Classical Lamination Theory Research Articles

Impact on Vectran/Epoxy composites: Experimental and numerical analysis

AbstractThe aim of this paper is to present a plane-stress damage model based on the Classical Lamination Theory (CLT), developed for polymer fibre-based composite. The proposed numerical model utilises a damage mechanics methodology coupled with fracture mechanics to predict composite failure, particularly under quasi-static and dynamic loadings. In addition, the proposed constitutive equations consider a single secant modulus to describe its tensile and compressive modulus, as opposed to the physically proposed tier models for polymer fibres which possesses a ‘skin-core’ structure. The result of single element and coupon-level modelling showed excellent correlation with the experimental results. In addition, it was also found that the proposed numerical model showed considerable accuracy on the response of the composite under low and high velocity impact loadings.

Effects of Elastic Couplings in a Compressed Plate Element with Cut-Out.

Analytical calculations were performed on carbon fiber-reinforced polymer (CFRP) laminates in an asymmetrical configuration. The asymmetric configuration of composites was investigated, where extension-twisting and extension-bending couplings were used to obtain the elastic element. Analysis of the presence of elastic couplings was conducted according to Classical Laminate Theory (CLT). Components of matrices A, B, and D, as well as the parameters Dc and Bt, were obtained using the MATLAB software environment. The results show that couplings between the extension and bending, as well as between the extension and twisting, were strongly dependent on specimen plies' orientation. Moreover, additional analysis was performed on the influence of layer angle on the terms which are components of the Bt and Dc coefficients. The results indicate that the angle of laying fibers around 45-50° significantly amplifies the effects of elastic couplings.

Failure Analysis and Optimization Design of Wing Skin Unbalanced Lay-Up

To clarify the influence of the unbalanced coefficient and the change in lay-up angle on the failure characteristics of the laminate in the static aeroelastic problem of the aircraft, numerical simulations were performed based on the classical laminate theory and the Tsai-Wu failure criterion, as well as the fluid-structure coupling calculation method. The structure’s stress-strain and failure curves are found to decrease as the unbalanced coefficient increases. The stress curve’s slope is relatively stable, whereas the strain and failure curves’ slopes change three times, indicating that strain may be the primary cause of structural failure. Unbalanced coefficient laminates are classified into three types based on their mechanical properties low unbalanced coefficient laminates (Unbalanced coefficient 0.2 to 0.3), quasi-balanced coefficient laminates (Unbalanced coefficient 0.4 to 0.6, Balanced laminate when the Unbalanced coefficient is 0.5), and high unbalanced coefficient laminates (Unbalanced coefficient 0.7 to 0.8). Within their respective spanning intervals, the mechanical properties of the three types of laminates remain relatively stable. An increase in the ply angle reduces both the elastic deformation of the structure and the failure factor. The variation patterns of structural strain and failure at 45° and 60° ply angles decrease as unbalanced coefficients increase, whereas the opposite is true for 30° ply angles. Finally, a two-level optimization method based on “equalized plies” and “equal-angle plies” was developed, resulting in a 23.93% reduction in elastic deformation and a 37.04% reduction in the laminated structure's failure coefficient when compared to the preoptimization results.

Failure Evaluation of Reinforced Concrete Beams Using Damage Mechanics and Classical Laminate Theory

The prediction of the behavior of reinforced concrete beams under bending is essential for the perfect design of these elements. Usually, the classical models do not incorporate the physical nonlinear behavior of concrete under tension and compression, which can underestimate the deformations in the structural element under short and long-term loads. In the present work, a variational formulation based on the Finite Element Method is presented to predict the flexural behavior of reinforced concrete beams. The physical nonlinearity due cracking of concrete is considered by utilization of damage concept in the definition of constitutive models, and the lamination theory it is used in discretization of section cross of beams. In the layered approach, the reinforced concrete element is formulated as a laminated composite that consists of thin layers, of concrete or steel that has been modeled as elasticperfectly plastic material. The comparison of numerical load-displacement results with experimental results found in the literature demonstrates a good approximation of the model and validates the application of the damage model in the Classical Laminate Theory to predict mechanical failure of reinforced concrete beam. The results obtained by the numerical model indicated a variation in the stress–strain behavior of each beam, while for under-reinforced beams, the compressive stresses did not reach the peak stress but the stress–strain behavior was observed in the nonlinear regime at failure, for the other beams, the concrete had reached its ultimate strain, and the beam’s neutral axis was close to the centroid of the cross-section.

Hierarchical modeling of elastic moduli of equine hoof wall

This study predicts analytically effective elastic moduli of substructures within an equine hoof wall. The hoof wall is represented as a composite material with a hierarchical structure comprised of a sequence of length scales. A bottom-up approach is employed. Thus, the outputs from a lower spatial scale serve as the inputs for the following scale. The models include the Halpin-Tsai model, composite cylinders model, a sutured interface model, and classical laminate theory. The length scales span macroscale, mesoscale, sub-mesoscale, microscale, sub-microscale, and nanoscale. The macroscale represents the hoof wall, consisting of tubules within a matrix at the mesoscale. At the sub-mesoscale, a single hollow tubule is reinforced by a tubule wall made of lamellae; the surrounding intertubular material also has a lamellar structure. The lamellae contain sutured and layered cells at the microscale. A single cell is made of crystalline macrofibrils arranged in an amorphous matrix at the sub-microscale. A macrofibril contains aligned crystalline rod-like intermediate filaments at the nanoscale. Experimentally obtained parameters are used in the modeling as inputs for geometry and nanoscale properties. The predicted properties of the hoof wall material agree with experimental measurements at the mesoscale and macroscale. We observe that the hierarchical structure of the hoof wall leads to a decrease in the elastic modulus with increasing scale, from the nanoscale to the macroscale. Such behavior is an intrinsic characteristic of hierarchical biological materials. This study can serve as a framework for designing impact-resistant hoof-inspired materials and structures.

Analysis of laminated composites composed of coupled layers by polar method

Composite laminated plates are made of two or more unidirectional plies (or layers) stacked together at various orientations, the layers are composed of two phases: the fibers and the matrices. The material property and orientation of the fibers inside of the matrix determines the elastic characteristics of the layers. If the conventional layers used to fabricate laminate, there is no elastic coupling between bending and extension, other types of layers (the satins for example) have coupled behaviors. The classical lamination theory (CLT) formulates the elastic behavior of a laminate composed of classical layers, but it should be modified to be able to include these coupled layers that is the aim of the first part of this article. The second aspect of coupled layers must be considered: when they turned over, some of their elastic characteristics change, this phenomenon is studied in a second part and a method is proposed, including the reversal into the CLT equations, give more useful equations describing the laminates made of coupled layers. Finally, some cases of uncoupled and quasi-homogeneous stacking sequences are studied.

Reduction of Thermal Residual Strain in a Metal-CFRP-Metal Hybrid Tube Using an Axial Preload Tool Monitored through Optical Fiber Sensors.

Thermal residual strains/stresses cause several defects in hybrid structures and various studies have reported the reduction of residual strain. This paper describes a method for reducing thermal residual strains/stresses in metal-CFRP-metal hybrid tubes (MCMHT). The proposed axial preload tool provides two ways to reduce the thermal residual strains/stresses during the co-cure bonding process: pre-compressing of the metal layers and pre-stretching of the unidirectional carbon fiber reinforced polymer (CFRP) layers. An online measurement technique with embedded optical fiber Bragg grating (FBG) sensors is presented. Thermal residual strains are evaluated based on classical lamination theory with the assumption of plane stress. The theoretical calculations and measurement results agree well. Furthermore, the dynamic characteristics of the MCMHTs are tested. The results show that the reduction of residual strain increases the natural frequency of the MCMHT, but is detrimental to the damping capability of the MCMHT, which imply that the intrinsic properties of the metal-composite hybrid structure can be modified by the proposed axial preload tool.

Laminated beams/shafts of annular cross-section subject to combined loading

A novel stress analysis method is developed for the efficient design of radially laminated annular beams/shafts subject to arbitrary load combinations. The analysis is conducted using classic laminate theory (CLT) in conjunction with a mechanics of materials (MoM) approach based on the plane section assumption. Global loads are related to the global deformations and are expressed in terms of the generalised laminate strains in CLT. The analysis is verified against MoM for a homogeneous and isotropic tube. Further validation against the finite element method is shown for general cases in terms of loading and laminate layups with almost perfect agreement.

A comparative analysis of thermos-mechanical behavior of CNT-reinforced composite plates: Capturing the effects of thermal shrinkage

In this study, an analytical model based on the classical laminate theory (CLT) is developed for the prediction of the effective thermal expansion coefficients (ETECs) of general angle-ply laminates (symmetrical and asymmetrical). The applications of the derived model are shown by solved examples for the prediction of ETEC of carbon nanotube-reinforced (CNTRC) angle ply laminates for various ply angles. CNTRC laminates with a negative thermal coefficient (NTC) are obtained and considered as a special case. For an extreme case, a laying angle of (35/-35)3T and (55/-55)3T, along with an NTC of −0.79 × 10−5/K is achieved. Meanwhile, the Reddy shear plate model is extended to the framework of Von Kármán nonlinearity. The corresponding dynamic equations are analytically established. With the help of the two-perturbation approach, the deflection time history curves of the forced vibration are obtained. Numerical results show that the thermal-vibration behaviors may be adjusted and controlled by changing the TEC and functionally graded pattern. The presented analytical results not only are theoretically fundamental for understanding the thermal-vibration behavior of FG-CNTRC but also serve as guidelines for NTC design of composited laminated structures.

Multi-objective optimization of vertical-axis wind turbine’s blade structure using genetic algorithm

Through the field of renewable energy, the vertical-axis wind turbine is preferable, especially when the wind speed is low to medium. The optimization of blade structure design is essential to enhance the usability of the vertical-axis wind turbine. This paper introduces an optimization approach for the uniform blade structure design used in the vertical-axis wind turbine. The blade cost represents 20% of the turbine overall cost, and inertia load is the dominating design load. This approach aims to optimize the weight and the cost while maintaining structural integrity. Designs of blade structure are based on a multi-objective model, including the composite material and geometric parameters, where multiple design parameters are included. The model enhances the requirement of computation time and resources by approximation cross-sectional properties and loading calculations. The cost index concept is investigated to introduce an efficient method for approximation, normalizing the cost from currency exchange and price changes. The formulated model is then validated using a finite element analysis package, where the model is the integration between the numerical geometric model and the classical laminate theory. Optimization models are then formulated based on genetic algorithm and Pareto frontier analysis. Blade design parameters are included in the optimization to cover a wide range of parameters. The geometric cross-sectional properties are estimated using empirical formulas to reduce computation time and resources. The presented approach augmented the blade design parameters and genetic algorithm optimization. Optimum results for NACA 0021 shows the blade mass range between 2.5 and 3 kg and the cost index from 40 to 90.

Analysis-oriented model for FRP tube-confined concrete: 3D interpretation of biaxial tube behaviour

Filament-wound fibre-reinforced polymer (FRP) tubes are an emerging FRP product employed in various FRP-concrete composite structures, such as concrete-filled FRP tubes (CFFTs). Due to the fibre orientations in the tube wall, the filament-wound FRP tube exhibits biaxial behaviour under simultaneous axial compression and hoop expansion, causing relaxation of the confining stress. Therefore, the conventional hoop tension test may result in overestimation of the confining stiffness. In this paper, the biaxial behaviour of FRP tubes is theoretically investigated using classical laminate theory in conjunction with an analysis-oriented model for FRP-confined concrete. The geometrical meaning of the biaxial tube behaviour is interpreted intuitively using the 3D geometrical approach previously proposed by the authors. For the convenience of analysis and design, this paper proposes a simplified approach to rectify the confining stiffness that considers both elastic and nonlinear biaxial effects. The predicted results show good agreement with the collected test data.

Study on mechanical properties of wind turbine blades with bend-twist coupling effect

Bend-twist coupling (BTC), a method of passive load alleviation for turbine blade, has a significant influence on blade mechanical properties. The coupling behavior between bending and twisting motions stems from the material anisotropy in blade laminate or from the unique blade geometry such as sweep, deflection, and pre-bending. The material-based approach is employed in this research to determine influence regularity of BTC design on blade mechanical properties. To begin with, the blade property analysis tool PreComp that integrates a shear flow method with the classical laminate theory is adopted to compute the cross-sectional stiffnesses of the blades with different degree of BTC effect. Next, the bend-twist coupling coefficients for the BTC blades with different fiber orientation are calculated. Finally, the remaining mechanical properties including static performance, modal characteristics and buckling limits for different BTC blades are determined by the finite element method and the influence of changes in the degree of BTC effect on all these mechanical properties is further evaluated. The results show that the BTC effect markedly influences the different mechanical properties of the blade in different patterns. The 20° BTC blade has the highest BTC coefficient and the edgewise BTC coefficient at 100 m is 2.5 times higher than the flapwise BTC coefficient, while the maximum value of the torsional modal frequency of 3.8429 Hz and the greatest critical buckling load of 4328.1 kN corresponds to the 10° BTC blade and the 15° BTC blade respectively.

Harnessing fiber induced anisotropy in design and fabrication of soft actuator with simultaneous bending and twisting actuations

Most of the soft dielectric elastomer actuators (DEAs) are able to provide either planar or twisting deformations only. Development of a bio-inspired actuator with functionalities similar to the mammalian tongue or octopus tentacles is highly desirable for soft robotics applications. Here, design and fabrication of a multi-layered soft DEA capable of simultaneous bending and twisting actuation is reported through a unified computational and experimental approach. An anisotropic layer is introduced to couple the bending and twisting deformation in the conventional DEA. The fiber spacing and fiber orientation in the anisotropic layer is optimized with classical laminate theory (CLT) and finite element (FE) analysis. A multi-layered DEA with bending-twisting actuation is experimentally fabricated as a ‘proof of concept’. The computational and experimental results suggest that bend-twist coupling in multi-layered DEA can be suitably designed by varying the fiber spacing and orientation in the anisotropic layer. The twisting actuation of DEA enhances at the expense of bending deformation with an increase in the fiber angle. Finally, it is shown that a single anisotropic layer having 2 mm fiber spacing and 45° fiber orientation induces sufficiently large bending and twisting actuations in DEA. The findings of the present study will be a significant step ahead to develop bio-mimicking anisotropic actuators and grippers for soft robotics applications.

Design and Analysis of Multi-Layered Composite Panels for In-Plane Loadings

Composites have a wide range of applications in the field of robotics, aerospace, aviation, sports, and automotive engineering. They have appealing properties such as high strength to weight ratio, good mechanical and electrical properties, and durability. Multilayered composites are prepared by stacking different layers of composites along different directions. This research focuses on the compression and tension response of multilayered composite panels without interference of bending by using in-plane loading. The aim of this research is to develop a generalized MATLAB code for a number of layers, to solve a model composite through analytical and MATLAB computations, to analyze the stress behavior in ANSYS (ACP) and finally to compare the results. For carrying out the analysis, a multi-layered, symmetric composite panel is modelled under in-plane loading. First, a mathematical model is formulized to solve the multi-layered composite panel under in-plane loading and analytical results are obtained. Next, a generic MATLAB code is developed, followed by simulations and computational study using ANSYS (ACP) module. The results of MATLAB and the solution of the mathematical model are found to be identical. Further, the results obtained from ANSYS (ACP) have shown the stresses in each layer and overall deformation of the composite panel. The overall results from three methods have shown that the stresses produced in a composite panel are symmetric across mirrored layers. However, there is a significant difference between the analytical and ANSYS (ACP) results, this is due to the limitations of the Classical Laminate Theory (CLT) which has been used in the analytical study. CLT does not take into effect the out-of-plane stresses. However, in real life scenarios, out-of-plane stresses exist under the in-plane loadings and have a significant effect around the edges and corners of the panel. If 10 percent of the edges are removed on both sides, the analytical results and simulations are found to be in good agreement. Further, after the ANSYS (ACP) analysis has been obtained for the panel, a sandwiched composite panel has been modelled by adding a core material of foam and polyethylene at the center of the composite. The thickness of the core material is varied to observe the change in the stress behavior. The results have shown that there is an increased stress behavior when a softer core is used or the thickness of the core material is increased.

Accelerating the Layup Sequences Design of Composite Laminates via Theory-Guided Machine Learning Models.

Experimental and numerical investigations are presented for a theory-guided machine learning (ML) model that combines the Hashin failure theory (HFT) and the classical lamination theory (CLT) to optimize and accelerate the design of composite laminates. A finite element simulation with the incorporation of the HFT and CLT were used to generate the training dataset. Instead of directly mapping the relationship between the ply angles of the laminate and its strength and stiffness, a multi-layer interconnected neural network (NN) system was built following the logical sequence of composite theories. With the forward prediction by the NN system and the inverse optimization by genetic algorithm (GA), a benchmark case of designing a composite tube subjected to the combined loads of bending and torsion was studied. The ML models successfully provided the optimal layup sequences and the required fiber modulus according to the preset design targets. Additionally, it shows that the machine learning models, with the guidance of composite theories, realize a faster optimization process and requires less training data than models with direct simple NNs. Such results imply the importance of domain knowledge in helping improve the ML applications in engineering problems.

FEA modelling and environmental assessment of a thin-walled composite drive shaft

Fibre reinforced plastics (FRP) composites have been widely used in the automotive industry with the primary focus on reduced mass. However, there are relatively few reports on their application on power transmission components, such as drive shafts. This paper explores the feasibility of replacing the traditional structural steel by light weight FRP composites in a drive shaft. Three FRP composites are considered against a steel drive shaft; basalt/epoxy, carbon/epoxy, and CNT (carbon nanotubes) reinforced carbon/epoxy composites. The mechanical performance was analysed by finite element analysis (FEA) tool and classical laminate theory (CLT), while the environmental performance was evaluated by life cycle assessment (LCA) method. The study shows that with careful design a composite drive shaft can outperform the mechanical performance of a steel shaft (up to 90% mass saving, and 50% higher Factor of Safety). The study found steel shafts were preferable to FRP shafts based on embodied energy (steel total embodied energy 150MJ, FRP +325MJ). Reductions in carbon footprint from reduced emissions due to weight savings meant a carbon/epoxy shaft was preferable to a steel shaft. Two new material indices were suggested which can be used to select materials based on minimum embodied energy and global warming potential.

A Three-Dimensional Equivalent Stiffness Model of Composite Laminates with Wrinkle Defects.

The stiffness of composite laminates is easily affected by wrinkle defects. In this paper, a new effective analytical model was proposed to predict the three-dimensional equivalent elastic properties of multidirectional composite laminates with wrinkle defects. Firstly, a geometric model was established according to the microscopic characteristics of wrinkle defects. Then, based on the classical laminate theory and homogenization method, the constitutive equation and flexibility matrix of the wrinkle region were established. Finally, the equivalent stiffness parameters of unidirectional and multidirectional laminates were derived, and the effects of different wrinkle parameters and ply-stacking sequences on the stiffness of unidirectional and multidirectional laminates were studied by using the analytical model. The results show that the mechanical properties of the lamina and laminates are affected by the out-of-plane angle and in-plane angle of the wrinkle defects. The accuracy of the analytical model has been verified by the numerical model and other theoretical models, and it has the characteristics of few parameters and a high efficiency. The analytical model can be used to predict the stiffness of composite structures with wrinkle defects simply, effectively, and quantitatively. It can also be used as a tool to provide the mechanical response information of laminates with wrinkle defects.

A Novel Microscopic Modeling Scheme for the Shape Memory Polymer Composites with respect to the Ambient Temperature

This paper is aimed at studying the effective mechanical property of shape memory polymer composites (SMPC) reinforced with natural short fibers. To this end, a novel modeling scheme was presented. The SMPC was firstly equivalent to the composite laminates, and the natural short fibers are also subtly equivalent to the ellipsoidal inclusions distributed in the matrix materials periodically. Moreover, a represented volume element along laminate thickness can be easily chosen, and its elastic constants are accurately acquired by employing a proper microscopic mechanical model. Herein, the high-fidelity generalized method of cells, which represents a good ability in predicting the effective mechanical behaviors of composites, was used. On this basis, the classic laminate theory was improved to suitable for describing the elastic constants and failure strength the SMPC with respect to ambient temperature. Numerical results show a good consistency to the experimental data. Moreover, a higher ambient temperature tends to sharply decrease their final failure strength. It is also revealed that the presented modeling method shows a great potential in calculating the effectively mechanical property of the natural short fiber-reinforced composites.

An Analytical Model for Cure-Induced Deformation of Composite Laminates.

Curing deformation prediction plays an important role in guiding the tools, curing process design, etc. Analytical methods can provide a rapid prediction and in-depth understanding of the curing deformation mechanism. In this paper, an analytical model is presented to study the cure-induced deformation of composite laminates. Based on the classical laminate theory, the thermal stress and deformation of composites during the curing process are calculated by considering the evolution of the mechanical properties of resin. Additionally, the coupling stiffness of the laminate is taken into consideration in the analytical model. An interface layer between the tool and the part is developed to simulate the variation of the tool–part interaction with the degree of resin cure. The maximum curing deformations and deformation profiles of different lay-up composite parts predicted by the proposed model are compared with the results of the finite element method and previous literature reports. Then, a comprehensive parametric study is carried out to investigate the influence of curing cycle, geometry, tool thermal expansion, and resin characteristics on the curing deformation of composite parts. The results reveal that geometry has a significant influence on the curing deformation of composite parts, but for dimensionally determined parts, curing deformation is mainly attributable to their own anisotropy in macro and micro aspects, as well as the stretching effect of the tool on the part. The percentage contribution of different factors to curing deformation composites with different lay-ups and geometries is also discussed.

Holes/cracks/inclusions in magneto-electro-elastic composite laminates under coupled stretching-bending deformation

For the general magneto-electro-elastic (MEE) composite laminates, not only the elastic, electric and magnetic effects but also the in-plane stretching and out-of-plane bending deformations would be all coupled together. Based upon the classical lamination theory and by suitably expanding all the elastic tensors to include the electric and magnetic effects as the responses in the 4th and 5th dimensions, we develop the expanded Stroh-like formalism for MEE laminates under coupled stretching-bending deformation, whose mathematical form is purposely arranged to be identical to the Stroh-like formalism for elastic laminates. With the expanded Stroh-like formalism the field solutions for an infinite MEE laminate with or without holes/cracks/inclusions are derived analytically. The loads we consider are (1) the generalized uniform stress resultants and bending moments at infinity, and (2) the generalized concentrated forces and moments at an arbitrary location. Here, the word “generalized” means that the forces/moments are mechanical as well as electric and magnetic. The beauty of the obtained solutions is that these analytical solutions preserve the mathematical form of their corresponding elastic solutions. The only difference is the content and size of the matrices and vectors involved in the mathematical expressions. These solutions for the general MEE laminates including all the possible coupling effects are presented the first time in the literature. The ones under concentrated forces/moments are also taken to be the fundamental solutions of boundary element method. The correctness of our solutions is then verified through the comparison between the analytical solutions and those calculated by the newly developed boundary element method.