Delamination effect on response of a composite beam by wavelet spectral finite element method

Transform methods are very useful to solve the ordinary and partial differential equations. Fourier and Laplace transforms are the most commonly used transforms. Wavelet transforms are most popular with electrical and communication engineers to analyse the signals. From last few years, Wavelet transforms are in use for structural engineering problems, like solution of ordinary and partial differential equations. Dynamical problems in structural engineering fall under two categories, one involving low frequencies (structural dynamics problems) and the other involving high frequencies (wave propagation problems). Spectral Finite Element (SFE) method is a transform method to solve the high frequency excitation problems which are encountered in structural engineering. SFE based on Fourier transforms has high limitations in handling finite structures and boundary conditions. SFE based with wavelet transforms is a very good tool to analyse the dynamical problems and eliminate many limitations. In this project, a model for embedded de-laminated composite beam is developed using the wavelet based spectral finite element (WSFE) method for the de-lamination effect on response using wave propagation analysis. The simulated responses are used as surrogate experimental results for the inverse problem of detection of damage using wavelet filtering. The technique used to model a structure that, through width de-lamination subdivides the beam into base-laminates and sub-laminates along the line of de-lamination. The base-laminates and sub-laminates are treated as structural waveguides and kinematics are enforced along the connecting line. These waveguides are modeled as Timoshenko beams with elastic and inertial coupling and the corresponding spectral elements have three degrees of freedom, namely axial, transverse and shear displacements at each node. The internal spectral elements in the region of de-lamination are assembled assuming constant cross sectional rotation and equilibrium at the interfaces between the base-laminates and sub-laminates. Finally, the redundant internal spectral element nodes are condensed out to form two-noded spectral elements with embedded de-lamination. The response is being obtained by coding programs in MATLAB