Large Deformations and Stability of the Two-Bar Truss Under Vertical Loads

Analytical formulations for the static equilibrium of truss structures are often based on concepts of linear elasticity. Geometric nonlinearities are taken into account, but the nonlinear constitutive behavior of the material is not considered. However, the assumption of linear elastic material is not consistent with the response of solids subjected to large deformations. In light of this, accurate models must take into account both geometric and constitutive nonlinearities. In the present work, we investigate the problem of the von Mises (or two-bar) truss subjected to a vertical load. The bars of the truss are composed of rubber so as to observe large displacements and deformations. We propose a theoretical model that is entirely developed in three-dimensional nonlinear elasticity. A compressible Mooney-Rivlin law is employed for the constitutive behavior of the rubber. Experimental tests on the von Mises truss subjected to a vertical load are carried out. Snap-through is observed and good agreement is found with the analytical predictions. Finally, a simple formulation to predict the critical Euler buckling load is presented and validated through experimental observation.