Detection of symmetry breaking bifurcations using finite element analysis packages

Abstract

Trusses with geometric and loading symmetries have been used in many structures to reduce the complexity of the design. Slight asymmetries in geometry and in loading could lead to bifurcation in the structural response. Failure of such structures still occur occasionally causing major damage to the property and to the human lives. A fully nonlinear structural analysis is expected to detect such symmetry breaking bifurcations. In this paper, we conducted the bifurcation analysis of a two-bar truss and a shallow arch structure with seven bars. Two program packages Gesa and Ansys based on finite elements method have been used to detect the symmetry breaking bifurcation points. However, unlike typical bifurcation analysis packages they cannot detect the bifurcation point without inserting a small perturbation in the initial geometry or the loading of the structure. Such a bifurcation can be easily missed in finite element-based analysis. The theoretical analysis reveals that the bifurcation leads to a much lower critical load in the presence of small asymmetry compared to the symmetric case. The results are verified by using Gesa program in Matlab for fully nonlinear analysis and with results by using Ansys commercial program. The two structural examples serve to illustrate the limitations of widely used finite element analysis packages for nonlinear bifurcation analysis.