Effects of Curvature on the Nonlinear Behaviour of Elastic Arches

摘要

Arches are structures which combine the bending member function of transmittingtransverse forces with the compression member function of transmitting axial forces. The axial deformations of an arch affect its deformed curvatures, giving rise to some high order curvature terms. These terms are not usually considered in the conventional nonlinear analysis of elastic arches, and their effects have not been investigated adequately. This paper develops a new curved finite element model for the nonlinear analysis of elastic arches which includes the effects of the high order terms in the deformed curvatures, and investigates the effects of these terms on the in-plane nonlinear behavior of elastic arches. The use of deformed curvatures with these high order terms can describe the deformations of arches more accurately. Numerical examples demonstrate that the model is efficient, effective and accurate and that the effects of the high order curvature terms on the in-plane nonlinear behavior of arches are significant in some cases. The nonlinear buckling and postbuckling behaviors of elastic pin-ended arches subjected to uniformly distributed radial loads are investigated numerically using the model. It is found that the existence of a linear bifurcation buckling load is not a sufficient conditions for linear bifurcation buckling to occur; that the effects of prebuckling deformations on the buckling of shallow arches are significant; and that the nonlinear buckling loads may be much lower than the linear buckling loads.