Damage Detection in Composite Materials Using Identification Techniques

The present paper describes an approach for damage detection in composite structures that has its basis in methods of system identification. Response of a damaged structure differs from predictions obtained from a mathematical model of the original structure, where such a model is typically a finite‐element representation of the structure. In the present work dealing with composite materials, two distinct analytical models, one using two‐dimensional (2D) elements in conjunction with the classical lamination theory and another using three‐dimensional (3D) elements were considered. The output error approach of system identification was employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response. The proposed method is an extension of the stiffness‐reduction approach for damage detection to realistic structures. Numerical simulation of measurements of static deflections, strains, and vibration modes were used in the identification procedure. The methodology was implemented for representative composite structures. Principal shortcomings in the proposed approach and possible methods to circumvent these problems are discussed in the paper.     

Thermal Postbuckling of Laminated Composite Plates with Temperature Dependent Properties

The paper deals with the theoretical investigation of the postbuckling of laminated composite rectangular plates subjected to uniform in-plane temperature. An analytical method based on Chebyshev polynomial is employed. The formulation is based on Reissner–Mindlin plate theory and von Kármán nonlinear kinematics. The resulting nonlinear coupled differential equations are linearized using quadratic extrapolation technique. Double Chebyshev finite series is used to discretize the differential equations. An incremental iterative approach is employed for the solution. The effects of temperature dependent mechanical and thermal properties on the limiting/critical temperature and the postbuckling response are studied. The numerical results for different boundary conditions and lamination schemes are presented. Analysis results indicate that temperature dependent properties reduce the critical/limiting temperature and postbuckling strength.     

System Identification of Partially Restrained Composite Plates Using Measured Natural Frequencies

A nondestructive evaluation technique established on the basis of a global minimization method is presented for the system identification of laminated composite plates partially restrained by elastic edge supports. Six natural frequencies extracted from the vibration data of the flexibly restrained plate are used to identify the system parameters of the plate. In the identification process, the trial system parameters are used in the Rayleigh–Ritz method to predict the theoretical natural frequencies of the plate, an error function is established to measure the sum of the differences between the experimental and theoretical predictions of the natural frequencies, and the global minimization method is used to search for the best estimates of the parameters by making the error function a global minimum. The accuracy and efficiency of the proposed technique in identifying the parameters of several flexibly supported plates made of different composite materials are studied via both theoretical and experimental approaches. The excellent results obtained in this study have validated the applicability of the proposed technique.     

Damage Detection through Analysis of Modes in a Partially Constrained Plate

The need for aircraft, both military and civilian, to serve longer and cost less to operate is ever present. The ability to potentially extend service life and reduce operating and maintenance costs are key factors in the many choices with aircraft programs. The field of structural health monitoring attempts to reduce labor and cost by allowing technicians to monitor selected properties of an aircraft’s structure to detect impending failure. This research examines methods to detect damage to a thermal protection system tile using representative aluminum plates. Plates are subjected to modal analysis in single and joined conditions in an attempt to provide the capability of sensing damage to a tile on the surface of a vehicle whereas the sensors remain on the substructure of the airframe. Jointly, the development of a means to model the system using finite-element techniques is explored. It is found that the finite-element modeling technique produces correlating modal frequencies within a 7.19% worst case average when compared to the physical tests. This leads to the ability to compare mode shapes and frequencies to detect damage in such a system.     

Multimetric Sensing for Structural Damage Detection

Vibration-based damage detection methods have been widely studied for structural health monitoring of civil infrastructure. Acceleration measurements are frequently employed to extract the dynamic characteristics of the structure and locate damage because they can be obtained conveniently and possess relatively little noise. However, considering the fact that damage is a local phenomenon, the sole use of acceleration measurements that are intrinsically global structural responses limits damage detection capabilities. This paper investigates the possibility of using both global and local measurements to improve the accuracy and robustness of damage detection methods. A multimetric approach based on the damage locating vector method is proposed. Numerical simulations are conducted to verify the efficacy of the proposed approach.     

Buckling of Laminated Composite Rectangular Plates

The present study estimates the critical/buckling loads of laminated composite rectangular plates under in-plane uniaxial and biaxial loadings. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. Chebyshev series is used for spatial discretisation and quadratic extrapolation is used for linearization. An incremental iterative approach is used for estimation of the critical load. Different combinations of simply supported, clamped and free boundary conditions are considered. The effects of plate aspect ratio, lamination scheme, number of layers and material properties on the critical loads are studied.     

Analysis of Hybrid Laminated Composite Plates

Hybrid laminated composite plates are analyzed using a nine‐noded isoparametric plate finite element based on Mindlin's theory. The shear flexibility is included in the finite element modeling. Shear flexibility is of importance, especially when different materials are used in the laminate design. Hybrid laminates consisting of graphite∕epoxy and kevlar∕epoxy plies are considered for illustration. The study indicates that hybrid laminates provide stiffnesses that are intermediate to the values obtained for single‐material laminates. The minimum deflection is achieved at different fiber orientation for thick plates compared to thin plates. The deflection behavior of hybrid laminates seems to be less affected by outer‐ply stiffness in the case of thick plates. Thick plates show less variation in the first natural frequency with fiber orientation but hybridization changes the natural frequency considerably. The first natural frequency of the hybrid laminate can be made higher than the stiffer single‐material laminate.     

Bounds on Flexural Properties and Buckling Response for Symmetrically Laminated Composite Plates

Nondimensional parameters and equations governing the buckling behavior of rectangular symmetrically laminated plates are presented that can be used to represent the buckling resistance, for plates made of all known structural materials, in a very general, insightful, and encompassing manner. In addition, these parameters can be used to assess the degree of plate orthotropy, to assess the importance of anisotropy that couples bending and twisting deformations, and to characterize quasi-isotropic laminates quantitatively. Bounds for these nondimensional parameters are also presented that are based on thermodynamics and practical laminate construction considerations. These bounds provide insight into potential gains in buckling resistance through laminate tailoring and composite-material development. As an illustration of this point, upper bounds on the buckling resistance of long rectangular orthotropic plates with simply supported or clamped edges and subjected to uniform axial compression, uniform shear, or pure in-plane bending loads are presented. The results indicate that the maximum gain in buckling resistance for tailored orthotropic laminates, with respect to the corresponding isotropic plate, is in the range of 26–36% for plates with simply supported edges, irrespective of the loading conditions. For the plates with clamped edges, the corresponding gains in buckling resistance are in the range of 9–12% for plates subjected to compression or pure in-plane bending loads and potentially up to 30% for plates subjected to shear loads.     

Free-Vibration Analysis and Material Constants Identification of Laminated Composite Sandwich Plates

Free vibration of symmetrically laminated composite sandwich plates with elastic edge restraints is studied via the Rayleigh–Ritz approach. The proposed Rayleigh–Ritz method is constructed on the basis of the layer-wise linear displacement theory. The accuracy of the method in predicting natural frequencies of composite sandwich plates with different boundary conditions is verified by the results reported in the literature or the experimental data obtained in this study. The proposed method is then applied to the material constant identification of free composite sandwich plates using the first six theoretical natural frequencies of the plates. In the identification process, trial material constants are used in the present method to predict the theoretical natural frequencies, a frequency discrepancy function is established to measure the sum of the squared differences between the experimental and theoretical natural frequencies, and a stochastic global minimization algorithm is used to search for the best estimates of the material constants by making the frequency discrepancy function a global minimum. Applications of the material constant identification technique are demonstrated by means of several examples.     

Hygrothermoelastic Postbuckling Response of Laminated Composite Plates

The paper deals with the effect of moisture and temperature on the postbuckling response of a laminated composite plate subjected to hygrothermomechanical loadings. Mechanical loading consists of uniaxial, biaxial, shear, and their combinations. The distribution of temperature and moisture on the surface is considered to be uniform. The degradation in material properties due to moisture and temperature is taken into account using a micromechanical model. The mathematical formulation is based on higher order shear deformation theory and von Karman’s nonlinear kinematics. The quadratic extrapolation technique and fast converging finite double Chebyshev series are used for linearization and spatial discretization of the governing nonlinear equations of equilibrium, respectively. The effects of temperature rise, moisture concentration, fiber-volume fraction, and plate parameters on buckling and postbuckling response of the plate are presented.     

Impedance-Based Method for Nondestructive Damage Identification

A structural damage identification technique based on the impedance method is presented in this paper using smart piezoelectric transducer (PZT) patches. A modeling framework is developed to determine the structural impedance response and the dynamic output forces of PZT patches from the electric admittance measurements. A damage identification scheme for solving the nonlinear optimization problem is proposed to locate and quantify the structural damage through the minimization of the discrepancy between the structural impedance response and the numerically computed frequency response. The proposed technique does not use modal analysis or model reduction, and only the electric admittance measurements of PZT patches and the analytical system matrices are required. A beam example has been employed to illustrate the effectiveness of the proposed algorithm numerically. Furthermore, the influence of the measurement noise on the results has been investigated.     

Repair of Steel Composite Beams with Carbon Fiber-Reinforced Polymer Plates

One significant cause of deterioration of steel bridge structures is the corrosion due to extensive use of deicing salts in winter weather. The investigation presented in this paper focused on the behavior of steel composite beams damaged intentionally at their tension flange to simulate corrosion and then repaired with carbon fiber-reinforced polymer (CFRP) plates attached to their tension areas side. Damage to the beams was induced by removing part of the bottom flange, which was varied between no damage and loss of 75% of the bottom flange. All beams were tested to failure to observe their behavior in the elastic, inelastic, and ultimate states. To help implement this strengthening technique, a nonlinear analytical procedure was also developed to predict the behavior of the section/member in the elastic, inelastic, and ultimate states. The test results showed a significant increase in the strength and stiffness of the repaired beams. Through the use of CFRP plates, all damaged beams were fully restored to their original (undamaged state) strength.     

Structural Damage Detection Using Dynamic Properties Determined from Laboratory and Field Testing

Studies have shown that experimentally determined dynamic properties can be used to identify the characteristics of a structure. In this paper, a damage detection technique is developed and demonstrated using system identification, finite-element modeling, and a modal update process. The proposed approach, SFM, provides a rapid estimate of damage locations and magnitudes. The proposed methodology is applied to three case studies. The first is a numerical simulation using computer generated data. The second is an ASCE benchmark problem for structural health monitoring, where the results can be compared to other researchers. The third is a full-scale highway bridge that was field tested using a forced vibration shaking machine. In this case study, the bridge was shaken in several states of damage and the proposed methodology was utilized to detect and determine the location and extent of the damage. It was found that, using the collected data, the SFM approach was able to consistently predict the location of damage as well as estimate the magnitude of the damage.     

Thermal Buckling Analysis of SMA Fiber-Reinforced Composite Plates Using Layerwise Model

Thermal buckling analysis of laminated smart composite plates subjected to uniform temperature distribution has been presented. Shape memory alloy (SMA) fibers whose material properties depend on temperature have been used as a smart material. A three-dimensional layerwise plate model has been employed in developing the system equations using variational approach. Finite-element method has been adopted for discretization of the laminate. Lagrangian interpolation functions have been used to approximate the displacement components along the thickness as well as in the in-plane direction. The actual variation of prebuckling stresses has been accounted for in the derivation of the geometric stiffness matrix of the laminates. An incremental load technique has been used in the analysis to take into account the nonlinearity in the material properties of the SMA arising due to their temperature dependence. The effects of thickness ratio, orthotropic ratio, fiber orientation, aspect ratio, stacking sequence and various boundary conditions on the critical buckling temperature have been examined in details. The results have been validated with those available in the literature.     

Peridynamic Analysis of Impact Damage in Composite Laminates

The traditional methods for analyzing deformation in structures attempt to solve the partial differential equations of the classical theory of continuum mechanics. Yet these equations, because they require the partial derivatives of displacement to be known throughout the region modeled, are in some ways unsuitable for the modeling of discontinuities caused by damage, in which these derivatives fail to exist. As a means of avoiding this limitation, the peridynamic model of solid mechanics has been developed for applications involving discontinuities. The objective of this method is to treat crack and fracture as just another type of deformation, rather than as pathology that requires special mathematical treatment. The peridynamic theory is based on integral equations so there is no problem in applying the equations across discontinuities. The peridynamic method has been applied successfully to damage and failure analysis in composites. It predicts in detail the delamination and matrix damage process in composite laminates due to low velocity impact, and the simulation results of damage area correlates very well with the experimental data.     

Damage Detection Utilizing the Damage Index Method to a Benchmark Structure

This paper addresses the first generation benchmark problem on structural health monitoring developed by the ASCE Task Group on Structural Health Monitoring. The focus of the problem is a four-story model of an existing physical model at the University of British Columbia where simulated data are used for the system identification. Modal parameters were extracted using the frequency domain decomposition method. Rather than relying on data from the undamaged structure, a new proposed methodology based on ratios between stiffness and mass values from the eigenvalue problem is presented to identify the undamaged state of the structure. Once the structural identification is complete, the damage index method is used to detect the location and severity of damage. By not relying on undamaged structure information, this approach may be applicable to existing structures that may already incorporate some amount of damage.     

Multivariate Statistical Approach to Structural Damage Detection

The issue of structural damage detection is addressed through an innovative multivariate statistical approach in this paper. By invoking principal component analysis, the vibration responses acquired from the structure being monitored are represented by the multivariate data of the sample principal component coefficients (PCCs). A damage indicator is then defined based on a multivariate exponentially weighted moving average control chart analysis formulation, involving special procedures to allow for the effects of the estimated parameters and to determine the upper control limits in the control chart analysis for structural damage detection applications. Also, a data shuffling procedure is proposed to remove the autocorrelation probably present in the obtained sample PCCs. This multivariate statistical structural damage detection scheme can be applied to either the time domain responses or the frequency domain responses. The efficacy and advantages of the scheme are demonstrated by the numerical examples of a five-story shear frame and a shear wall as well as the experimental example of the I-40 Bridge benchmark.     

Structural Health Monitoring and Damage Assessment Using Frequency Response Correlation Criteria

Two frequency response correlation criteria, namely the global shape correlation (GSC) function and the global amplitude correlation (GAC) function, are established tools to quantify the correlation between predictions from a finite-element (FE) model and measured data for the purposes of FE model validation and updating. This paper extends the application of these two correlation criteria to structural health monitoring and damage detection. In addition, window-averaged versions of the GSC and GAC, namely WAIGSC and WAIGAC, are defined as effective damage indicators to quantify the change in structural response. An integrated method of structural health monitoring and damage assessment, based on the correlation functions and radial basis function neural networks, is proposed and the technique is applied to a bookshelf structure with 24 measured responses. The undamaged and damaged states, single and multiple damage locations, as well as damage levels, were successfully identified in all cases studied. The ability of the proposed method to cope with incomplete measurements is also discussed.     

Damage Containment and Residual Strength of Composite Laminates

Damage in composite laminates caused by low‐velocity impact may produce significant reductions in compressive strength. Lockheed conducted an experimental program to investigate the damage‐containment capability of simple composite laminates of two graphite‐epoxy systems: T300/5208 and AS/3501‐6. Four different lay‐ups, including two hybrid laminates, were investigated for each material system. Results are presented for comparison. Laminates with Kevlar layers, especially where the layer is on the surface of the laminate, demonstrate better impact resistance.     

Identification of Structural Systems Using an Evolutionary Strategy

The problem of system identification is an inverse problem of difficult solution. Currently, difficulties lie in the development of algorithms that use measured data from the system to characterize it without significant a priori knowledge of the system. In this paper, a parameter estimation technique based on an evolution strategy (an optimization algorithm inspired by natural evolution) is presented to overcome some of the difficulties encountered in the field. Using this method, a set of direct problems is solved instead of directly tackling the inverse problem. If the uniqueness of the identification solution is guaranteed for the assumed model and the available data, this heuristic method is able to find a solution without incurring restrictions of other classical optimization methods, like the need for reliable initial estimates and convergence to local optima. Some results obtained with this algorithm are presented for the identification of 3 degrees of freedom (DOF) and a 10?DOF structural system under conditions including limited input/output data, noise polluted signals, and no prior knowledge of mass, damping, or stiffness of the system.