Free vibration analysis of cross-ply laminated beam structures using refined beam theories and B-spline basis functions

Abstract

In this article, 1 D refined beam theories based on Carrera Unified Formulation (CUF) and the Isogeometric approach (IGA) are synthesized for the free vibration analysis of laminated beam structures. The B-spline basis functions utilized in IGA are employed to approximate the displacement field due to their interesting features in analysis. Taylor expansions are utilized in the framework of CUF which presents finite element matrices in the form of fundamental nuclei that is independent of type and order of expansion. Higher-order B-spline basis functions attenuate the effect of shear locking properly and higher-order theories presented by CUF are free from Poisson locking phenomenon and utilizations of shear correction factor. Also, equivalent single layer (ESL) models have been utilized as a solution field description approach. Several numerical results including composite beams are carried out and it is shown that coupling IGA and CUF ends in a suitable methodology to analyze laminated beam structures.

Keywords:

• B-spline functions
• refined beam theories
• free vibration
• carrera unified formulation
• laminated beams