A new time domain spectral plate finite element (FE) is developed to provide fast numerical calculations of guided waves and transient phenomena in laminated composite and sandwich plates. A new multifield layerwise laminate theory provides the basis for the FE, which incorporates cubic Hermite polynomial splines for the approximation of the in-plane and transverse displacement fields through the thickness of the plate, enabling the modeling of symmetric and antisymmetric wave modes. The time domain spectral FE with multi-degrees-of-freedom (DOF) per node is subsequently formulated, which uses integration points collocated with the nodes to yield consistent diagonal lumped mass matrix which expedites the explicit time integration process. Numerical simulations of wave propagation in aluminum, laminated carbon/epoxy and thick sandwich plates are presented and validated with an analytical solution and a three-dimensional (3D) solid element; moreover, the capability to accurately and rapidly predict antisymmetric and symmetric guided waves is demonstrated.
Issue Section:
Research Papers
Keywords:
Dynamics
References
1.
Diaz Valdes
, S. H.
, and Soutis
, C.
, 2000
, “Health Monitoring of Composites Using Lamb Waves Generated by Piezoelectric Devices
,” Plast. Rubber Compos.
, 29
(9
), pp. 475
–481
.2.
Giurgiutiu
, V.
, 2005
, “Tuned Lamb Wave Excitation and Detection With Piezoelectric Wafer Active Sensors for Structural Health Monitoring
,” J. Intell. Mater. Syst. Struct.
, 16
(4
), pp. 291
–305
.3.
Raghavan
, A.
, and Cesnik
, C. E. S.
, 2005
, “Finite-Dimensional Piezoelectric Transducer Modeling for Guided Wave Based Structural Health Monitoring
,” Smart Mater. Struct.
, 14
(6
), pp. 1448
–1461
.4.
Crawley
, E. F.
, and Lazarus
, K. B.
, 1991
, “Induced Strain Actuation of Isotropic and Anisotropic Plates
,” AIAA J.
, 29
(6
), pp. 944
–951
.5.
Wang
, C. S.
, and Chang
, F. K.
, 2000
, “Diagnosis of Impact Damage in Composite Structures With Built-in Piezoelectrics Network
,” Proc. SPIE
3990
, pp. 13
–19
.6.
Diamanti
, K.
, Soutis
, C.
, and Hodgkinson
, J. M.
, 2007
, “Piezoelectric Transducer Arrangement for the Inspection of Large Composite Structures
,” Composites Part A
, 38
(4
), pp. 1121
–1130
.7.
Velichko
, A.
, and Wilcox
, P. D.
, 2007
, “Modeling the Excitation of Guided Waves in Generally Anisotropic Multilayered Media
,” J. Acoust. Soc. Am.
, 121
(1
), p. 60
.8.
Sikdar
, S.
, and Banerjee
, S.
, 2016
, “Guided Wave Propagation in a Honeycomb Composite Sandwich Structure in Presence of a High Density Core
,” Ultrasonics
, 71
, pp. 86
–97
.9.
Santoni-Bottai
, G.
, and Giurgiutiu
, V.
, 2012
, “Exact Shear-Lag Solution for Guided Waves Tuning With Piezoelectric-Wafer Active Sensors
,” AIAA J.
, 50
(11
), pp. 2285
–2294
.10.
Yu
, L.
, Bottai-Santoni
, G.
, and Giurgiutiu
, V.
, 2010
, “Shear Lag Solution for Tuning Ultrasonic Piezoelectric Wafer Active Sensors With Applications to Lamb Wave Array Imaging
,” Int. J. Eng. Sci.
, 48
(10
), pp. 848
–861
.11.
Raghavan
, A.
, and Cesnik
, C. E. S.
, 2007
, “3-D Elasticity-Based Modeling of Anisotropic Piezocomposite Transducers for Guided Wave Structural Health Monitoring
,” ASME J. Vib. Acoust.
, 129
(6
), p. 739
.12.
Banerjee
, S.
, and Pol
, C. B.
, 2012
, “Theoretical Modeling of Guided Wave Propagation in a Sandwich Plate Subjected to Transient Surface Excitations
,” Int. J. Solids Struct.
, 49
(23–24
), pp. 3233
–3241
.13.
Ahmad
, Z. A. B.
, Vivar-Perez
, J. M.
, and Gabbert
, U.
, 2013
, “Semi-Analytical Finite Element Method for Modeling of Lamb Wave Propagation
,” CEAS Aeronaut. J.
, 4
(1
), pp. 21
–33
.14.
Barouni
, A. K.
, and Saravanos
, D. A.
, 2016
, “Layerwise Semi-Analytical Method for Modeling Guided Wave Propagation in Laminated and Sandwich Composite Strips With Induced Surface Excitation
,” J. Aerosp. Sci. Technol.
, 51
, pp. 118
–141
.15.
Bartoli
, I.
, Marzani
, A.
, Lanza di Scalea
, F.
, and Viola
, E.
, 2006
, “Modeling Wave Propagation in Damped Waveguides of Arbitrary Cross-Section
,” J. Sound Vib.
, 295
(3–5
), pp. 685
–707
.16.
Marzani
, A.
, Viola
, E.
, Bartoli
, I.
, Lanza di Scalea
, F.
, and Rizzo
, P.
, 2008
, “A Semi-Analytical Finite Element Formulation for Modeling Stress Wave Propagation in Axisymmetric Damped Waveguides
,” J. Sound Vib.
, 318
(3
), pp. 488
–505
.17.
Datta
, S. K.
, Shah
, A. H.
, Bratton
, R. L.
, and Chakraborty
, T.
, 1988
, “Wave Propagation in Laminated Composite Plates
,” J. Acoust. Soc. Am.
, 83
(6
), pp. 2020
–2026
.18.
Nanda
, N.
, Kapuria
, S.
, and Gopalakrishnan
, S.
, 2014
, “Spectral Finite Element Based on an Efficient Layerwise Theory for Wave Propagation Analysis of Composite and Sandwich Beams
,” J. Sound Vib.
, 333
(14
), pp. 3120
–3137
.19.
Chrysochoidis
, N. A.
, and Saravanos
, D. A.
, 2009
, “High-Frequency Dispersion Characteristics of Smart Delaminated Composite Beams
,” J. Intell. Mater. Syst. Struct.
, 20
(9
), pp. 1057
–1068
.20.
Mullen
, R.
, and Belytschko
, T.
, 1982
, “Dispersion Analysis of Finite Element Semidiscretizations of the Two-Dimensional WaveEquation
,” Int. J. Numer. Methods Eng.
, 18
(1
), pp. 11
–29
.21.
Doyle
, J. F.
, 1997
, Wave Propagation in Structures
, Springer
, New York
.22.
Zak
, A.
, and Krawczuk
, M.
, 2010
, “Assessment of Rod Behaviour Theories Used in Spectral Finite Element Modelling
,” J. Sound Vib.
, 329
(11
), pp. 2099
–2113
.23.
Zak
, A.
, and Krawczuk
, M.
, 2012
, “Assessment of Flexural Beam Behaviour Theories Used for Dynamics and Wave Propagation Problems
,” J. Sound Vib.
, 331
(26
), pp. 5715
–5731
.24.
Ostachowicz
, W. M.
, 2008
, “Damage Detection of Structures Using Spectral Finite Element Method
,” Comput. Struct.
, 86
(3–5
), pp. 454
–462
.25.
Nanda
, N.
, and Kapuria
, S.
, 2015
, “Spectral Finite Element for Wave Propagation Analysis of Laminated Composite Curved Beams Using Classical and First Order Shear Deformation Theories
,” Compos. Struct.
, 132
, pp. 310
–320
.26.
Chakraborty
, A.
, and Gopalakrishnan
, S.
, 2005
, “A Spectrally Formulated Plate Element for Wave Propagation Analysis in Anisotropic Material
,” Comput. Methods Appl. Mech. Eng.
, 194
(42–44
), pp. 4425
–4446
.27.
Chakraborty
, A.
, and Gopalakrishnan
, S.
, 2006
, “A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate
,” ASME J. Vib. Acoust.
, 128
(4
), p. 477
.28.
Samaratunga
, D.
, Jha
, R.
, and Gopalakrishnan
, S.
, 2014
, “Wavelet Spectral Finite Element for Wave Propagation in Shear Deformable Laminated Composite Plates
,” Compos. Struct.
, 108
(1
), pp. 341
–353
.29.
Kudela
, P.
, Krawczuk
, M.
, and Ostachowicz
, W.
, 2007
, “Wave Propagation Modelling in 1D Structures Using Spectral Finite Elements
,” J. Sound Vib.
, 300
(1–2
), pp. 88
–100
.30.
Rekatsinas
, C. S.
, Nastos
, C. V.
, Theodosiou
, T. C.
, and Saravanos
, D. A.
, 2015
, “A Time-Domain High-Order Spectral Finite Element for the Simulation of Symmetric and Anti-Symmetric Guided Waves in Laminated Composite Strips
,” Wave Motion
, 53
, pp. 1
–19
.31.
Kudela
, P.
, Zak
, A.
, Ostachowicz
, W.
, Krawczuk
, M.
, Kudela
, P.
, Zak
, A.
, and Krawczuk
, M.
, 2007
, “Modelling of Wave Propagation in Composite Plates Using the Time Domain Spectral Element Method
,” J. Sound Vib.
, 302
(4–5), pp. 728
–745
.32.
Zak
, A.
, Krawczuk
, M.
, and Ostachowicz
, W.
, 2006
, “Propagation of in-Plane Elastic Waves in a Composite Panel
,” Finite Elem. Anal. Des.
, 43
(2
), pp. 145
–154
.33.
Kim
, Y.
, Ha
, S.
, and Chang
, F.-K.
, 2008
, “Time-Domain Spectral Element Method for Built-In Piezoelectric-Actuator-Induced Lamb Wave Propagation Analysis
,” AIAA J.
, 46
(3
), pp. 591
–600
.34.
Ha
, S.
, and Chang
, F.-K.
, 2010
, “Optimizing a Spectral Element for Modeling PZT-Induced Lamb Wave Propagation in Thin Plates
,” Smart Mater. Struct.
, 19
(1
), p. 15015
.35.
Komatitsch
, D.
, Barnes
, C.
, and Tromp
, J.
, 2000
, “Simulation of Anisotropic Wave Propagation Based Upon a Spectral Element Method
,” Geophysics
, 65
(4
), p. 1251
.36.
Li
, F.
, Peng
, H.
, Sun
, X.
, Wang
, J.
, and Meng
, G.
, 2012
, “Wave Propagation Analysis in Composite Laminates Containing a Delamination Using a Three-Dimensional Spectral Element Method
,” Math. Probl. Eng.
, 2012
, pp. 1
–19
.37.
Peng
, H.
, Meng
, G.
, and Li
, F.
, 2009
, “Modeling of Wave Propagation in Plate Structures Using Three-Dimensional Spectral Element Method for Damage Detection
,” J. Sound Vib.
, 320
(4–5
), pp. 942
–954
.38.
Rekatsinas
, C. S.
, and Saravanos
, D. A.
, 2016
, “A Time Domain Spectral Layerwise Finite Element for Wave SHM in Composite Strips With Physically Modelled Active Piezoelectric Actuators and Sensors
,” J. Intell. Mater. Syst. Struct.
, (epub).39.
Plagianakos
, T. S.
, and Saravanos
, D. A.
, 2009
, “Higher-Order Layerwise Laminate Theory for the Prediction of Interlaminar Shear Stresses in Thick Composite and Sandwich Composite Plates
,” Compos. Struct.
, 87
(1
), pp. 23
–35
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