Application of the Southwell Method to Determine the Critical Load of Compression Rods Made of Nonlinear Materials

Experimental determination of the critical force of a compression bar made of linear material does not pose major problems. The widely used Southwell method is also applicable to bars with cross-sections varying in length. The purpose of the research undertaken was to demonstrate that this method can also be successfully applied to bars made of elastic materials exhibiting nonlinear σ(ε) characteristics. Using analytical relationships for a rod satisfying the assumptions of Euler-Bernoulli theory, F(δ) relationships were derived for a rod with an initial arc imperfection, and Southwell diagrams were constructed on this basis. Nonlinear equilibrium paths F(δ) were also determined numerically using the COSMOS/M program for this purpose. For the pre-assumed different nonlinear characteristics, full confirmation of the validity of the application of the Southwell method for determining the critical force was obtained.