Rigid body qualified curved beam approach for lateral torsional buckling of arches

Abstract

The curved beam finite element approach based on the potential energy formulation is widely recognized as a versatile tool for lateral torsional buckling analysis of arches. However, there exist a variety of potentials, which were developed with distinct assumptions. The diversity of energy-based curved beam theories introduces confusions in practical applications. This paper aims to examine various potential energy formulations as to whether or not they obey the rigid body rule which is a prerequisite for valid second-order analysis. The induced moments at the ends of curved beam element that have been neglected from and/or the distributed moments that should be removed from available potentials are identified to help them become rigid body qualified. Based on the revised potential functional, a curved beam finite element formulation has been developed to effectively predict yet with less effort the out-of-plane critical load for circular and parabolic arches subject to various loading and constraint conditions. The results of numerical examples demonstrate that a potential energy formulation eligible for describing the out-of-plane behavior of curved beam is required to be rigid body qualified by fulfilling two aspects: (i) the neglected end moments that are imperative for satisfying the rigid body rule must be considered unless the virtual work done by them vanishes, and (ii) undesirable distributed moments that may be induced when undergoing the rigid body motion should be removed by considering all essential potential components.