Improved Layerwise Theory Research Articles

Modeling of partially delaminated composite plates resting on two-parameter elastic foundation with improved layerwise theory

In this work, we aim to build the mathematical model for delaminated composite plates resting on elastic foundation by means of improved layerwise theory and finite element implementation for free vibration analysis. The proposed model takes into account the transverse normal and shear deformation of the elastic foundation so as to investigate their effect on the dynamic characteristics of delaminated plates. The four-node plate element is used for the finite element formulations with Langrage interpolation functions for in-plane structural unknowns and Hermite cubic interpolation functions for out-of-plane structural unknowns. The delamination is simulated by means of Heaviside unit step functions allowing for the discontinuity of displacement fields. The effects of both longitudinal locations and interfacial locations of delamination are investigated. The results show that when the delamination located closer to the clamped end and at the middle plane, it has much more severe influence on its natural frequencies. The foundation parameters also have significant effect on the natural frequencies and frequency shift due to delamination. Different layup stacking sequences are also considered in this study.

Investigation of delamination effect on nonlinear vibration behaviors of a composite plate resting on nonlinear elastic foundation

The aim of the present work is to investigate the delamination effect on nonlinear vibration behaviors of composite plate resting on nonlinear elastic foundation. The composite plate is assumed to be pre-delaminated with various delamination locations and modeled with an improved layerwise theory and finite element method. The delamination is simulated by the Heaviside unit step function allowing for the discontinuity of displacement fields. By means of the variational principle, the nonlinear governing equations can be obtained and further solved by the direct iterative method. The model takes into account three foundation parameters so as to investigate their effect on the nonlinear vibration characteristics. Three longitudinal locations and three interfacial locations are considered, and both clamped-free and clamped–clamped boundary conditions are considered to investigate the nonlinear vibration behaviors. The results show that different from the linear vibration, with the existence of delamination, the nonlinear fundamental frequencies may exceed the fundamental frequency of the healthy plate when the vibration amplitude ratio reaches a certain value. This finding may help engineers understand the nonlinear vibration behaviors and further detect the delamination in composite plate resting on nonlinear foundations in presence of delamination.

Characterization of delamination effects on free vibration and impact response of composite plates resting on visco-Pasternak foundations

In this study, the free vibration and impact response of composite plates with interfacial delamination are investigated based on the improved layerwise theory with finite element implementation. The interaction between the composite plate and the surrounding medium is simulated by the visco‐Pasternak foundation model. Hamilton's principle is used to derive the equations of motion for the delaminated composite plates. The impact responses of the delaminated composite plates are later solved by the Newmark algorithm for both clamped-free (C-F) and clamped-clamped (CC) boundary conditions. Influence of the foundation parameters, damping parameter, longitudinal and interfacial delamination locations on eigenfrequencies and transient history are investigated and discussed. Numerical results illustrate that delamination reduces the natural frequencies and the middle plane delamination possesses the largest damage effect. With a stiffer foundation, the damped eigenfrequencies increase significantly and the transient responses also converge much faster. Moreover, the existence of delamination affects the higher frequencies dramatically which may further help identify delamination locations in composite plates resting on visco-Pasternak foundations for structural health monitoring.

Active Vibration Control of a Piezo-Bonded Laminated Composite in the Presence of Sensor Partial Debonding and Structural Delaminations.

In this paper, the active vibration control of a piezo-bonded laminated composite is investigated in the presence of sensor partial debonding and structural delamination. Improved layerwise theory, higher-order electric potential field, and the finite-element method were employed to develop an electromechanically coupled model for the two types of damage (i.e., sensor partial debonding and delamination). The developed model was numerically implemented on a single-input-multi-output (SIMO) system to demonstrate the effects of sensor partial debonding and structural delamination on the ability of a constant gain velocity feedback (CGVF) controller to attenuate vibration. The two types of damage were assessed in terms of controlled outputs of the sensors, nodal displacements, and control input signals being applied to the actuator to suppress vibrations. The obtained results showed that the sensor partial debonding and structural delamination have opposite effects on the vibration-attenuation characteristics of the CGVF controller. The presence of partial debonding in the sensor made the controller less able to suppress vibrations because of a spurious sensing signal, whereas structural delamination increased the control authority of the controller because of the loss of structural stiffness that results from structural delamination.

Improved LayerWise Theory method application to stress analysis for composite tube in pure bending

An improved approach using LayerWise theory (LWT) is developed for the stress analysis in pure bending composite tubes. The variables in the circumferential direction are separated from the local displacement, so the eigenvalue techniques are avoided. Then the composite tube is discretized only in the radial direction, and the related displacement in the local displacement is assumed as the simple interpolation polynomial function. Based on the principle of minimum potential energy, the local nodal variables are solved to calculate the strains and stresses for the composite tube. Several composite tubes are analyzed to illustrate the proposed approach feasibility. Besides, the exact solution by unified connected parameter method is employed for comparison. They are in good agreement with each other.

Assessment of delaminated smart composite laminates via system identification and supervised learning

This paper proposes the synergetic integration of system identification and artificial intelligence for the detection and assessment of delamination damages in smart composite laminates. An electromechanically coupled mathematical model is developed for the healthy and delaminated smart composite laminates on the basis of improved layerwise theory, higher order electric potential field and finite element method. A discriminative feature space is constructed for the healthy and delaminated structures via system identification from their structural vibration responses. The discriminative features are used for the training and cross-validation of various supervised machine learning classifiers and an optimal classifier is identified. The optimal classifier is employed to make predictions on unseen test delamination cases, and its predictions are validated via a dimensionality reduction tool. The obtained results show that the proposed technique could be employed as a reliable tool for nondestructive evaluation of smart composite laminates.

Bending and free vibration of multilayered functionally graded doubly curved shells by an improved layerwise theory

An improved layerwise theory is established for the bending and vibration responses of multi-layered functionally graded doubly curved shells with material properties varying gradually and continuously across the whole shell thickness. The theory accounts for shear deformation and normal strain effects by assuming for each layer, a displacement field with zigzag first-order in-plane displacements and through-the-thickness parabolic transverse displacement. Moreover, it is assumed a stress field satisfying the loading conditions on the external shell faces and the continuity conditions of the internal stresses at the layers interfaces, so, there is no need for introducing in the present formulation any shear correction factor. For this purpose, a mixed variational statement is used. The continuity conditions for the displacements at the layers interfaces are used to decrease the degrees of freedom of the theory. Bending and free vibration problems are solved for FGM single- and three-layered sandwich open cylindrical and spherical shells with completely simply supported or clamped edges. Comparisons for some present results with numerical results obtained by other authors due to advanced 2D and 3D elasticity solutions are made showing the high efficiency of the present theory in predicting the bending and vibration parameters. Graphics are presented to demonstrate the importance of the normal strain effect for the static bending and free vibration of the considered shells.

Assessment of sensor debonding failure in system identification of smart composite laminates

System identification is an inverse algorithm of developing/improving mathematical representation of a physical system from input-output responses. This paper assessed a mathematical model of smart composite laminate identified with spurious output data due to sensor debonding failure. Improved layerwise theory and higher-order electric potential field were incorporated to develop electromechanically coupled finite element based mathematical model of the smart composite laminate with or without sensor debonding failure. The input-output data of the developed model were fed into the direct system identification algorithm to identify the state-space model of the smart structure. The developed theory was numerically implemented on a 16-layer cross-ply laminate with surface bonded piezoelectric sensor and actuator. Results showed that system identification algorithm misapprehended the true dynamic behavior of the smart structure in the presence of sensor debonding failure. In addition, principal component analysis was used to detect the presence and severity of partial sensor debonding in the identified state-space model.

Multilayer Perceptron for Classification of Structural delamination and Transducers Debonding in Smart Composite Laminates

This paper investigates the feasibility of multilayer perceptron (MLP) for the classification of structural delamination and transducers debonding in smart composite laminates. Structural vibration response is employed to extract the discriminative features for multiple damages. The dynamic model of the smart structure with inter-ply delaminations and partially debonded piezoelectric sensor and actuator is developed by incorporating improved layerwise theory, higher order electric potential field and finite element method. The developed model is solved in the time domain to obtain the transient response of the healthy and damaged structures through a surface bondedpiezoelectric sensor for random input excitations applied through a piezoelectric actuator. The input-output information is fed into a system identification algorithm to identify damage sensitive features for the healthy anddamaged state of the smart composite laminate. The discriminative features are classified through MLP in a supervised manner and its classification accuracy is evaluated in terms of true positive (TP) rate, false positive (FP) rate, precision and area under the receiver operating characteristic curve (ROC area).

Modeling and assessment of partially debonded piezoelectric sensor in smart composite laminates

As substantive components of intelligent structures, piezoelectric sensors need to perform their intended function without any spuriousness. In this work, a mathematical model has been developed to characterize the performance degradation of a piezoelectric sensor due to its debonding from a smart composite laminate. The electromechanically coupled governing equation of motion is developed by incorporating improved layerwise theory and higher electric potential field along with the finite element method and Extended Hamilton's principle. The problem governing equation is solved by Newmark time-integration algorithm to assess the performance of a piezoelectric sensor in the presence of partial debonding at the edge and inner side of the sensor. The partially debonded piezoelectric sensor is investigated in frequency domain via power spectral density of the sensor output. The degradative performance of the partially debonded sensor is generalized for random loadings via basic signal statistics. The numerical results show that the developed model recover the presence and extent of partial debonding between the piezoelectric sensor and the host laminate.

Analysis of sensor-debonding failure in active vibration control of smart composite plate

In this article, the effect of a sensor-debonding failure on the active vibration control of a smart composite plate is investigated numerically. A mathematical model of the smart structure with a partially debonded piezoelectric sensor is developed using an improved layerwise theory, a higher-order electric-potential field that serves as the displacement field, and the potential variation through the piezoelectric patches. A state-space form that is based on the reduced-order model is employed for the controller design. A control strategy with a constant gain and velocity feedback is used to assess the vibration-control characteristics of the controller in the presence of the sensor-debonding failure. The obtained results show that sensor-debonding failure reduces the sensor-output, control-input signal, and active damping in magnitude that successively degrades the vibration attenuation capability of the active vibration controller. The settling time and relative tip displacement of the controlled structure increase with the increasing length of partial debonding between the piezoelectric sensor and host structure. Furthermore, a damage-sensitive feature along with multidimensional scaling showed excellent results for the detection and quantification of sensor-debonding failure in the active vibration control of smart structures.

Actuator failure assessment in smart composite laminates via principal component analysis

In this work, we propose a principal component analysis and system identification–based failure assessment approach for evaluating the partial actuator debonding failures in smart composite structures. Actuator debonding failure changes the structural dynamic characteristics and reduces the actuation capabilities as well in smart composite structures. First, the modeling of actuator debonding in smart composite laminate is developed using the finite element method, which incorporates the improved layerwise theory and higher-order electric potential field for the electromechanical coupling. Second, the structural responses obtained from the developed modeling are fed into the system identification to identify the system parameters of both healthy and damaged systems. Third, the achieved system parameters are further used for the statistical analysis by principal component analysis to extract the failure-sensitive features. Finally, a numerical example is studied using a 16-layer cross-ply laminate ([0/90]4s) as the substrate with various actuator debonding sizes. The results show that the actuator debonding failures can be well assessed, and the failure intensity and location can also be evaluated using the proposed approach.

Active vibration control of smart composite laminates with partial debonding of actuator

The effect of actuator debonding on the performance of active vibration control is analytically investigated through an optimal control strategy. An improved layerwise theory with Heaviside step functions, which addresses discontinuous displacement fields, is used for modeling the actuator debonding. General finite element procedures are developed to derive the governing equation taking into consideration the electro-mechanical coupling effect. A reduced-order model based on the state-space model is adopted for the design of the active controller. Generally, debonding in actuators reduces their load carrying capability, dynamic properties and vibration control characteristics. The effect of debonding on the vibration control is investigated by the proposed analytical modeling. Numerical results using a 16-layer cross-ply laminate with healthy actuator and partially debonded actuator are given for the investigation of the vibration suppression efficiency and control effort. It is observed that the control authority of the composite laminates with partially debonded piezoelectric actuator is dramatically reduced by increasing the size of the actuator debonding. Since debonding failure may occur during the service life of smart composite laminates, the results showed that actuator debonding must be considered as an uncertainty parameter in the design of active controllers.

Investigation of actuator debonding effects on active control in smart composite laminates

This article presents a numerical study of active vibration control of smart composite laminates in the presence of actuator debonding failures. A comparison between the smart composite laminates with healthy actuator and various partially debonded actuator cases is performed to investigate the debonding effects on the vibration suppression. The improved layerwise theory with Heaviside’s unit step function is adopted to model the displacement field with actuator debonding failure. The higher order electric potential field is adopted to describe the potential variation through the thickness. The finite element method–based formulations are derived using the plate element, taking into consideration the electro-mechanical coupling effect. The reduced-order model is represented by the state-space form and further for the vibration suppression using a simple constant gain velocity feedback control strategy. For the purpose of demonstration, a 16-layer cross-ply substrate laminate ([0/90]4s) is employed for the numerical study. The results show that the actuator debonding affects the closed-loop frequencies, active damping ratios, and efficiency of vibration suppression.

Active recovery of vibration characteristics for delaminated composite structure using piezoelectric actuator

In this paper, an active control algorithm was adopted, in order to recover the vibration characteristics of a delaminated composite structure, and control performances were numerically investigated. Delamination of the laminated composite structure was modeled, using the improved layerwise theory. Higher order electric potential was used to describe the electro-mechanical coupling of a piezoelectric actuator. Dynamic equations of motion were derived, using a finite element scheme. Mode shapes and corresponding natural frequencies for healthy and damaged structures were identified. After implementing an active control algorithm in the system model, vibration characteristics of the controlled composite structure were compared to those of healthy and damaged composite structures. Vibration characteristics of the delaminated composite structure were effectively recovered to those of the healthy structure, and structural performances were also restored to those of the healthy structure.

Dynamic Characteristics Recovery of Delaminated Composite Structure

본 논문에서는 복합재 구조물에 손상이 있을 경우, 손상에 의해 변화된 구조물의 동적특성을 손상이 없는 상태로 회복하여, 전체 시스템의 안정성을 유지할 수 있도록 하였다. 층간 분리가 있는 구조물의 유한요소모델 구축을 위하여 향상된 층간 변위장 모델을 적용하였으며, 유한요소해석을 진행하여 구조물의 고유 진동수와 모드 형상을 관찰하였다. 능동제어 알고리즘과 압전 작동기를 적용하여 구조물의 진동 응답특성을 확인하였으며, 이를 바탕으로 손상된 구조물의 동적특성을 손상이 없는 상태로 회복할 수 있음을 확인하였다.In this paper, feasibility of dynamic characteristics recovery of delaminated composite structure is numerically studied by using active control algorithm and piezoelectric actuator. Macro-fiber composite(MFC), which has great flexibility and high actuating force, is considered as an actuator in this work. After construction of finite element model for delaminated composite structure based on improved layerwise theory, modal characteristics are investigated and changes of natural frequencies and mode shapes, caused by delamination, are observed. Then, active control algorithm is realized and implemented to system model and control performances are numerically evaluated. Dynamic characteristics of delaminated composite structure are effectively recovered to those of healthy composite structure.

Transient analysis of biocomposite laminates with delamination.

The transient analysis of smart biocomposite laminates with delamination at ply interfaces is investigated, by using an electro-mechanical coupled improved layerwise theory. The piezoelectric coupling effect was modeled using higher order electric potential. Four-node plate elements were used for finite element implementation. Linear Lagrange interpolation functions were used for in-plane structural unknowns and electric unknowns, and a Hermite cubic interpolation function was used for out-of-plane structural unknowns. Single delamination was seeded in the biocomposite laminates at three different locations, to study the effects of delamination. Numerical results were obtained by using the Newmark-beta algorithm. The results showed that the time history of nodal displacement and sensor output didn't give enough information of delamination. However, the power spectral density of the time history provided clear information of the delamination effects. From the results, it is expected that the proposed theory has the potential to predict the dynamic characteristics and delamination effects in smart biocomposite laminates.

Frequency response analysis of a delaminated smart composite plate

A frequency analysis of smart composite plate with delamination at ply interface was investigated in this article. The modeling was based on an electro-mechanical coupled improved layerwise theory, with implementing finite element method. Four-node plate elements with Lagrange and Hermite cubic interpolation functions were used for in-plane structural unknowns, electric unknowns, and out-of-plane structural unknowns. The general modal reduction method was applied to solve the second-order differential equation. Numerical results showed significant shift of natural frequencies in the frequency response of tip displacement and three sensor outputs due to the presence of delamination. It is found that the delamination locations also influence the natural frequencies of smart composite structure. Thus, the proposed methodology could be a useful tool to develop system identification and structural health monitoring techniques of smart composite structure.

PCA-based damage classification of delaminated smart composite structures using improved layerwise theory

A Principal Component Analysis (PCA)-based damage classification method is proposed, to analyze delaminated smart composite structure. The delamination of smart composite laminates was modeled using the improved layerwise theory. The transient sensor signals obtained from the proposed model were analyzed by the system identification algorithm, to identify the system parameters for both healthy and delaminated structures. The identified system parameters were used to classify the damage categories, and to assess the damage severity, based on PCA results. The numerical results of cross-ply and angle ply composite laminates demonstrated that the proposed method resulted in excellent damage classification ability of delaminated smart composite structures.

MFC와 능동 제어를 이용한 손상된 복합재의 동적 특성 복원

In this work, active control algorithm is adopted to reduce delamination effects of the damaged composite structure and control performance with MFC actuator is numerically evaluated. Finite element model for the damaged composite structure with piezoelectric actuator is established based on improved layerwise theory. In order to achieve high control performance, MFC actuator, which has increased actuating force, is considered as a piezoelectric actuator. Mode shapes and corresponding natural frequencies for the damaged smart composite structure are studied. After design and implementation of active controller, dynamic characteristics of the damaged smart composite structure are investigated.