C-1-continuous time-domain spectral finite element for modeling guided wave propagation in laminated composite strips based on third-order theory

The model-based structural health monitoring techniques for composite structures based on guided waves demand fast and accurate computation of the wave propagation response. This article presents a computation-ally efficient and accurate time-domain spectral finite element to simulate ultrasonic guided wave propagation in laminated composite beam and infinite panel-type structures based on Levinson-Bickford-Reddy's refined third-order theory. The element has four degrees of freedom (DOFs) per node, irrespective of the number of layers in the laminate. The C1-continuity of the deflection as required by the theory is achieved by employing the generalized Hermite-type spectral Lobatto basis functions, developed recently by the authors, while the C0-continuous Lobatto basis functions interpolate the axial displacement and shear rotation. The governing equations are derived using Hamilton's principle. A detailed numerical study is performed to assess the new element's accuracy, efficiency, and convergence for free vibration, Lamb wave propagation of fundamental symmetric and anti-symmetric modes, and impact wave propagation of composite beams and infinite panels. The study reveals that the new spectral element predicts more accurate, faster converged, and efficient solutions than its conventional counterpart and other available C0-continuous spectral elements with a layer-independent number of DOFs for composite structures.