Efficient Layerwise Time-Domain Spectral Finite Element for Guided Wave Propagation Analysis of Multi-layered Panels

Abstract

Guided wave-based structural health monitoring techniques require accurate and fast simulation tools for high-frequency wave propagation in the laminate structures. This article develops an accurate and computationally efficient time-domain spectral finite element (SFE) for wave propagation analysis of laminated composite and sandwich beam and panel-type structures based on the efficient layerwise zigzag theory. It considers the axial displacement to follow a global third-order variation with a layerwise linear variation across the thickness. The independent variables are reduced to only three by imposing the interfacial continuity of transverse shear stress and shear traction-free conditions at the top and bottom surfaces. Regardless of the number of layers in the laminate, the element has only four degrees of freedom (DOFs) per node $u_0$, $w_0$, $\frac{dw_0}{dx}$, and $\psi _0$. The deflection $w_0$ is interpolated using the C$^1$-continuous Lobatto basis function, whereas $u_0$ and $\psi _0$ employ the C$^0$-continuous Lobatto basis shape functions. A thorough numerical study is accomplished to validate and evaluate the proposed element’s accuracy and efficiency for free vibration and Lamb wave propagation analysis of laminated composite and sandwich panels. The study reveals that the developed element is superior to its conventional counterpart and other existing 1D elements with a similar number of DOFs.