A spectral finite element with embedded delamination for modeling of wave scattering in composite beams

A spectral finite element for modeling of wave scattering in laminated composite beam with embedded delamination is proposed. The method uses fast Fourier transform (FFT) for transformation of the temporal variables into frequency dependent variables and conventional node-based finite element (FE) approach for spatial discretization in frequency domain. The base-laminates and the sub-laminates are treated as structural waveguides, which form the internal spectral elements. The region of delamination is modeled by assuming constant cross-sectional rotation. Equilibrium at the interfaces between the base-laminate and the sub-laminates is imposed using efficient matrix methodology. The internal element nodes are finally condensed to form a single equivalent beam element with embedded delamination and is called damaged spectral element. Only three quantities need to be specified for automated construction of the proposed element. These are the local coordinates of one of the delamination tips and delamination length. The main advantage is the easy insertion of delamination in finite element model and efficient correlation of measured waveforms in structural health monitoring applications. Response predicted by the proposed model has been compared with 2D FE analysis and fairly matching results are found. Sensitivity studies due to parametric variation in delaminated configuration are performed. Methodologies to identify locations and extent of delaminations for structural diagnostics are also highlighted.

[1]  Warna Karunasena,et al.  Plane-strain-wave scattering by cracks in laminated composite plates , 1991 .

[2]  Gui-Rong Liu.  A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates , 2002 .

[3]  C. Jebaraj,et al.  SENSITIVITY ANALYSIS OF LOCAL/GLOBAL MODAL PARAMETERS FOR IDENTIFICATION OF A CRACK IN A BEAM , 1999 .

[4]  Usik Lee,et al.  Determination of Nonideal Beam Boundary Conditions: A Spectral Element Approach , 2000 .

[5]  Thomas Farris,et al.  A Global/Local approach to lengthwise cracked beams: dynamic analysis , 1991 .

[6]  S. Chinchalkar.  DETERMINATION OF CRACK LOCATION IN BEAMS USING NATURAL FREQUENCIES , 2001 .

[7]  Francois Leonard,et al.  FREE-VIBRATION BEHAVIOUR OF A CRACKED CANTILEVER BEAM AND CRACK DETECTION , 2001 .

[8]  J. N. Reddy,et al.  Modeling of delamination in composite laminates using a layer-wise plate theory , 1991 .

[9]  Grant P. Steven,et al.  VIBRATION-BASED MODEL-DEPENDENT DAMAGE (DELAMINATION) IDENTIFICATION AND HEALTH MONITORING FOR COMPOSITE STRUCTURES — A REVIEW , 2000 .

[10]  Sathya Hanagud,et al.  Dynamics of delaminated beams , 2000 .

[11]  Huai Min Shang,et al.  A strip-element method for analyzing wave scattering by a crack in a fluid-filled composite cylindrical shell , 2000 .

[12]  Costas Soutis,et al.  A structural health monitoring system for laminated composites , 2001 .

[13]  R. Gadelrab,et al.  THE EFFECT OF DELAMINATION ON THE NATURAL FREQUENCIES OF A LAMINATED COMPOSITE BEAM , 1996 .

[14]  Tribikram Kundu,et al.  Elastic wave scattering by cracks and inclusions in plates: in-plane case , 1992 .

[15]  D. Roy Mahapatra,et al.  Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities , 2002 .

[16]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

[17]  Guirong Liu,et al.  Locating and sizing of delamination in composite laminates using computational and experimental methods , 2001 .

[18]  Todd O. Williams,et al.  A generalized multilength scale nonlinear composite plate theory with delamination , 1999 .

[19]  Takahiro Hayashi,et al.  Multiple reflections of Lamb waves at a delamination. , 2002, Ultrasonics.

[20]  Junji Tani,et al.  Transient Waves in Anisotropic Laminated Plates, Part 1: Theory , 1991 .

[21]  Constantinos Soutis,et al.  Application of the Rapid Frequency Sweep Technique for Delamination Detection in Composite Laminates , 1999 .

[22]  A. S. Naser,et al.  Structural Health Monitoring Using Transmittance Functions , 1999 .

[23]  P. Cawley,et al.  The interaction of Lamb waves with delaminations in composite laminates , 1993 .

[24]  James F. Doyle,et al.  Wave Propagation in Structures , 1989 .

[25]  Siak Piang Lim,et al.  Study on characterization of horizontal cracks in isotropic beams , 2000 .

[26]  Jan Drewes Achenbach,et al.  Strip Element Method to Analyze Wave Scattering by Cracks in Anisotropic Laminated Plates , 1995 .

[27]  D. Roy Mahapatra,et al.  A spectral finite element model for analysis of axial–flexural–shear coupled wave propagation in laminated composite beams , 2003 .

[28]  Mark J. Schulz,et al.  Locating Structural Damage Using Frequency Response Reference Functions , 1998 .

[29]  P. M. Mujumdar,et al.  Flexural vibrations of beams with delaminations , 1988 .

[30]  A. H. Shah,et al.  Scattering of lamb waves by a normal rectangular strip weldment , 1991 .

[31]  D. Roy Mahapatra,et al.  Spectral-Element-Based Solutions for Wave Propagation Analysis of Multiply Connected Unsymmetric Laminated Composite Beams , 2000 .

[32]  Gerard C. Pardoen,et al.  Effect of Delamination on the Natural Frequencies of Composite Laminates , 1989 .