Dulip Samaratunga

Wavelet spectral finite element for modeling guided wave propagation and damage detection in stiffened composite panels

Ultrasonic-guided wave propagation in stiffened composite panels is modeled using the wavelet spectral finite element method. The model is capable of analyzing transient response resulting from loads with short time duration, such as impacts. The model can also be used to predict the response for known excitations commonly used in ultrasonic wave–based structural health monitoring/nondestructive inspection systems. Wavelet spectral finite element is an efficient and accurate technique for wave propagation modeling in structures. Governing equations of laminated plate elements used in the model are based on the first-order shear deformation theory, which yields accurate solutions up to wavelengths close to plate thickness. Daubechies compactly supported scaling functions are used to approximate the partial differential equations in time and one spatial dimension. Resulting ordinary differential equations are rearranged and solved for wavenumbers by assuming a harmonic solution in the transformed frequency-wavenumber domain. The global dynamic stiffness matrix of the spectral plate element is formed relating transformed nodal forces and displacements. Stiffened panel is then assembled following a procedure similar to conventional finite element method, and the resulting matrix equation is solved in the frequency-wavenumber domain. Wavelet spectral finite element results are validated with conventional finite element simulations performed in Abaqus®. In addition to transient response prediction, the usefulness of wavelet spectral finite element–based skin–stiffener model is shown in structural health monitoring for detecting skin–stiffener debond and transverse surface crack.

Wavelet Spectral Finite Element Based User-Defined Element in ABAQUS for Modeling Delamination in Composite Beams

Wave propagation in a delaminated composite beam is investigated using the wavelet spectral finite element (WSFE) method. WSFE-based elements are implemented in Abaqus® through the user-defined element (UEL) option. Since Abaqus® operations can use real values only, all complex numbers in WSFE model are decoupled into real and imaginary parts and their real numbers are used in the computations. Final solution is obtained by forming a complex value using the two real number solutions. For modeling delamination, a beam is divided into two base-laminates (for parts of the beam without delamination) and two sub-laminates covering the delamination zone. Multi-point constraint (MPC) subroutine in Abaqus® is used to define the displacement relation between nodes of these four parts of the delaminated beam. Wave motion predicted by the UEL is validated with 2D finite element method (FEM) analysis using Abaqus®. The developed UEL largely retains computational efficiency of the WSFE method and extends its ability to model complex features (such as a delamination).

The Wavelet Spectral Finite Element-based user-defined element in Abaqus for wave propagation in one-dimensional composite structures

A Wavelet Spectral Finite Element (WSFE)-based user-defined element (UEL) is formulated and implemented in Abaqus (commercial finite element software) for wave propagation analysis in one-dimensional composite structures. The WSFE method is based on the first-order shear deformation theory to yield accurate and computationally efficient results for high-frequency wave motion. The frequency domain formulation of the WSFE leads to complex-valued parameters, which are decoupled into real and imaginary parts and presented to Abaqus as real values. The final solution is obtained by forming a complex value using the real number solutions given by Abaqus. Four numerical examples are presented in this article, namely an undamaged beam, a beam with impact damage, a beam with a delamination, and a truss structure. A multi-point constraint subroutine, defining the connectivity between nodes, is developed for modeling the delamination in a beam. Wave motions predicted by the UEL correlate very well with Abaqus simulations. The developed UEL largely retains the computational efficiency of the WSFE method and extends its ability to model complex features.

Wavelet Spectral Finite Element Modeling for Health Monitoring of Adhesively Bonded Joints

Wave propagation in an adhesively bonded lap joint is studied experimentally and the results are used to validate the Wavelet Spectral Finite Element (WSFE) lap joint model. A single lap joint made up of aluminum adherands bonded using epoxy adhesive is used as the test structure. A piezo electric (PZT) transducers bonded on the test structure is used as the pulser, which is excited with a tone burst signal. The structure is mode-tuned to determine the optimum excitation frequency range. The dynamic forces exerted on the test structure by the bonded PZT are determined using Finite Element Analysis (FEA) and employed as the input forces for the WSFE simulations. The results obtained from WSFE and experiments are compared at multiple locations on the test structure for several excitation frequencies. The WSFE and experimental results show a very good agreement and waves propagating past the lap joint are very sensitive to adhesive strength.

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

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.

Wavelet spectral finite element method for modeling wave propagation in stiffened composite laminates

Ultrasonic wave propagation in composite panels with stiffener is studied using wavelet spectral finite element (WSFE) method. WSFE is used to model dynamics of 2D finite composite panels with stiffeners accurately. Transverse shear flexibility is included in the model such that the accuracy holds up to wavelengths close to plate thickness. The global dynamic stiffness matrix of the structure is assembled following a procedure similar to regular finite element method and then solved in frequency-wavenumber domain. Wavelet transform is used to approximate the wave equations in time and one spatial dimension. WSFE results are validated with regular finite element method using Abaqus ® . The utility of 2D WSFE based models to analyze built-up composite structures is shown in the context of skin-stiffener debonding detection..

Experimental Identification of Delamination Size and Location Based on Signal Correlations

The paper presents a study of delamination damage identification and experimental investigation of composite plates based on Lamb wave structural health monitoring data. The delamination damage identification method identify the existence and location of the delamination using the concept of peak amplitude decrease factor computed from Lamb wave data of two adjacent sensing positions. The delamination damage can be located by the monotonicity change of the peak amplitude decrease factors. Experimental study is carried out to investigate the effectiveness of the identification method. The experimental testing consists of generating Lamb wave signals with piezoelectric sensors on four composite plates with different healthy states and acquiring data at four different sensing positions on each of the plates using Laser Doppler Vibrometer. The experimental results and the identification method results are compared.