Influence of chirality on buckling of inextensible rings subject to dead loading

A variational approach is studied to understand buckling of inextensible rings made from chiral filaments and subject to dead loading. In opposite to previous literatures in which only in-plane bifurcation is allowed, i.e., the ring deforms only in its plane, in this work we consider both in-plane and out-of-plane bifurcation, i.e., the ring deforms both in its plane and out of its plane. For circular rings made from filaments without chirality, we find that they lose instability via out-of-plane bifurcation at critical values of loading smaller than those published. For circular rings made from filaments with chirality, they lose instability via coupling between in-plane and out-of-plane bifurcation at critical values of loading smaller than those at which bifurcation would happen without chirality. The destabilizing effect of chirality, however, can be reduced by increasing the twisting rigidity relative to the bending rigidity.