A layerwise time domain spectral finite element method for guided wave propagation analysis in laminated composite and sandwich beams

Layerwise (LW) linear displacement theories, which are based on an expansion of Mindlin’s first-order shear deformation theory (FSDT) in each layer, are often employed for static and vibration analyses of composite and sandwich beams, plates, and shells; however, no spectral element has yet been developed based on these theories for guided wave propagation in such structures. In this article, a time domain spectral finite element method (SFEM) based on a layerwise linear displacement theory, which directly imposes displacement continuity between the individual layers, is developed for the first time to analyze ultrasonic guided wave propagation in laminated composite and sandwich beams. The effectiveness of the proposed method is validated with the published results from the literature. The numerical study reveals that the developed LW-SFEM predicts more accurate and efficient solutions than the FSDT based SFEM and the conventional FEM. The FSDT-SFEM fails to predict the antisymmetric mode wave propagation response in sandwich beams correctly, yielding errors as high as 55% compared to the semi-analytical finite element solutions. In comparison to LW-SFEM, the conventional FEM needs more than 4.28 times the degrees of freedom and 4.04 times the computing time to obtain the same level of accuracy for the same problem.