Development of an Equivalent Shell Finite Element for Modelling Damped Multi-Layered Composite Structures

Abstract

A new equivalent shell finite element (FE) for modelling damped multi-layered structures is presented in this study. The method used for developing the new FE for such structures is based on the idea that the strain energy of the equivalent single-layer FE must be equal to the sum of the strain energies of individual layers. The so-called energy coefficients are defined for this purpose for the extensional, bending and shear deformations of the composite structure. These coefficients are then determined and used as correction multipliers during stacking the elemental matrices of individual layers. Two approaches, based on second-order strain or stress distribution assumption through the composite thickness, are investigated for deriving the shear energy coefficients. The damping capability of the FE developed here originates from using complex Young's modulus to define the material properties of individual layers. The resulting equivalent single-layer shell element with four nodes has six degrees-of-freedom per node. The accuracy, advantages and limitations of the composite FE developed in this work are investigated using experimental as well as theoretical results. In the light of the finding of these investigations, further enhancement in the formulation is made by also utilising a new shear correction factor for the individual layers in the equivalent shell element. Final results for free- and constrained-layered structures confirm that the equivalent shell FE developed here can be used effectively for the prediction of the modal properties of damped multi-layered structures.