Unsymmetric Laminates Research Articles

Dynamics of a supercritical composite shaft mounted on viscoelastic supports

Abstract The damping in a carbon fiber reinforced plastic (CFRP) laminate is greater than that which occurs in most metallic materials. In the supercritical regime, the damping can trigger unstable whirl oscillations, which can have catastrophic effects. The vibrations occurring in a supercritical composite drive shaft are investigated here in order to predict instabilities of this kind. A simply supported carbon/epoxy composite tube mounted on viscoelastic supports is studied, using an approximation of the Rayleigh–Timoshenko equation. The damping process is assumed to be hysteretic. The composite behavior is described in terms of modulus and loss factor, taking homogenized values. The critical speeds are obtained in several analytical forms in order to determine the effects of factors such as the rotatory inertia, the gyroscopic forces, the transverse shear and the supports stiffness. Assuming that the hysteretic damping can be expressed in terms of the equivalent viscous model, the threshold speed is obtained in the form of an analytical criterion. The influence of the various factors involved is quantified at the first critical speed of a subcritical composite shaft previously described in the literature. The influence of the coupling mechanisms on the unsymmetrical composite laminate and the end fittings is also investigated using a finite element model. None of these parameters were found to have a decisive influence in this case. Those having the greatest effects were the transverse shear and the supports stiffness. The effects of the composite stacking sequence, the shaft length and the supports stiffness on the threshold speed were then investigated. In particular, drive shafts consisting only of ±45° or ±30° plies can be said to be generally unstable in the supercritical regime due to their very high loss factors.

The effect of moisture ingress on through-thickness residual stresses in unsymmetric composite laminates: A combined experimental–numerical analysis

Some unsymmetric polymer–matrix composite laminates show multi-stable behaviour, which can provide opportunities for morphing composite structures. It is known that through-thickness residual stresses are introduced in unsymmetric laminates during the manufacturing process. In this research work, a combined experimental–numerical analysis is proposed to study the effect of moisture ingress on unsymmetric composite laminates by analysing through-thickness residual stresses at dry and saturation states. A range of unsymmetric cross-ply laminates were manufactured using carbon–fibre epoxy pre-preg material. The laminates were subsequently immersed in water to full saturation. The curvatures of dry and saturated test coupons were measured and compared to quantify the effects of moisture ingress on the shapes of the unsymmetric laminates. In addition, a finite element model was developed to predict the experimentally measured curvatures of the dry laminates. By calibrating the numerical model, the through-thickness residual stresses were analysed for different unsymmetric cross-ply layup conditions. The calibrated dry model was then extended to develop a moisture-dependent numerical model in order to incorporate the effect of moisture ingress on the shapes of unsymmetric laminates. The moisture-dependent model was calibrated with the experimentally measured curvatures and then used to predict the through-thickness residual stresses in the fully saturated unsymmetric cross-ply laminates. It is shown that moisture ingress can considerably influence through-thickness residual stresses and thus the shapes of unsymmetric laminates.

Analytical model for adhesively bonded composite panel-flange joints based on the Timoshenko beam theory

An analytical model for adhesively bonded composite panel-flange joints is developed using the kinematic relations of the Timoshenko beam theory and the constitutive equations in linear elasticity. The governing equations are derived for the normal and shear stresses in the adhesive layer of a composite joint containing two symmetric or unsymmetric laminates (as adherends) with equal- or unequal-thickness. For a composite joint with two equal-thickness symmetric adherends, closed-form solutions are obtained for the normal and shear stresses in the adhesive layer. Due to the consideration of the transverse shear effect in the current model, the solution for the normal (peel) stress derived here is different from that provided in an existing model using the Bernoulli–Euler beam theory-based classical laminate theory, even though the solution for the shear stress obtained here is the same as that given in the latter. The new model is quantitatively illustrated and compared with the existing model for two sample cases of composite panel-flange joints. The numerical results reveal that the peel stress for the joint under pure bending is tensile over the entire length of the adhesive and its values near the two ends of the adhesive are significantly larger than those predicted by the existing Bernoulli–Euler beam theory-based model.

Cured shape and snap-through of bistable twisting hybrid [0/90/metal]T laminates

Abstract This paper presents a bistable twisting CFRP-metal hybrid laminate which has an external isotropic metallic layer. Different from the pure unsymmetric CFRP laminate and the hybrid unsymmetric laminate with an inner metallic layer, the laminate presented can be transformed from one negative curvature to another negative curvature instead of from one negative curvature to another positive curvature. Their room temperature shapes can be a unique paraboloid shape, a twisted cylindrical shape, or a twisted cylindrical shape that can be snapped through to another twisted cylindrical shape. The cured shape of the hybrid laminate is studied using analytical, finite element and experimental techniques. The investigation is focused on the hybrid laminate with lay-up of [0/90/metal] T , and shows that the principal direction of cured curvature is 45°. The predicted cured shape and the snap-through loads agree well with experimental results.

Non-linear stability analysis of laminated composite plates on one-sided foundation by hierarchical Rayleigh–Ritz and finite elements

In this paper, the influence of one-sided foundation on the unilateral buckling behavior of laminated composite orthotropic plates is investigated under compressive load. Derivation of governing equations is based on Kirchhoff's hypotheses and the principle of minimum total potential energy. The solutions are performed by the hierarchical Rayleigh–Ritz (HRRM) and finite element methods (HFEM) and are compared. Most of previous research studies on the unilateral buckling of plates are limited to single-layer plates. The results show that unsymmetric lamination experiences lower critical loads than those of symmetric lamination due to the existence of extensional–bending coupling in unsymmetric laminated sequencing schemes. Influences of aspect ratio, fiber orientation, the number of plies, Young's modulus ratio, and different boundary conditions on the unilateral buckling load are examined. The numerical results are validated with previous works studying unilateral buckling of single-layer plates resting on one-sided foundation.

Unsymmetric three-layer laminate with soft core for photovoltaic modules

Unsymmetrical laminates are designed for the use in new lightweight construction of photovoltaic modules. One feature of the laminate is relatively thin and compliant polymeric core layer for embedding solar cells. To assess mechanical properties of the core a three-layer beam is proposed as a model structure. For the structural analysis a layer-wise beam theory is developed. Robust relationships between the maximum deflection, the transverse shear strain of the core layer and the applied force in a three-point-bending test of laminated beam samples are derived. Furthermore, a three-dimensional finite element analysis is performed to verify the assumptions of the beam theory. Three-point-bending tests for laminated beams are performed. The experimentally obtained load–deflection curves are compared with the theoretical results.

On the Through-the-Width Multiple Delamination, and Buckling and Postbuckling Behaviors of Symmetric and Unsymmetric Composite Laminates

Multiple delamination causes severe degradation of the stiffness and strength of composites. Interactions between multiple delamination, and buckling and postbuckling under compressive loads add the complexity of mechanical properties of composites. In this paper, the buckling, postbuckling and through-the-width multiple delamination of symmetric and unsymmetric composite laminates are studied using 3D FEA, and the virtual crack closure technique with two delamination failure criteria: B-K law and power law is used to predict the delamination growth and to calculate the mixed-mode energy release rate. The compressive load-strain curves, load-central deflection curves and multiple delamination process for eight composite specimens with different initial delamination sizes and their distributions as well as two angle-ply configurations 04//(±θ)6//04 (θ = 0° and 45°, and “//” denotes the delaminated interface) are comparatively studied. From numerical results, the unsymmetry decreases the local buckling load and initial delamination load, but does not affect the global buckling load compared with the symmetric laminates. Besides, the unsymmetry affects the unstable delamination and buckling behaviors of composite laminates largely when the initial multiple delamination sizes are relatively small.

Modeling Bistable Composite Laminates for Piezoelectric Morphing Structures

A sequential modeling effort for bistable composite laminates for piezoelectric morphing structures is presented. Thin unsymmetric carbon fiber composite laminates are examined for use of morphing structures using piezoelectric actuation. When cooling from the elevated cure temperature to room temperature, these unsymmetric composite laminates will deform. These postcure room temperature deformation shapes can be used as morphing structures. Applying a force to these deformed laminates will cause them to snap through to another shape. This bistability arises from the fabrication process of the thin unsymmetric laminates. The snap through force studied here will be controlled by using piezoelectricity. Macrofiber composite (MFC) actuators are used for piezoelectric actuation. In this research, an analytical modeling method is presented to accurately depict the piezoelectric morphing structures. Sequential numerical modeling of the cure process to account for residual stresses and postcured shapes and piezoelectric morphing structure is done to predict the piezoelectric actuated displacements of the thin unsymmetric composite laminates. Analytical and numerical models are compared to experimental methods and results.

Effect of Ply-Level Material Uncertainty on Composite Elastic Couplings in Laminated Plates

Elastic couplings can strongly effect the structural behavior of composites by their presence or absence. We show that uncertainties in composite material properties at the ply-level can lead to undesirable couplings in laminates designed with no couplings. Moreover, uncertainty can alter the couplings in lay-ups where couplings are introduced deliberately for structural or aeroelastic tailoring. For numerical results, a symmetric balanced and an unsymmetric unbalanced laminate are considered. Material uncertainties are numerically quantified using Monte Carlo simulations for different number of plies, ply angles, and loading conditions and their effect is found to be substantial.

Pressure loading, end- shortening and through- thickness shearing effects on geometrically nonlinear response of composite laminated plates using higher order finite strip method

A semi-analytical finite strip method is developed for analyzing the post-buckling behavior of rectangular composite laminated plates of arbitrary lay-up subjected to progressive end-shortening in their plane and to normal pressure loading. In this method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. Thin or thick plates are assumed and correspondingly the Classical Plate Theory (CPT) or Higher Order Plate Theory (HOPT) is applied. The in-plane transverse deflection is allowed at the loaded ends of the plate, whilst the same deflection at the unloaded edges is either allowed to occur or completely restrained. Geometric non-linearity is introduced in the strain–displacement equations in the manner of the von-Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. The Newton–Raphson method is used to solve the non-linear equilibrium equations. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the through-thickness shearing effects as well as the effect of pressure loading, end-shortening and boundary conditions. The study of the results has revealed that the response of the composite laminated plates is particularly influenced by the application of the Higher Order Plate Theory (HOPT) and normal pressure loading. In the relatively thick plates, the HOPT results have more accuracy than CPT.

Curvature tailoring of unsymmetric laminates with an initial curvature

An unsymmetric laminated composite having bi-stability is interesting as a morphing structure because it can sustain large deformation without energy supply and the deformed state is stable. Especially, inducing different curvature values at each stable state is important for the practical application of unsymmetric laminates. In this study, we propose a method for tailoring the curvature of unsymmetric cross-ply laminates by curing the composite on a curved tool plate. The results show that the final normal curvature tensor of unsymmetric laminates is the summation of the tool plate curvature tensor and the normal curvature tensor of the laminates.

Assumed-modes modeling of piezoelectric energy harvesters: Euler–Bernoulli, Rayleigh, and Timoshenko models with axial deformations

A generalized framework is presented for the electromechanical modeling of base-excited piezoelectric energy harvesters with symmetric and unsymmetric laminates. The electromechanical derivations are given using the assumed-modes method under the Euler–Bernoulli, Rayleigh, and Timoshenko beam assumptions in three sections. The formulations account for an independent axial displacement variable and its electromechanical coupling in all cases. Comparisons are provided against the analytical solution for symmetric laminates and convergence of the assumed-modes solution to the analytical solution with increasing number of modes is shown. Model validations are also presented by comparing the electromechanical frequency response functions derived herein with the experimentally obtained ones in the absence and presence of a tip mass attachment. A discussion is provided for combination of the assumed-modes solution with nonlinear energy harvesting and storage circuitry. The electromechanical assumed-modes formulations can be used for modeling of piezoelectric energy harvesters with moderate thickness as well as those with unsymmetric laminates and varying geometry in the axial direction.

Morphing of Bistable Composite Laminates Using Distributed Piezoelectric Actuators

The use of bistable unsymmetric cross-ply laminates for morphing application has received growing attention in the last few years. So far, most studies use large rectangular piezoelectric Macro Fiber Composite (MFC) patches bonded at the center of the laminate to induce snap-through. However, the use of large rectangular MFC patches bonded in the center of the laminates significantly influences the shape of the laminate by greatly reducing the curvature at the midsection of the laminate where the MFC patches are bonded. This paper presents a study where narrow cocured MFC strips distributed over the entire surface are used to induce snap-through of unsymmetric cross-ply laminates. This MFC configuration allows having a more uniform curvature in the laminate. Since the strips are bonded on both sides, reverse snap-through should be obtained. The study was both theoretical and experimental. A finite element nonlinear analysis was used to predict the two stable cylindrical configurations and the snap-through induced by MFC actuation. For the experimental study, a laminate-MFC structure was manufactured and tested. The shapes were measured using a 3D image correlation system as a function of applied voltage. Good correlations for the cylindrical shape and displacement field were observed.

Dynamical Analysis of Long Fiber-Reinforced Laminated Plates with Elastically Restrained Edges

This paper presents a variational formulation for the free vibration analysis of unsymmetrically laminated composite plates with elastically restrained edges. The study includes a micromechanics approach that allows starting the study considering each layer as constituted by long unidirectional fibers in a continuous matrix. The Mori-Tanaka method is used to predict the mechanical properties of each lamina as a function of the elastic properties of the components and of the fiber volume fraction. The resulting mechanical properties for each lamina are included in a general Ritz formulation developed to analyze the free vibration response of thick laminated anisotropic plates resting on elastic supports. Comprehensive numerical examples are computed to validate the present method, and the effects of the different mechanical and geometrical parameters on the dynamical behavior of different laminated plates are shown. New results for general unsymmetrical laminates with elastically restrained edges are also presented. The analytical approximate solution obtained in this paper can also be useful as a basis to deal with optimization problems under, for instance, frequency constraints.

Natural vibration of unsymmetric cross-ply laminates

This study considers the linear vibration characteristics of square [ 0 n / 90 n ] T laminates relative to their room-temperature static equilibrium configurations. A Rayleigh–Ritz approach combined with Hamilton's principle is used to provide approximate solutions to this vibration problem. The vibration mode shapes are assumed to have the same spatial dependence as used in past investigations to study the room-temperature configurations of these laminates, and are thus assumed to be perturbations on the static equilibrium configurations. Hamilton's principle then results in the so-called zero- and first-order equations. The zero-order equations lead to the classic static equilibrium results of past investigations, presented here in nondimensional form with analytical solutions at the bifurcation point. The first-order equations, combined with zero-order results, lead to the vibration characteristics for each zero-order static configuration. Interest centers on the lowest natural frequency and the associated mode shape for laminates clamped at their midpoints, with special attention as to how these vibration characteristics depend on the laminate side-length-to-thickness ratio. With an imaginary-valued frequency, the static saddle configuration for side-length-to-thickness ratios larger than the critical value is correctly assessed as unstable. A finite element model is also used to study the vibration characteristics and to compare with the findings for the developed analysis. The qualitative comparisons between the developed analysis and the finite element model are generally good, and the quantitative comparisons are also satisfactory.

Planform effects upon the bistable response of cross-ply composite shells

This research aims at investigating the bistable characteristics of unsymmetric cross-ply laminates resulting from thermally induced stresses while curing. The bistable characteristics are examined with a focus on the change in geometry for a subset of configurations, namely, rectangular, trapezoidal and triangular. To this end, these geometries are systematically investigated leading to a set of non-dimensional parameters establishing the values required for bistable behavior. A new apparatus is designed to measure the magnitude of the force required for snap-through and snap-back. The influence of friction at the supports of the tested panels is minimized by utilizing air cushion for frictionless motion. Predictions from a nonlinear finite element based methodology using the ABAQUS™ code are validated through comparisons with test data.

Differential Cubature Method for Static Solution of Laminated Shells of Revolution with Mixed Boundary Conditions

The bending analysis of laminated shells of revolution, such as spherical, conical and cylindrical panels, is carried out utilizing the differential cubature method (DCM). To do so, a general software based on the DCM is developed which can tackle shells of revolution with symmetric and unsymmetric lamination sequence. Analysis of shells with general Loading and various combinations of clamped, simply supported, free and mixed boundary condition, may be carried out having acceptable accuracy. Using first order shear deformation theory, fifteen first order partial differential equations are obtained which contain fifteen unknowns in terms of displacements, rotations, moments and forces. Utilizing all of these equations results in the capability of the method to deal with any kinds of boundary conditions. Comparison of the results obtained by the DCM, shows very good agreement with the results of other numerical and analytical methods, while having less computational effort.

Piezoelectrically driven morphing structures based on bistable unsymmetric laminates

Due to their anisotropy multilayered fibre-reinforced polymers tend to generate residual stresses, which are primarily influenced by thermal and hygroscopic processes. In the case of an unsymmetric reinforcement architecture, those residual stresses may induce large out-of-plane deformations in thin-walled laminates. Here, specific stacking sequences support the development of so called bistable laminates which are characterised by two distinct deformation states which can be converted by applying forces or bending moments. In combination with appropriate actuator systems, like piezoceramic transducers, such bistable composites can purposefully be used to design compliant mechanisms and novel morphing structures that stand out for a permanent change of shape only by a small energy supply. For the structural analysis and the computation of the necessary actuation voltage to initiate the snap-through of bistable composite structures with piezoceramic actuators, non-linear semi-analytical and numerical simulation methods have been elaborated. First active bistable prototypes have been manufactured and successfully tested.

Large Deflection Compressional Analysis of Unsymmetric Delaminated Composite Plates with Consideration of Contact Phenomenon

In this study, an efficient method is developed to investigate the compressive large deflection behavior of unsymmetric composite laminates with multiple through-the-width delaminations. The analytical method is based on the first order shear deformation theory (FSDT) and its formulation is developed on the basis of the Rayleigh-Ritz approximation technique by the implementation of the simple and complete polynomial series. The method can handle both local deflection of the delaminated sublaminate and global deflection of the whole plate. Also, the contact among sublaminates is investigated. The three-dimensional finite element analysis is performed by using ANSYS5.4 general purpose commercial software, and the results are compared with those obtained by the analytical model.

Analysis of unsymmetric CFRP–metal hybrid laminates for use in adaptive structures

The potential of using multistable composite materials for adaptive structures is currently receiving interest from the aerospace community because they possess more than one single equilibrium configuration. Unsymmetric CFRP laminates are studied which have an inner isotropic metallic layer. These hybrid laminates are studied using analytical, finite element and experimental techniques. The thermal contraction of the isotropic layer upon cool down from cure induces large in-plane thermal loads which act remotely from the laminate’s neutral plane, increasing snap-through moments and out-of-plane displacements. The curvatures of the hybrid laminates can be doubled compared to pure unsymmetric CFRP laminates.