Elastica buckling analysis of a simple frame (Q1073616)

A nonlinear stability analysis based on an analytical approach of elastic type is performed for the first time on a simple two-bar frame. In order to obtain an exact determination of its buckling and postbuckling behavior the effect of compressibility of the bar centroidal axis is taken into account. This effect implies very slight increase in the buckling load which can be safely ignored. Moreover, it is found that even in the most extreme cases of geometry and stiffness, the critical buckling displacements are of negligibly small magnitude contrary to existing results obtained by the nonlinear kinematic stability analysis. The two foregoing findings enable us to replace the limit point by a bifurcation point. Such a simplification, being correct in an asymptotic sense, allows the application of a stability analysis of frames by considering their bars as incompressible. A variety of numerical results shows the degree of accuracy and the range of applicability of the aforementioned nonlinear kinematic stability analysis by comparing it with the exact method of stability analysis proposed herein.