GBT-based dynamic analysis of thin-walled members with circular axis

This paper presents an extension of the linear Generalized Beam Theory (GBT) formulation for members with circular axis, previously developed by the authors Peres et al., (2016), Peres et al., (2018), to the linear dynamic case. The proposed formulation makes it possible to calculate natural frequencies (and associated vibration mode shapes) and time-history responses of members with circular axis and arbitrary flat-walled cross-sections, undergoing complex global–distortional–local deformation. The remarkable modal decomposition features of GBT, stemming from the fact that the kinematic description of the beam is based on a superposition of structurally meaningful cross-section deformation modes, render the finite element implementation of the proposed formulation extremely accurate and computationally efficient, as demonstrated in the illustrative numerical examples presented throughout the paper. Both standard (displacement-based) and mixed (strain–displacement-based) finite elements are implemented and it is concluded that the predictive capacity of the latter is superior, as it is insensitive to the various forms of membrane locking appearing in curved members, even though it does not involve additional DOFs (the strain DOFs are eliminated from the element stiffness matrix).