Leveraging spectral analysis to elucidate membrane locking and unlocking in isogeometric finite element formulations of the curved Euler–Bernoulli beam

In this paper, we take a fresh look at using spectral analysis for assessing locking phenomena in finite element formulations. We propose to “measure” by comparing the difference between eigenvalue and mode error curves computed on coarse meshes with “asymptotic” “overkill” meshes, both plotted respect normalized number. To demonstrate intimate relation membrane accuracy, focus example of circular ring discretized isogeometric curved Euler–Bernoulli beam elements. show that transverse-displacement-dominating modes are locking-prone, while circumferential-displacement-dominating naturally locking-free. use errors assess five formulations terms their locking-related efficiency: displacement-based formulation full reduced integration three locking-free based B-bar, discrete strain gap Hellinger–Reissner methods. Our study shows uncovers effects across spectrum eigenvalues eigenmodes, rigorously characterizing unlocking