Wavelet spectral finite element modeling for wave propagation in adhesively bonded composite joints

摘要

Transient dynamics and wave propagation across adhesively bonded lap joints are studied using the wavelet spectral finite element (WSFE) method. The adherands are considered as shear deformable plates with five degrees of freedom describing in-plane and out-of-plane displacements. Partial differential equations, governing the wave motion of adherands, are derived using Hamilton's principle. The adhesive layer is assumed to be a linearly distributed shear and transverse normal springs. The governing PDEs are coupled due to the presence of the adhesive layer, making it very complex to solve. The WSFE method is used for solving the differential equations. In WSFE, time and one spatial dimension are approximated using Daubechies scaling functions, reducing the PDEs to ODEs which are functions of one spatial dimension only. The ODEs are solved exactly by assuming a harmonic solution in the transformed frequency-wavenumber domain. The solution is validated with conventional finite element simulations performed using the commercial software ABAQUS. Additional examples are provided to demonstrate the utility of the model in order to understand complex the wave propagation mechanism through bonded lap joints.