A variational model is used to study the behavior of a flexible but inextensible loop spanned by a liquid film, with the objective of explaining the stability and buckling of flat circular configurations. Loops made from filaments with intrinsic curvature and/or intrinsic twist density are considered, but attention is restricted to filaments with circular cross sections and uniform mechanical properties. Loops made with intrinsic curvature but no intrinsic twist density exhibit in-plane and out-of-plane buckling modes corresponding to stable solution branches that bifurcate from the branch of flat circular solutions and out-of-plane buckling occurs at a lower value of the dimensionless surface tension of the liquid film than does in-plane buckling. Additionally, however, the destabilizing influence of the intrinsic curvature can be countered by increasing the torsional rigidity relative to the flexural rigidity. For a loop with both intrinsic curvature and intrinsic twist density, only one branch of stable solutions bifurcates from the flat circular solution branch, the in-plane and out-of-plane buckling modes are intertwined, and bifurcation occurs at a value of the dimensionless surface tension less than that governing the behavior of loops made from filaments that are intrinsically rectilinear. Moreover, increasing the torsional rigidity relative to the flexural rigidity has no or little stabilizing effect if the loop is either too short or too long and, in contrast to what occurs for loops with only intrinsic curvature, if the intrinsic twist density is sufficiently large then the destabilizing influence of the intrinsic curvature cannot be countered by increasing the torsional rigidity relative to the flexural rigidity, regardless of the length of the loop.

We use variational method to examine buckling of chiral elastic rings spanned by fluid films. We find that the critical surface tension of the fluid film at which buckling occurs depends on the degree of chirality, regardless whether the ring possesses left-handed chirality or right-handed chirality. Additionally, the chirality always has a destabilizing effect on buckling, yielding to buckle at a critical surface tension smaller than that of the achiral elastic rings. The destabilizing effect of chirality, however, can be reduced by increasing the twisting rigidity to bending rigidity of filaments (twist-to-bend ratio).