with negligible errors. The paper provides a simplified solution to model the presented problem and offers a practical alternative to more precise and complex models.