A Linearised θ Numerical Scheme for the Vibrations of Inextensible Beams

Abstract

A linearised finite element numerical scheme for the vibration of inextensible beams is developed. The proposed scheme is based on the methodology introduced by S. Bartels [15] and satisfies a linearised form of the inextensibility constraint. The time m arching procedure is based on repeated use of the theta-parameter integration quadrature. Three parameters are introduced in total and appropriately selected such that the energy conservation features are improved compared to the Bartels algorithm while the inextensibility constraint is satisfied as accurately as possible. Cubic Hermite polynomials are employed for the spatial discretisation. The Bartels algorithm is retrieved as a special case. Several numerical experiments are presented demonstrating the theoretically predicted enhanced inextensibility mimicking and optimum values of the method parameters are identified.