Bifurcation and stability of a three-hinged rod under a conservative load

The bifurcation solutions and their stability of a three-hinged rod under conservative compressive force are investigated. The equations for the system are non-linear, and possess some symmetry properties. The symmerty group concepts are employed to exploit these symmetry properties. The symbolic computer software, Mathematica, is used for the analytical and numerical solutions. The loci of codimension-one singularity are plotted on a two-dimensional control parameter space. These curves partition the parameter space into regions of qualitatively similar bifurcation diagrams. The bifurcation solutions and their stability at typical points in the parameter diagram, and the perturbation of codimension-one singularities are discussed.