考虑面内破坏过程的含分层损伤复合材料加筋层合板的动力响应

基于复合材料层合板一阶剪切理论，推导了复合材料层合板单元的刚度阵和质量阵列式；同时采用了Adams应交能法与Rayleigh阻尼模型相结合的方法，构造了相应的阻尼阵列式；为了防止在低阶模态中分层处出现的上、下子板不合理的嵌入现象，建立了含分层损伤复合材料加筋层合板动力分析的分层分析模型和虚拟界面联接模型。在上述模型和理论基础上，采用了Tsai提出的刚度退化准则和动力响应分析的精细积分法，对含分层损伤复合材料加筋层合板结构进行了动力响应和破坏分析。通过算例，分别讨论了外载频率、分层位置，以及破坏过程的刚度退化对含损伤复合材料加筋层合板动力响应特征的影响，得到了一些具有理论和工程价值的结论。     

General analytical solution to bending of composite laminated beams with delaminations

Based on the first-order shear deformable beam theory, a refined model for composite beams containing a through-the-width delamination is presented, and the deformation at the delamination front is considered. Different from the ordinary delami- nated beam theory, each of the perfectly bonded portions of the new model is constructed as two separated beams along the interface without assuming a plane section at the de- lamination front. The governing equations of the delaminated portions and bonded ones are established, combined with continuity conditions of displacements and internal forces. Solutions of delaminated composite beams with different boundary conditions, delamina- tion locations and sizes axe shown in excellent agreement with the finite element results, showing efficiency and applicability of the present model.     

Buckling of delaminated bi-layer beam-columns

An improved analytical model is presented to analyze the delamination buckling of a bi-layer beam-column with a through-the-width delamination. Both the transverse shear deformation and local delamination tip deformations are taken into consideration, and two delaminated sub-layers as well as two substrates in the intact (un-delaminated) regions are modeled as individual Timoshenko beams. A deformable interface is introduced to establish the continuity condition between the two substrates in the intact regions. Consequently, a flexible joint is formed at the delamination tip, and it is different from the conventional rigid joint given in most of studies in the literature, in which the local delamination tip deformations are completely ignored. In contrast to the local delamination buckling in our previous study (Qiao et al., 2010), the present model accounts for the global deformations of the intact region in the delaminated composite beam-column, thus capable of capturing the buckling mode shape transitions from the global, to global–local coexistent, and to local buckling for asymmetric delamination as the interface delamination increases. Good agreement of the present analytical solutions with the full 2-D elastic finite element analysis demonstrates the local deformation effects around the delamination tip and verifies the accuracy of the present model. Parametric studies are conducted to investigate the effects of loading eccentricity, delaminated sub-layer thickness ratio, and interface compliance on the critical buckling load for the delaminated composite beam-column. Transitions of buckling modes from the global to local delamination buckling are also disclosed as the thickness of one sub-layer reduces from the thick sub-layer to a thin film. The developed delamination buckling solution facilitates the design analysis and optimization of laminated composite structures, and it can be used with confidence in buckling analysis of delaminated composite structures.     

Vibration analysis of rotating fully-bonded and delaminated sandwich beam with CNTRC face sheets and AL-foam flexible core in thermal and moisture environments

Abstract

In the present study, the high-order free vibration analysis of rotating fully-bonded and delaminated sandwich beams; with and without vertical contact; containing AL-foam flexible core and carbon nanotubes reinforced composite (CNTRC) face sheets subjected to thermal and moisture field are investigated by using generalized differential quadrature method (GDQM). The compressible core and face sheets of sandwich beam, respectively, are composed of Aluminum alloy foam with variable mechanical properties in the thickness direction and CNTRC with temperature dependent material properties. In this study, the high-order sandwich panel theory (HSAPT) for AL-foam flexible core and Euler-Bernoulli beam theory for CNTRC face sheets are considered. By employing Hamilton’s principle, the governing partial differential equations of motion and associated boundary and continuity conditions for various types of regions (fully-bonded, delaminated with contact, delaminated without contact) are derived and then discretized by using GDQM. The final formulations lead to 14 partial differential equations for the entire structure including five equations for fully-bonded two-headed parts of AL-foam cored sandwich beam (AL-FCSB) and four equations for delaminated middle part of AL-FCSB beam which are combined in axial and transverse deformations. A parametric study is performed to investigate the influence of some important parameters such as existence of delaminated region, type of delaminated region (with or without contact), longitudinal position of delaminated region, slenderness ratio, face sheet thickness ratio, CNT volume fraction, temperature rise, moisture concentration, rotating speed, and hub radius. The obtained results reveal that the 1st frequency of delaminated AL-FCSB beam, whether with or without vertical contact, is less remarkably than ones of fully-bonded AL-FCSB beam which its value for the case of delaminated ‘with contact’ is larger than that of ‘without contact’. Moreover, the 1st frequency variation of the delaminated AL-FCSB beam is symmetrical with regard to the longitudinal position of the debonded region such that the 1st natural frequency declines with moving the debonded region toward the center of the beam. The study of vibration behavior of rotating sandwich beams is very important in design of rotating structural systems, specially damaged ones, such as airplanes, helicopter rotor blades, and robot arms. One of the most important types of damage encountered in mentioned cases is the decomposition of two layers or delamination. Working these rotating structures in the media, are always along with variations of temperature and humidity and hence their mechanical properties may be changed due to the environment conditions.

Communicated by S. Velinsky     

On irregularity-based damage detection method for cracked beams

A new damage detection technique using irregularity profile of a structural mode shape is proposed in this paper. The mode-shape of a cracked beam is first obtained analytically by using a general function. Its irregularity profile is then extracted from the mode shape by a numerical filter. The location and size of the crack in the beam can be determined by the peak value appearing on the irregularity profile. Two types of numerical filters, i.e., triangular and Gaussian, are examined. It has been found that the former filter is more effective in damage detection than the latter one. Numerical simulations suggest that the irregularity-based method requires a relatively low measurement resolution. Noise stress tests are carried out to demonstrate the effectiveness and robustness of this method under the influence of noise. As a validation, the proposed method is applied to detect crack damage in an E-glass/epoxy laminated composite beam. The successful detection of the crack in the composite beam demonstrates that the irregularity-based method is capable of assessing both the location and size of the crack and can be used efficiently and effectively in damage identification and health monitoring of beam-type structures.     

含分层损伤复合材料层合板剩余压缩强度研究

准确预测含分层损伤层合板的剩余压缩强度,对复合材料具有十分重要 意义。本文基于层合板一阶剪切理论,建立了一种考虑复合材料多种损伤的含分层层合板刚度退化模型,通过数值算例分析了分层屈曲临界载荷与材料强度极限的关系以及刚度退化对含分层层合板前后屈曲行为的影响。     

Vibration of composite beams with two overlapping delaminations

Delaminations in composite laminates may develop from small cracks due to fabrication and impact loading, or from places of high stress concentration. The locations of the delaminations are not determinate. In this research, an analytical solution for the free vibration of a composite beam with two overlapping delaminations is presented. The delaminated beam is analyzed as seven interconnected beams using the delaminations as their boundaries. The continuity and equilibrium conditions are satisfied between the adjoining regions of the beams. Classical beam theory is applied to each of the beams. Complex vibration behaviors emerge for different sizes and locations of the delaminations. Comparison with analytical results reported in the literature verifies the validity of the present solution.Christian N Della wishes to thank Nangyang Technological University for the scholarship.     

FRP strengthened walls with delaminated regions – Geometrically nonlinear response

The paper studies the geometrically nonlinear behavior of walls that are strengthened with fiber reinforced polymer (FRP) composite materials but include pre-existing delaminated regions. The paper uses an analytical–numerical methodology. Three specially tailored finite elements that correspond to perfectly bonded regions, to delaminated regions where the debonded layers are in contact, and to delaminated regions where the debonded layers are not in contact are presented. All finite elements are based on a high order multi layered plate theory. The geometrical nonlinearity is introduced by means of the Von Karman nonlinear strains whereas the contact nonlinearity is handled iteratively. The validity and convergence of the finite element models is demonstrated for each type of element through comparison with closed form analytical solutions available for specific cases. The unified model that combines the three types of finite element is then used for studying the nonlinear behavior of a locally delaminated FRP strengthened wall under in-plane normal and in-plane shear loads. Finally, conclusions regarding the effect of the delamination on the response of the strengthening system, on the conditions that evolve in the bonded region that surrounds the delamination, and on the global response of the multi-layered structure are drawn. Additional conclusions regarding the application of the modeling approach to other delamination sensitive layered structural systems close the paper.     

Interlaminar stresses and energy release rates in delaminated orthotropic composite plates

The classical laminated plate theory is applied to calculate the stresses and energy release rate function in symmetrically delaminated orthotropic plates. First, the equilibrium of classical plate forces, moments and interfacial shear stresses is formulated. Second, the displacement continuity between the interface plane of a double-plate model was considered. The governing equation system of the double-plate model consists of ten equations. As an example a delaminated, orthotropic, simply-supported plate subjected to a point force is analyzed. The distribution of the plate forces as well as the interlaminar shear stresses over the uncracked part were determined. Moreover, the mode-II and mode-III energy release rate distributions along the crack front were calculated by the J-integral. The 3D finite element model of the delaminated composite plate was also created. The results indicate a reasonably good agreement between analysis and numerical calculation.     

Calculation of higher natural frequencies of simply supported elastic composite beams using Riccati matrix method

A composite beam is composed of an upper slab and a lower beam connected at the interface by shear transmitting studs. In this paper, an improved and efficient numerical model for the calculation of higher natural frequencies of an elastic composite beam is presented. The numerical model uses the Riccati transfer matrix method. First, the exact field transfer matrix for an element of the beam is represented using the combination of the Analog Beam Method and the transfer matrix method. Second, applying Riccati method to the beam system, the natural frequencies can be easily calculated. The advantage of the present model is to overcome the numerical instabilities of the ordinary transfer matrix method, especially when calculating the higher natural frequencies of structures. A numerical example is given to illustrate and compare the results with those available from other methods. Finally, a parametric study is given to examine the effect of various parameters of the elastic composite beam on its free vibration behavior.     

Generalized layerwise mechanics for the static and modal response of delaminated composite beams with active piezoelectric sensors

A coupled linear layerwise laminate theory and a beam FE are formulated for analyzing delaminated composite beams with piezoactuators and sensors. The model assumes zig-zag fields for the axial displacements and the electric potential and it treats the discontinuities in the displacement fields due to the delaminations as additional degrees of freedom. The formulation naturally includes the excitation of piezoelectric actuators, their interactions with the composite laminate, and the effect of delamination on the predicted sensory voltage. The quasistatic and modal response of laminated composite Gr/Epoxy beams with active or sensory layers having various delamination sizes is predicted. The numerical results illustrate the strong effect of delamination on the sensor voltage, on through the thickness displacement and on the stress fields. Finally, the effect of delamination on modal frequencies and shapes are predicted and compared with previously obtained experimental results.     

A Combined Static/Dynamic Technique for Damage Detection of Laminated Composite Plates

There is a growing demand to develop viable techniques for effective damage detection of composite structures, and the dynamics-based approach has been broadly used in structural health monitoring. A new combined static/dynamic technique for improved damage detection of laminated composite plates is presented. The promise of the technique is that under the sustaining static load, the abnormality of dynamic response due to damage may become more pronounced and easy to be detected. The experimental program consists of testing an E-glass/epoxy composite plate with an embedded delamination under a pre-set static compressive force, and the dynamic response of laminated composite plates is measured using two different actuator–sensor systems: (1) PZT (lead–zirconate–titanate) actuators and scanning laser vibrometer (SLV) sensing system (PZT–SLV), and (2) PZT actuators and Polyvinylidenefluoride (PVDF) sensors (PZT–PVDF). The influence of sustaining static forces to dynamic response of delaminated composite plates is evaluated. The numerical finite element (FE) analysis is also conducted to verify the effectiveness of this technique. The experimental and numerical mode shapes are used to detect the presence, location, and size of the delamination and to study the effect of static load on dynamic response. Two relatively new damage detection algorithms (i.e., Simplified Gapped Smoothing Method (GSM) and Generalized Fractal Dimension (GFD)) are employed to analyze the Uniform Load Surface (ULS) calculated from the experimental and numerical data. From the dynamic response and analysis results using the damage detection algorithms, it is observed that as the sustaining static load increases, the delamination is much easier to be identified through the enlarged damage parameters. The present combined static/dynamic technique is capable of magnifying the effect of damage, thus improving the effectiveness of damage detection.     

F E M analysis of delamination buckling in composite plates and shells

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New accurate efficient modeling techniques for the vibration analysis of T-joint thin-walled box structures

We propose new accurate efficient modeling techniques for the vibration analysis of T-joint thin-walled box structures. The essence of the present techniques is to use beam elements to model thin-walled members of the joint, but the elements are based on an eight-degree-of-freedom (8-DOF) beam theory capable of handling warping and distortion. Two approaches are considered to model the interfacing joint region connected to three adjacent thin-walled box structures: the first one is to model the joint region with plate elements and the second one is to use a joint element derived to be consistent with nearby 8-DOF beam elements. The efficiency of the present techniques comes from the use of beam elements to model the box structures while the accuracy comes from the use of the higher-order beam theory accounting for warping and distortion. The procedures to match the dissimilar elements and to develop the joint element are also presented in this work. The effectiveness of the present approaches is demonstrated by numerical examples.     

Buckling analysis of two layer delaminated beams with bridging

Stitching has been used as through-thickness reinforcement to reduce the effects of delamination. In stitching, the delamination will be held by stitches in the form of crack/interface bridging. In the present work, the reinforcement of stitching threads is assumed to provide continuous linear restoring tractions opposing the delamination opening. A generalized mathematical model is developed to study the buckling analysis of two layer delaminated beams with bridging by using Rayleigh–Ritz energy method. The delaminated beam is analyzed as four interconnected beams using the delamination as their boundary. Lagrange multipliers are used to enforce the boundary and continuity conditions between the junctions of the interconnected beams. The developed mathematical model is solved as an eigenvalue problem in which the lowest eigenvalue gives the buckling load. Effective-bridging modulus, a new nondimensionalized parameter, is introduced to study the influence of bridging on the delamination buckling. It is shown that bridging strongly influences the buckling load of the delaminated beams and a monotonic relation is observed between the buckling load and the effective-bridging modulus. Parametric studies in terms of delamination sizes and locations along spanwise and thicknesswise positions on the buckling load have been carried out. The bridging is found to be effective for shallow delaminations of moderate length, and for deep and long delaminations. Spanwise positions of delamination strongly influence the buckling loads. In addition, an analytical model for obtaining upper bounds of the buckling load is developed by using Euler–Bernoulli beam theory. Effective-slenderness ratio, a new nondimensionalized parameter is defined and it is found to be controlling the buckling mode configurations, i.e., local, global and mixed modes.     

Postbuckling behaviors of open section composite struts with edge delamination using a layerwise theory

We investigate the mechanical stability of L-section and T-section composite struts with single edge delamination. We propose a solution procedure based on a layerwise theory and the first order shear deformation theory by taking into consideration of the von Karman geometrical nonlinearity. We derive the nonlinear equilibrium equations according to the minimum total potential energy principle, and solve them using Rayleigh–Ritz method and Newton–Raphson method. In modeling the delaminated L-section and T-section struts, we divide the structures into regions, and exert continuity conditions between different regions. The proposed model is capable of analyzing both local buckling of the base laminate and sublaminate as well as the global buckling of the whole structure. We present numerical results to provide an insight into effects of size of delamination on buckling mode and post-buckling behaviors of the struts. We perform the three-dimensional finite element analysis using the ABAQUS commercial software. The results show a very good agreement with those obtained by the analytical method. The results indicate that the presence of delaminations not only reduces the load-carrying capacity of open section struts remarkably, but also plays a pivotal role in the critical buckling load and buckling mode shape of the struts.     

Nonlinear delamination buckling and expansion of functionally graded laminated piezoelectric composite shells

In this paper, an analytical method is presented to investigate the nonlinear buckling and expansion behaviors of local delaminations near the surface of functionally graded laminated piezoelectric composite shells subjected to the thermal, electrical and mechanical loads, where the mid-plane nonlinear geometrical relation of delaminations is considered. In examples, the effects of thermal loading, electric field strength, the stacking patterns of functionally graded laminated piezoelectric composite shells and the patterns of delaminations on the critical axial loading of locally delaminated buckling are described and discussed. Finally, the possible growth directions of local buckling for delaminated sub-shells are described by calculating the expanding forces along the length and short axis of the delaminated sub-shells.     

Post-buckled propagation model for compressive fatigue of impact damaged laminates

An analytical model for prediction of compressive fatigue threshold strains in composite plates with barely visible impact damage (BVID) is presented. The model represents the complex damage morphology as a single circular delamination at a critical level and calculates the strain at which thin-film buckling of the circular delaminated region occurs. The threshold strain is defined as the strain at which the strain energy release rate for the fracture of post-buckled delaminated plies along the delamination is equal to the critical Mode I value (G_1C) for the resin. The model predicts the critical through-thickness level for delamination, the stability of delamination growth and also the sensitivity to experimental error in geometric measurements of the damage area. Results obtained using the model show an agreement of fatigue strain to within 4% of experimental values for four sets of data reported in the literature.     

Damage detection method in complicated beams with varying flexural stiffness

A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method (SSEM), and its applicability condition is introduced. For a beam with the continuously varying flexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.