An exact high order beam element

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Hierarchical theories of structures based on Legendre polynomial expansions with finite element applications (2017, methodology): “The stiffness terms were obtained by Eisenberger [10] directly from the governing differential equations that describe the deformations of the cross-section for higher-order theories.”
Non-uniform warping including the effects of torsion and shear forces. Part I: A general beam theory (2007, background): “These theories have generally been performed to study, separately, the effects of torsional warping (Benscoter, 1954; Vlasov, 1961; Batoz and Dhatt, 1990; Mentrasti, 1991; Prokic̀, 1993; Gruttmann et al., 1999; Sapountzakis and Mokos, 2003, 2004; Roberts and Al-Ubaidi, 2001; Eisenberger, 2003; Saadé”
Refined beam elements with arbitrary cross-section geometries (2010, unknown): “Exact stiffness coefficients of a high-order isotropic beam element have been formulated by Eisenberger [12].”
Refined beam elements with only displacement variables and plate/shell capabilities (2012, background): “Petrolito [24] and Eisenberger [13] dealt with the exact stiffness matrix analysis of a high-order beam element: the refined displacement field was based on a cubic variation of the axial displacement over the cross-section of the beam whereas the lateral displacement was kept constant, and comparis”