Variationally consistent Elishakoff beam theory: Two finite element implementations and application to flexural wave propagation in carbon nanotubes.

In this contribution, a variationally consistent novel Elishakoff beam theory considering long-range interactions has been developed, which succeeds in emulating the dynamic behaviour of CNTs with both (5,5) and (10,10) armchairs, something that has not been attained previously. This theory is based on the modification of the Timoshenko one, and is taken here for the first time as a basis for two finite element implementations, their equations of motion been written either as a coupled set of equations in terms of displacement and rotation (reducible formulation) or as a single equation in terms of displacement only (irreducible formulation). Both stability and accuracy analyses are performed, concluding that the irreducible form allows longer time steps, while providing appropriate accuracy throughout the whole wavenumber range. [Display omitted] • A novel variationally consistent Elishakoff beam theory has been here developed. • The dynamic behaviour of both (5,5) and (10,10) CNTs is successfully emulated. • Long-range forces are cleverly considered here by increasing the potential energy. • This theory underlies two finite element implementations (reducible and irreducible). • Stability and accuracy analyses reveal a superior performance of the irreducible form. [ABSTRACT FROM AUTHOR]