A spectral finite element model for analysis of axial–flexural–shear coupled wave propagation in laminated composite beams

Abstract

A spectral finite element model (SFEM) for analysis of axial–flexural–shear coupled wave propagation in thick laminated composite beams is presented. Range of validity of the first order shear deformation in the context of higher order Lamb wave modes is discussed. Concept of spectral element shape function, dynamic strain–displacement matrix and dynamically consistent force vector are derived. An exact dynamic stiffness matrix is derived, which is used in finite element (FE) analysis. Computation is performed in the Fourier domain at FFT sampling points over broad frequency band. Post-processing of the response is performed in both the frequency domain as well as in the time domain, which is suitable for structural diagnostics and broad-band wave propagation problems. To extend the range of engineering applications of SFEM, linear damping models are formulated. Effect of viscous damping on group speeds and wave amplitudes are studied for graphite–epoxy composite beams. Response under impact type loading is compared with time domain FE results. Numerical examples are presented, where the effect of axial–flexural–shear coupling is characterized. Efficient application of the model is shown considering laminated beam with ply-drops. Also a global/local model for estimation of Mode-II crack tip field in a delaminated thick composite beam is presented.