0
Research Papers

On the Accuracy of a Four-Node Delaminated Composite Plate Element and Its Application to Damage Detection

[+] Author and Article Information
Cesar F. Casanova

Department of Structural & Continuum
Mechanics,
Universitat Politècnica de València,
Spain;
Department of Applied Physics,
University of Granada,
Spain
e-mail: ceferca@cam.upv.es

A. Gallego

Department of Applied Physics,
University of Granada,
Spain
e-mail: antolino@ugr.es

M. Lázaro

Department of Structural & Continuum
Mechanics,
Universitat Politècnica de València,
Spain
e-mail: malana@mes.upv.es

The DKQ element is a C0 element.

|ΩfgdΩ|(Ωf2dΩ)1/2(Ωg2dΩ)1/2

For C1 bending elements, the trial solution w = {w0, θx0, θy0} H2 Sobolev space; analogously it can be proven that the composite element also passes the “Patch Test.”

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received August 1, 2012; final manuscript received March 5, 2013; published online June 19, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 135(6), 061003 (Jun 19, 2013) (10 pages) Paper No: VIB-12-1215; doi: 10.1115/1.4023994 History: Received August 01, 2012; Revised February 26, 2013

This paper presents a new four-node composite element, which incorporates nd delaminations through its thickness. Based on the extended finite element method (X-FEM) technology, the element is particularized on a CLT (classical laminate theory). Delamination is considered in the kinematic equations with additional degrees of freedom. The result is a four-node quadrilateral element requiring only two single FEM (finite element method) formulations, a bending one and a membrane one. An important result is that this formulation has the same accuracy as when separate elements are considered (“four region approach”). It is furthermore proven that the delaminated element passes the “patch test” if the selected FEM formulations to build the element pass the test in the pure single problems, making this methodology very attractive to develop other fractured elements. To illustrate this result, two benchmark problems were studied: first a complete delaminated cantilever plate, and second a complete delaminated circular plate. The element was tested in the context of SHM (structural health monitoring). Frequency shifts, damage indexes, and changes in mode shapes and frequency response functions (FRF) were obtained to quantify the severity of damage due to delamination.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Rytter, A., 1993, “Vibration Based Inspection of Civil Engineering Structures,” Ph.D. thesis, Department of Building Technology Structural Engineering, University of Aalborg, Aalborg, Denmark.
Zou, Y., Tong, L., and Steven, G. P., 2000, “Vibration-Based Model-Dependent Damage (Delamination) Identification and Health Monitoring for Composite Structures—A Review,” J. Sound Vib., 230(2), pp. 357–378. [CrossRef]
Doebling, S. W., Farrar, C. R., Prime, M. B., and Shevitz, D. W., 1996, “Damage Identification and Health Monitoring of Structural and Mechanical Systems From Changes in Their Vibration Characteristics: A Literature Review,” technical report, Los Alamos National Laboratory, Los Alamos, NM.
Farrar, C. R., Doebling, S. W., and Nix, D. A., 2001, “Vibration-Based Structural Damage Identification,” Philos. Trans. R. Soc. London Ser. A, 359(1778), pp. 131–149. [CrossRef]
Balageas, D., Fritzen, C., and Güemes, A., 2007, Structural Health Monitoring, ISTE, Oxford, UK.
Alvandi, A., and Cremona, C., 2006, “Assessment of Vibration-Based Damage Identification Techniques,” J. Sound Vib., 292(1–2), pp. 179–202. [CrossRef]
Fritzen, C. P., and Bohle, K., 1999, “Identification of Damage in Large Scale Structures by Means of Measured FRFs-Procedure and Application to the I40-Highway Bridge,” Damage Assessment of Structures, Proceedings of the International Conference on Damage Assessment of Structures (DAMAS 99), Dublin, Ireland, June 28–30, pp. 310–319.
Bohle, K., and Fritzen, C. P., 2003, “Results Obtained by Minimising Natural Frequency and MAC-Value Errors of a Plate Model,” Mech. Syst. Signal Process., 17(1), pp. 55–64. [CrossRef]
Yu, L., and Yin, T., 2010, “Damage Identification in Frame Structures Based on FE Model Updating,” ASME J. Vib. Acoust., 132(5), p. 051007. [CrossRef]
Liu, W., Gao, W. C., and Sun, Y., 2009, “Application of Modal Identification Methods to Spatial Structure Using Field Measurement Data,” ASME J. Vib. Acoust., 131(3), p. 034503. [CrossRef]
Jenq, S. T., and Lee, W. D., 1997, “Identification of Hole Defect for GFRP Woven Laminates Using Neural Network Scheme,” Structural Health Monitoring: Current Status and Perspectives, F. K.Chang, Ed., International Workshop on Structural Health Monitoring, Stanford University, Stanford, CA, September 18–20, pp. 741–751.
Feng, M. Q., and Bahng, E. Y., 1999, “Damage Assessment of Bridges With Jacketed RC Columns Using Vibration Test,” Smart Structures and Materials 1999: Smart Systems for Bridges, Structures and Highways, S. C.Liu, ed., Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), Conference on Smart Systems for Bridges, Structures, and Highways at Smart Structures and Material s 1999, Newport Beach, CA, March 1–2, pp. 316–327.
Zak, A., Krawczuk, M., and Ostachowicz, W., 2001, “Vibration of a Laminated Composite Plate With Closing Delamination,” J. Intell. Mater. Syst. Struct., 12(8), pp. 545–551. [CrossRef]
Zak, A., Krawczuk, M., and Ostachowicz, W., 2000, “Numerical and Experimental Investigation of Free Vibration of Multilayer Delaminated Composite Beams and Plates,” Comput. Mech., 26(3), pp. 309–315. [CrossRef]
Hanagud, S., and Luo, H., 1997, “Damage Detection and Health Monitoring Based on Structural Dynamics,” Structural Health Monitoring: Current Status and Perspectives, F. K.Chang, ed., International Workshop on Structural Health Monitoring, Stanford University, Stanford, CA, September 18–20, pp. 715–726.
Kim, H. Y., and Hwang, W., 2002, “Effect of Debonding on Natural Frequencies and Frequency Response Functions of Honeycomb Sandwich Beams,” Composite Struct., 55(1), pp. 51–62. [CrossRef]
Krawczuk, M., and Ostachowicz, W., 2002, “Identification of Delamination in Composite Beams by Genetic Algorithm,” Sci. Eng. Composite Mater., 10(2), pp. 147–155. [CrossRef]
Ling, H. Y., Lau, K. T., Cheng, L., and Jin, W., 2005, “Fibre Optic Sensors for Delamination Identification in Composite Beams Using a Genetic Algorithm,” Smart Mater. Struct., 14(1), pp. 287–295. [CrossRef]
Wei, Z., Yam, L. H., and Cheng, L., 2005, “Delamination Assessment of Multilayer Composite Plates Using Model-Based Neural Networks,” J. Vib. Control, 11(5), pp. 607–625. [CrossRef]
Sanders, G. W., Akhavan, F., Watkins, S. E., and Chandrashekhara, K., 1997, “Fiber Optic Vibration Sensing and Neural Networks Methods for Prediction of Composite Beam Delamination,” Smart Structures and Integrated Systems—Smart Structures and Materials 1997, M. E.Regelbrugge, ed., Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), Conference on Smart Structures and Integrated Systems—Smart Structures and Materials 1997, San Diego, CA, March 3–6, pp. 858–867.
Watkins, S. E., Sanders, G. W., Akhavan, F., and Chandrashekhara, K., 2002, “Modal Analysis Using Fiber Optic Sensors and Neural Networks for Prediction of Composite Beam Delamiation,” Smart Mater. Struct., 11(4), pp. 489–495. [CrossRef]
Harrison, C., and Butler, R., 2001, “Locating Delaminations in Composite Beams Using Gradient Techniques and a Genetic Algorithm,” AIAA J., 39(7), pp. 1383–1389. [CrossRef]
Figueiredo, E., Park, G., Farinholt, K. M., Farrar, C. R., and Lee, J.-R., 2012, “Use of Time-Series Predictive Models for Piezoelectric Active-Sensing in Structural Health Monitoring Applications,” ASME J. Vib. Acoust., 134(4), p. 041014. [CrossRef]
Zwink, B. R., 2012, “Nondestructive Evaluation of Composite Material Damage Using Vibration Reciprocity Measurements,” ASME J. Vib. Acoust., 134(4), p. 041013. [CrossRef]
Saravanos, D. A., and Hopkins, D. A., 1996, “Effects of Delaminations on the Damped Dynamic Characteristics of Composite Laminates: Analysis and Experiments,” J. Sound Vib., 192(5), pp. 977–993. [CrossRef]
Reddy, J. N., 1997, Mechanics of Laminated Composite Plate and Shells. Theory and Analysis, 2nd ed., CRC, Boca Raton, FL.
Delia, C. N., and Shu, D., 2007, “Vibration of Delaminated Composite Laminates: A Review,” ASME Appl. Mech. Rev., 60, pp. 1–20. [CrossRef]
Damghani, M., Kennedy, D., and Featherston, C., 2011, “Critical Buckling of Delaminated Composite Plates Using Exact Stiffness Analysis,” Comput. Struct., 89(13–14), pp. 1286–1294. [CrossRef]
Tafreshi, A., 2004, “Efficient Modelling of Delamination Buckling in Composite Cylindrical Shells Under Axial Compression,” Composite Struct., 64, pp. 511–520. [CrossRef]
Melenk, J. M., and Babuska, I., 1996, “The Partition of Unity Finite Element Method: Basic Theory and Applications,” Comput. Methods Appl. Mech. Eng., 139(1–4), pp. 289–314. [CrossRef]
Babuska, I., and Melenk, J. M., 1997, “The Partition of Unity Method,” Int. J. Numer. Methods Eng., 40(4), pp. 727–758. [CrossRef]
Chattopadhyay, A., Dragomir-Daescu, D., and Gu, H., 1997, “Dynamic Response of Smart Composites With Delaminations,” Structural Health Monitoring: Current Status and Perspectives, F. K.Chang, ed., International Workshop on Structural Health Monitoring, Stanford University, Stanford, CA, September 18–20, pp. 729–740.
Chattopadhyay, A., Kim, H. S., and Ghoshal, A., 2004, “Non-Linear Vibration Analysis of Smart Composite Structures With Discrete Delamination Using a Refined Layerwise Theory,” J. Sound Vib., 273(1–2), pp. 387–407. [CrossRef]
Swann, C., Chattopadhyay, A., and Ghoshal, A., 2005, “Characterization of Delamination by Using Damage Indices,” J. Reinforced Plastics Composites, 24(7), pp. 699–711. [CrossRef]
Dvorkin, E. N., and Vassolo, S. L., 1989, “A Quadrilateral 2-D Finite Element Based on Mixed Interpolation of Tensorial Components,” Eng. Comput., 6, pp. 217–224. [CrossRef]
Batoz, J. L., and Bentahar, M., 1982, “Evaluation of a New Quadrilateral Thin Plate Bending Element,” Int. J. Numer. Methods Eng., 18(11), pp. 1655–1677. [CrossRef]
Taylor, R. L., 2005, FEAP. A Finite Element Analysis Program: Programmer Manual, University of California, Berkeley, Berkeley, CA, http://www.ce.berkeley.edu/ rlt.
Zienkiewicz, O. C., Taylor, R. L., and Zhu, J. Z., 2005, The Finite Element Method: Its Basis and Fundamentals, 6th ed., Elsevier, Oxford, UK., Vol. 1.

Figures

Grahic Jump Location
Fig. 1

Four regions approach

Grahic Jump Location
Fig. 2

(a) Delaminated cantilever beam. (b) FEM model.

Grahic Jump Location
Fig. 3

(a) Relative error in L2 norm for separate elements (DKQ) and delaminated element. (b) Relative error in eigenfrequencies (1–4). Lines (DKQ), dots (delaminated element).

Grahic Jump Location
Fig. 4

(a) Delaminated circular clamped plate (quarter represented). (b) FEM model.

Grahic Jump Location
Fig. 5

(a) Relative error in L2 norm for separate elements (DKQ) and delaminated element. (b) Relative error in eigenfrequencies (1–3). Lines (DKQ), dots (delaminated element).

Grahic Jump Location
Fig. 6

Delaminated FEM model of a cantilever beam. Green elements represent the delamination.

Grahic Jump Location
Fig. 7

Eigenvector 6 of displacements for extensions I, II, and III. (a) Composite [0 90]3S. (b) Composite [0 90 45 −45 0 90]S. The undamaged one is represented by 0. The vertical dashed line represents the center of the delamination.

Grahic Jump Location
Fig. 8

Eigenvector 6 of curvatures for extensions I, II, and III. (a) Composite [0 90]3S. (b) Composite [0 90 45 −45 0 90]S. The undamaged one is represented by 0. The vertical dashed line represents the center of the delamination.

Grahic Jump Location
Fig. 9

Frequency shifts (%) for composite [0 90]3S for modes 5, 6, and 7. (a) Influence of the delamination extension. Delamination center at x=0.45 L. (b) Influence of delamination location, with extension 10%.

Grahic Jump Location
Fig. 10

Eigenvector 6 of displacements for different delamination locations. Extension is 10%.

Grahic Jump Location
Fig. 11

Composite clamped plate. Sections where eigenvectors are obtained (F1 and F2). Actuator (A1). Sensor (S1). Delamination (D).

Grahic Jump Location
Fig. 12

Eigenvectors of second mode at section x = 0.13 m (F1). Extensions I, II, and III. (a) Displacements w. (b) Curvatures κx.

Grahic Jump Location
Fig. 13

Eigenvectors of second mode at section y = 0.58 m (F2). Extensions I, II, and III. (a) Displacements w. (b) Curvatures κy.

Grahic Jump Location
Fig. 14

FRF at location x=0.75 m and y=0.30 m. (a) Extensions 0, I, II, and III. (b) Extensions 0, IV, V, and VI.

Grahic Jump Location
Fig. 15

Selected bandwidths of FRF (to compute damage indexes). (a) Extensions 0, I, II, and III. (b) Extensions 0, IV, V, and VI. Marked eigenfrequency 1139 Hz.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In