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.