On buckling of non-uniform shallow arch under a central concentrated load

Abstract

This paper presents analytical study of a non-uniform shallow arch under a central concentrated load. The non-uniformity is characterized by three constant stiffness regions. The least potential energy principle is used to obtain the equilibrium equations. The anti-symmetric buckling axial compression and buckling modes are shown to be identical with those of Euler-Bernoulli beam. The initial imperfection effect is also investigated theoretically and a parametric study on the different geometric parameters has been carried out on the snap-through symmetric buckling load and anti-symmetric buckling load. The comparison against the finite element analysis shows the accuracy of the theoretical model. We show that the stiffer center case is always economically better than the stiffer end case. The two limiting cases with largest degree of non-uniformity are analytically analyzed by using the augmented potential energy with the Lagrangian multiplier. The closed-form condition for the occurrence of symmetric snap-through buckling is presented for one limiting case. This paper serves to enhance the understanding of the effect of the non-uniformity of shallow arch on its load carrying capacity.