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To efficiently design the stiffness of the laminated composite blade‐like structure, an analytical method to assess deformation of variable cross‐section laminated beam under cantilever bending load was developed, in which a local ply density matrix method was introduced to characterize the ply‐up in arbitrary cross‐section after ply drop‐off process and infinitesimal element segment method was used to convert complex variable cross‐section specimen into local equal cross‐section beam structure. The model was validated by the cantilever beam experiment with relative predicted error of stiffness of 5.7%. Inner and outer ply drop‐off models were analyzed using the proposed analytical method. The results show that: (1) stiffness of the outer ply drop‐off model is the highest, at 13.07 N/mm, while that of the inner ply drop‐off model 2 is the lowest, about 17.8% lower than the outer ply drop‐off model; (2) maximum relative deformation difference between the inner ply drop‐off model 2 and outer ply drop‐off model is 21.7% at the free side of the cantilever beam. It indicates that anti‐deformation ability of the variable cross‐section laminated structure can be efficiently designed by the proposed analytical method, especially for the section close to the free side. Highlights: Developed a bending stiffness prediction method for composite beam.Variable cross‐section feature of the composite laminate was considered.Local ply density matrix method was introduced to characterize ply drop‐off.Proposed method was validated by cantilever beam bending experiment.Inner and outer ply drop‐off models were compared by the proposed method. [ABSTRACT FROM AUTHOR]

Composite structures are optimized in shape by terminating specific plies gradually. However, stress concentration at the ply drop-off can cause interlaminar delamination from the ply edge. In this study, Ply Curving Termination (PCT), which is introduced by locally curving fibers at 0° ply edges, is used to enhance tensile strength of the ply drop-off. To clarify the dependence of the PCT strength on the curved fiber angle (PCT angle), static tensile tests using ply drop-off specimens are conducted, followed by detailed damage observations using X-ray CT. The results indicates that the strength significantly increases with PCT but the fracture behavior differs depending on the PCT angle. Interestingly, specimens with large PCT angles fail from the position where the fibers curve, away from the ply edge. This PCT-specific failure mechanism is then elucidated using finite element analysis and the virtual crack closure technique, indicating that shear lag caused by the stiffness change due to fiber curving is important. Finally, using the revealed PCT failure mechanism, PCT angles that are the most effective in enhancing tensile strength is discussed. [ABSTRACT FROM AUTHOR]

Delamination (the separation between plies) is a common failure in Fiber Reinforced Polymer (FRP) laminated composites. The presence of delamination reduces the structural stiffness and changes in dynamic responses. The change in dynamic parameters can be successfully used for assessing structural health monitoring (SHM) for composite structures. SHM requires large amount of numerical/experimental data. This study focuses on the influence of the delamination parameters (size and in-plane location) on vibration behavior of a laminated tapered fiber reinforced polymer (FRP) composite plate with ply drop-off. Furthermore, developing a surrogate model as a fast-executing model to predict the shift in the natural frequency to reduce the computational effort for solving forward problems. The layerwise theory (LWT) has been used, and the delamination is modeled by "constrained mode" were solved using the finite element method (FEM). The numerical model was validated with an experimental modal analysis of tapered plates without delamination to make the model more robust. The effect of delamination was studied using surface plots produced using response surface methodology (RSM). The results show that the delamination size and location significantly affect the natural frequency shift. The RSM and ANN models were considered as surrogate models, and it was evaluated using an experimental modal analysis. The results shows that the single-output ANN model can predict the shift in the natural frequency with a minimum Root Mean Square Error (RMSE). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a more effective meshfree shape function for free vibration analysis of ply drop-off laminated rectangular plates. The proposed meshfree Tchebychev-radial point interpolation method (TRIPM) shape function uses the Tchebychev polynomials and multi-quadrics (MQ) radial functions as the basis. The first order shear deformation theory (FSDT) is applied to the formulation for free vibration analysis of ply drop-off laminated rectangular plate, and the field functions are approximated by TRIPM shape function. The governing equations and boundary conditions for the substructures of ply drop-off laminated plate are derived, and the equations of the whole system are obtained by combining them using a continuous condition. The boundary and continuous conditions are generalized by the introduction of an artificial spring technique, and the type of boundary conditions is selected according to the spring stiffness. The accuracy and reliability of the proposed method are verified by comparing the results of the literature and the finite element program ABAQUS. The free vibration characteristics including natural frequencies and mode shapes of ply drop-off laminated rectangular plates with various geometrical dimensions and boundary conditions are presented through numerical examples. [ABSTRACT FROM AUTHOR]

• The draping formability while considering the manufacturing of CFRTP B-pillar. • Design of CFRTP B-pillar structure with variable stiffness considering ply drop-off. • Dynamic impact simulation of CFRTP B-pillar with variable stiffness. • The layup optimization of CFRTP B-pillar based on side impact. This study focuses on enhancing of crashworthiness and lightweight of the automotive B-pillar structure by using continuous carbon fiber reinforced thermoplastic composites (CFRTP) and optimized layer design. Firstly, the B-pillar is divided into four regions with variable stiffness. Quasi-static three-point bending test and numerical simulation are performed to calculate the stiffness of the structure. Then, the four regions of the B-pillar with different CFRTP layers are structurally designed to realize variable stiffness. Considering manufacturing requirements, a draping simulation is employed to predict potential layer defects. The results demonstrate that B-pillar structural performance is enhanced after the reorientation of CFRTP prepreg. Afterward, the crashworthiness of the CFRTP B-pillar considering the ply drop-off is evaluated and compared with the traditional Q235 steel counterparts. The results indicate that the CFRTP B-pillar exhibits superior crashworthiness but a substantial reduction in mass by 53.1%. Finally, the multi-island genetic algorithm (MIGA) is employed to achieve the optimal layer design scheme for lay-up optimization of the CFRTP B-pillar, and the crashworthiness of the CFRTP B-pillar with variable stiffness is further improved. The current work highlights a structural design strategy for CFRTP components for vehicles, which is crucial for the updating of automobile engineering. [Display omitted] [ABSTRACT FROM AUTHOR]

• Identify delamination severity in a thickness tapered FRP composite plate. • The Damage Index and Curvature Damage Factor algorithms were compared. • The mode shape curvature was obtained from experimental modal analysis. • Performance of the algorithm to identiy size and location were discussed. Delamination frequently occurs in composite laminates composed of fibre-reinforced polymer (FRP) and is considered a typical type of failure. The structural health monitoring (SHM) of structures with composites can be assessed by utilising changes in dynamic responses caused by a reduction in structural stiffness resulting from delamination. However, to ensure successful SHM, an inverse problem solution is required. Solving inverse problems can be computationally expensive and time-consuming, especially for large and complex structures. This study examined the efficiency of different damage identification techniques in detecting delamination in tapered composite plates. Four damage detection algorithms were tested, including the mode shape curvature (MSC), gapped smoothing method (GSM), mode shape curvature square (MSCS), and the gapped smoothing method square (GSMS) were implemented as damage index (DI) and curvature damage factor (CDF). A tapered composite plate composed of glass-fibre reinforced polymer was subjected to experimental modal analysis, including one undelaminated plate and three artificially delaminated plates. The delamination areas in the artificially damaged composite plates ranged from 1.5% to 8% of the plate area and were located at different interfaces. The results showed that statistical treatment further enhanced the damage identification, the CDF using the GSMS method performed the best overall, particularly in identifying the size and locations of delamination. The study also found that adding more modes to the averaging process increased CDF sensitivity and reduced uncertainty. This study suggests that the CDF method using GSMS is a promising approach for detecting delamination in tapered composite plates, with potential applications in aerospace, automotive, and civil engineering. [ABSTRACT FROM AUTHOR]

To ensure the safe operation of the helicopter throughout its lifetime, the primary structure has to be designed taking into account damage tolerance criteria. This has been considered in the design process, for example, by using multiple load paths as well as by taking into account the presence of certain structural defects like impacts or manufacturing defects in composite parts when performing the dimensioning and lifetime calculations. This paper describes and presents an effort performed for damage tolerance (DT) aspects of rotorcraft horizontal tail (HT) through multi-scale (MS) modeling computational approach to assess the growth rate of damages from fatigue under spectrum loading from rotorcraft mission profile and consideration of the effects of material variability to assess structural advantages. Main emphasis was laid on the design of the cyclic loaded components in order to achieve unlimited life with high flaw tolerance. A micromechanics-based multi-scale progressive failure analysis (MS-PFA) approach that detects damage and fracture evolution is carried out to assess the durability and damage tolerance (D&DT) of HT with effect of defects: (1) ply drop-off and features at the reduced skin thicknesses along the length of spar; (2) fiber waviness exhibited in thick sections; and (3) void shape, size, distribution. Fatigue life is estimated under service spectrum block loading conditions in critical mission by determining the material stiffness and strength degradation, failure load and cycles. [ABSTRACT FROM AUTHOR]

The thermal buckling characteristics of non-uniformly heated tapered laminated composites plates with ply drop-off have been investigated numerically. Detailed parametric studies have been carried out for the effects of taper configuration, temperature variation, aspect ratio and structural boundary conditions on critical buckling temperatures and buckling mode shapes. It is found that the nature of taper as well as the applied temperature field have considerable effects on the critical buckling temperatures of laminated composite tapered plates. Square plates buckle at the highest temperature when subjected to the decreasing temperature profile. Additionally, it is noted that Taper B and Taper C plates show the best behavior under buckling for most structural boundary conditions. Moreover, the change in buckling mode shapes with respect to temperature profile and taper configuration is significant for rectangular plates in comparison with square plates. [ABSTRACT FROM AUTHOR]

In this study, the free vibration responses of the laminated composite beams with varying cross-section formulated by considering the cross sectional variation along longitudinal (thickness) and transverse (width) directions of the beam are investigated. The governing differential equations of motion of the various taper models of rotating laminated composite beams with varying section are presented in the finite element formulation based on higher order shear deformation theory (HSDT) including the rotating effects such as centrifugal force and pre-stress. The finite element formulation developed for the free vibration analysis of non-uniform laminated composite beams is validated by comparing the natural frequencies evaluated using the present finite element method (FEM) with those obtained from the experimental measurements. Various parametric studies are also performed to study the effect of taper models, rotational speed and ply orientation on the dynamic characteristics of the composite beam with varying section. It was concluded that significant variation in natural frequencies could be yielded by tapering both in the thickness and width directions of laminated composite beam. It was also concluded that the natural frequencies of the non-uniform composite beams can be altered by tailoring or dropping off the plies to fulfil the design requirements of rotating components. [ABSTRACT FROM AUTHOR]

In this study, the free and forced vibration responses of rotating delaminated thickness tapered (non-uniform) composite plates are investigated. The governing differential equations of motion of the various models of a rotating mid-plane delaminated thickness tapered laminated composite plate are presented in the finite element formulation based on classical laminated plate theory (CLPT) including the various rotational effects. The finite element formulation developed for the free vibration analysis of rotating delaminated tapered composite plate is validated by comparing the natural frequencies evaluated using the present finite element method (FEM) with those obtained from the experimental measurements. Various parametric studies are also performed to study the effect of taper models, rotational speed, length and location of delamination on the dynamic characteristics of the tapered composite structure. It was observed that the percentage of decrease in natural frequencies of delaminated composite plate when compared to intact composite plate at lower modes is lesser than those compared to higher modes irrespective taper models and rotating speeds considered. Further, it was noticed that the decreasing percentage of natural frequencies of the mid-plane delaminated different taper models of composite plate over intact plate increase in the order of TM2, TM1, TM3 and uniform composite. [ABSTRACT FROM AUTHOR]

In this study, dynamic delamination behavior in asymmetric GFRP tapered laminates under quasi-static tensile loading is investigated experimentally and numerically. Abaqus/Explicit cohesive interface modeling is utilized to simulate delamination initiation and dynamic propagation. Time-frame based delamination mechanisms predicted in simulations are compared to in-situ high-speed camera images for four geometrically asymmetric specimens containing grouped and ungrouped drop-off types. It is observed that the ply drop-off type governs not only the strength of the tapered beam but also the delamination progression path and its stability. For specimens with consecutive drop-offs, a good agreement is obtained between the experimental observations and numerical results in terms of delamination onset location, propagation patterns, and instability of delamination growth. For specimens with ungrouped drop-offs, a modified cohesive strength approach is shown to be necessary to enhance the aforementioned correlations. The effect of such modification on delamination propagation manner is explicitly shown for the first time in this paper. [ABSTRACT FROM AUTHOR]

This paper aims to predict the spring-in of U-shaped composite parts with ply drop-offs rapidly and precisely. To this end, an integrated approach was proposed by combining an analytical model for the zones of equal thickness with a proxy model for the effects of ply drop-offs. Firstly, a parametric finite element analysis (FEA) of ply drop-offs was used to collect initial data for the proxy model. Based on these data, the response surface method (RSM) and analysis of variance (ANOVA) were used to determine the input parameters of the proxy model. Then, considering the computational efficiency and accuracy, the radial basis function (RBF) model was selected for ply drop-offs among three data-driven methods to couple with the analytical model for the equal-thickness zones. As the prediction results of the proposed approach were compared with the experimental results, acceptable accuracy was achieved, and computation time was greatly reduced compared to FEA. Consequently, the integrated approach can quickly and accurately predict the spring-in of U-shaped composite parts with ply drop-offs. • An integrated analytical and data-driven method was used to predict curing deformation of U-shaped parts with ply drop-offs. • The proposed approach could quantify the effect of material, flange, lay-up, and ply drop-offs on the spring-in angle. • While maintaining high efficiency, the prediction results of the proposed approach matched well with experimental data. [ABSTRACT FROM AUTHOR]

The prediction of delamination onset is a challenging task in the design of thick tapered composite laminates, where multiple ply terminations (“drop-offs”) are present. This paper addresses the development of a global-local finite element-based design approach for tapered laminates, whereby layered Timoshenko beam models are employed to predict delamination initiation from individual drop-offs. This modelling strategy provides a fast and conservative method for evaluating the strength of tapered composite laminates. Parametric test cases are presented in order to validate the methodology and understand its limitations. Finally, the application of the tool to a relatively thick tapered composite test specimen comprising multiple ply-drops is demonstrated. [ABSTRACT FROM AUTHOR]

This study investigates the dynamic properties of the thickness tapered laminated composite plate. The governing differential equations of motion of the various configurations of a thickness tapered composite plate are presented in the finite element formulation using classical laminated plate theory. The validity of the developed finite element formulation is demonstrated by comparing the natural frequencies evaluated using the present finite element method with those derived from the experimental measurements and presented in available literature. Various parametric studies are also performed to investigate the effect of taper configuration, aspect ratio, taper angle and ply orientation on free vibration responses of the structures. The comparison of the free vibration mode shapes of uniform and various tapered configurations of tapered laminated composite plates are also presented. Influences of taper angle on the free vibration fundamental mode shapes under various boundary conditions and various ply configurations are also presented. The forced vibration response of a composite plate is also investigated to study the dynamic response of tapered composite plate under the harmonic force excitation in various tapered configurations. It is concluded that the dynamic properties of a composite plate could be tailored by dropping of the plies to yield various tapered composite plate. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation of impact and compression after impact (CAI) of a tapered composite laminate using a discrete ply model. Three types of damage: matrix cracking, delamination and fiber rupture are considered in the model. The presence of ply drop-off generates some discontinuities in the stress field and therefore adds difficulties to the simulation. Analyses of numerical results are performed to understand the damage and failure mechanisms in both tests. Numerical results in terms of force-displacement curves, delamination shape, CAI displacement field and residual strength are compared with experimental data. Impact simulation is in good correlation with the tests. CAI strength is under predicted and depends on quality of the meshing of the transition region. This study highlights the importance of modeling intra-ply matrix cracking for impact simulation. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of CAI (compression after impact) of tapered composite laminate. Two types of layup with thickness changing from 4 mm to 6 mm are considered. A new CAI testing rig, suitable for the specimens and a brief description of impact damage are presented first. Then, the behavior of impacted specimens under compressive loading is discussed along with the effects of ply drop-off parameters (taper angle, ply drop-off disposition and configuration) and impact point location on the failure mechanism. Finally, the residual strength in CAI of tapered laminates is compared with equivalent flat laminates. The results show that compressive behavior of the specimens is mostly governed by a coupling between compression and bending, generated by the discontinuity of the neutral axis in the tapered region. Despite this difference of behavior with flat laminates, the presence of ply drop-off has little effect on the residual strength in CAI. [ABSTRACT FROM AUTHOR]

• Identify delamination severity in a thickness tapered FRP composite plate. • The numerical model is generated using LWT and validated with experimental results. • The surrogate model is used to predict frequency shifts (forward ANN). • Two computational algorithms, SARGA and ANN, were used to identify delamination. The typical failure in fibre-reinforced polymer (FRP) laminated composites is delamination. It reduces structural stiffness and changes in dynamic responses, which can be successfully used for assessing structural health monitoring (SHM) of composite structures. SHM often requires the solution of an inverse problem. This study focuses on solving the inverse problem with minimal computational time to predict delamination size, in-plane location, and interface. For the inverse model, two computational intelligence algorithms, the surrogate-assisted real-coded genetic algorithm (SARGA) and an artificial neural network (ANN) were used. A surrogate model is a fast-executing model for predicting the shift in the natural frequency using a forward ANN. For ANN training, the database size was optimized. The layerwise theory was solved using the finite element method for a laminated tapered FRP plate with ply drop-off, and 'constrained mode' is used to model the delamination. The experimental modal analysis was conducted on a glass-fibre reinforced polymer tapered composite plate with one intact plate and three artificially delaminated plates. The algorithms are validated using numerically simulated and experimentally measured frequencies. The numerical validation showed a better prediction of delamination size, in-plane location, and interface when compared with the experimental validation. Nevertheless, SARGA can reasonably predict the size, in-plane (x) location and interface of the delamination with an average overlapping ratio of 72.89%. The comparison of algorithms demonstrates the application of SARGA with the frequency-based approach for delamination detection and real-time condition monitoring in real-world applications. [ABSTRACT FROM AUTHOR]

In this study, vibration characteristics of a tapered laminated thick composite plate have been investigated using finite element method by including the shear deformation and rotary inertia effects. The governing differential equations of motion of a tapered laminated thick composite plate are presented in the finite element formulation based on first-order shear deformation theory for three types of taper configurations. The effectiveness of the developed finite element formulation in identifying the various dynamic properties of a tapered laminated thick composite plate is demonstrated by comparing natural frequencies evaluated using the present FEM with those obtained from the experimental measurements and presented in the available literature. Various parametric studies are also performed to investigate the effect of taper configurations, aspect ratio, taper angle, angle ply orientation and boundary conditions on free and forced vibration responses of the structures. The comparison of the transverse free vibration mode shapes of the uniform and tapered composite plates under various boundary conditions is also presented. The forced vibration response of a composite plate is investigated to study the dynamic response of tapered composite plate under the harmonic force excitation in various tapered configurations. It is concluded that the dynamic properties of laminated thick composite plates could be tailored by dropping off the plies to yield various tapered composite plate. [ABSTRACT FROM AUTHOR]

The mechanisms and structural parameters affecting the interlaminar stress field in laminates with ply drop-offs have been investigated to help better understand the effects of different parameters in such laminates. Based on equilibrium considerations, two fundamental mechanisms that give rise to interlaminar stresses have been identified: the termination effect, caused by the load transfer from the terminated ply group to the continuous ply groups; and the offset effect, caused by the redistribution of the load in the outer continuous ply groups through an offset in the through-thickness direction from the undropped region to the dropped region. The characteristics of the two mechanisms and the factors that affect the interlaminar stress field caused by these mechanisms are described by considering two specific laminate configurations in which these mechanisms can be isolated. Factors of particular importance are the magnitudes of the far-field loads in the terminated and outer continuous ply groups, the offset distance, and the taper angle. Parametric studies of five factors are conducted via an analytical method for configurations under in-plane and bending loads to obtain general trends of the interlaminar stress field and a better understanding of the contributions of the two fundamental mechanisms. The structural parameters considered are the taper angle, the location of the terminated plies, the overall stiffness and layup sequence of the terminated ply group, and the number of terminated plies, The overall characteristics and trends of the interlaminar stresses can be explained easily in terms of the two fundamental mechanisms. The current study presents a clear view of the mechanisms giving rise to interlaminar stresses. Such a perception can be used to understand and anticipate interlaminar stress field trends in generic laminates with ply drop-offs in a simple and systematic manner. This can be particularly useful in preliminary design where these trends can be anticipated for the many configurations often under consideration, without performing actual analysis of these many potential configurations. [ABSTRACT FROM AUTHOR]

A combination of analytical and numerical method is employed to solve the ply drop-off problem. The singular stress fields in the drop-off region are characterized by using the eigenfunction expansion method. A global element capable of capturing the singular behavior is developed and incorporated into a general finite element analysis to provide an overall accurate solution of the stress fields in the ply drop-off region. This facilitates the use of a coarse mesh at the ply drop-off location even there are singular fields. The validation of the global–local finite element method has been carried out with the help of numerical examples. [Copyright &y& Elsevier]

Static and tension–tension fatigue tests have been undertaken on carbon-fiber/epoxy specimens with tapered sections. The effects of the value of the slope angle, a delamination in the tapered section, and ageing have been investigated. The results of this study show that the stress amplitude of the civil-aircraft fatigue spectrum does not create any damage in the tapered section and has no contribution to the propagation of delamination when 132 g/m2 material is used, with maximum 20° tapered specimens. A static strength reduction is induced by ageing. No effect on duration is observed. A statistical analysis is made to fix, on a A-value or B-value basis, the relationship between fatigue stress, fatigue life and residual strength. [Copyright &y& Elsevier]