Laminated Plate Model Research Articles

Mechanical behavior of GFRP-Polymer sandwich composites with montmorillonite nanoclay

Abstract A sandwich composite consists of high stiffness and high strength outer layers called face sheets and low-density inner layers called core. In the present study, the sandwich composites comprising glass fabric/epoxy face sheets and epoxy modified with montmorillonite (MMT) nanoclay core are fabricated by a co-curing method. The sandwich panels show higher static tensile and three-point flexural properties such as ultimate strength, elastic modulus, and failure strain on adding up to 3 wt.% of MMT nanoclay contents than pristine sample. The former properties reduce at 4 and 5 wt.% of nanoclay contents owing to the formation of clustering of clay particles within the matrix. The stress-strain behavior of sandwich panels with 0–5 wt.% of MMT nanoclays obtained by laminated plate model follows experiments. The maximum lateral deflection of sandwich panels with nanoclays predicted by assuming them to be a simply supported beam is in-line with experimental results. For low-velocity single impact perforation load, the maximum force of sandwich panels improves on the infusion of up to 3 wt.% of clay while maximum displacement decreases. The ballistic limit velocity and energy absorption of panels improve on adding up to 3 wt.% of clay. Beyond the ballistic limit at different initial velocities, the residual velocity of sandwich panels decreases on addition of up to 3 wt.% of clay and energy absorption increases.

Band gap study of periodic piezoelectric micro-composite laminated plates by finite element method and its application in feedback control

Phononic crystals are materials or structures with periodic variations of elastic constants and density. Elastic waves in phononic crystals cannot propagate within a certain frequency range, called the band gap, due to the interference of their internal structure. This article investigates how fiber orientation affects the band gap properties of periodic micro-composite laminated plates. We examined the impact of five common composite laminate configurations on the system’s band gap and discovered that the antisymmetric configuration had superior high-frequency band gap performance. Based on this finding, we further explored how the antisymmetric angle influenced the system’s band gap. Since the study was conducted at a micro scale, micro structural effects were considered. Therefore, we used the modified coupled stress elastic dynamics and a four-node quadrilateral non-conforming element to discretize the micro composite laminated plate model, which had the nodal compatibility of high-order elasticity theory. Moreover, we employed feedback control to the proposed structure to dynamically adjust the band gap width according to different practical needs. This research supports the design of periodic micro-composite laminated plates and the piezoelectric feedback control system, which can control the vibration and wave propagation behaviors of micro structures using coupled piezoelectric sensors and actuators. The piezoelectric feedback control employed two control methods: direct proportional control and acceleration control. This article compared the single and multiple control methods of these two approaches to determine the optimal control strategy.

Modeling and vibration control of a rotating flexible plate actuated by MFC

The macro fiber composite (MFC) is a novel piezoelectric intelligent material, which is widely used in the field of vibration control due to its flexibility and larger actuation forces than PZT. In this paper, a laminated plate model considering the anisotropy of MFC is developed and applied to the vibration control of a rotating plate. The laminated plate is defined as a layerwise model, which deformation is described by the Absolute Nodal Coordinate Formulation (ANCF). The MFC laminated plate element contains 48 degrees of freedom (DOFs) where the effect of MFC element can be internally incorporated without increasing the DOFs of system. Simultaneously, a neural network PD control is adopted to control the vibration of the rotating plate. Eventually, static, dynamic, and modal analyses are performed to investigate the effects of different parameters. Several vibration simulations are carried out to illustrate the ability of MFC patches on vibration control. The findings in this article would be applied to mechanical prediction and control for rotor blades of helicopters, solar panels, etc.

Analitičko ispitivanje poroznih laminiranih ploča od funkcionalno gradiranih kompozita ojačanih ugljeničnim nanocevima (FG-CNTRC) na izvijanje i slobodne vibracije

Introduction/purpose: The aim of this study is to examine the buckling and free vibration behavior of laminated composite plates reinforced with carbon nanotubes when various sources of uncertainty are taken into account with 1 the main focus being the existence of porosity. Methods: A porous laminated plate model is developed using a high order shear deformation theory. Different configurations of functionally graded aligned single-walled carbon nanotubes throughout the thickness of each layer are being investigated. The effective properties of materials are evaluated through the extended rule of mixture while considering an upper bound for the effect of porosity. The governing equations are derived and solved using the virtual work principle and Navier's approach. The validity of the current formulation is confirmed by comparing the results with the existing data from literature sources. The impact of numerous parameters such as porosity, carbon nanotube volume fraction, reinforcement distribution types, lamination scheme, and the number of layers on the buckling and free vibration responses is investigated in detail. Results: A key finding of this study is the significant reduction in buckling resistance of laminated FG-CNTRC plates due to porosity, contrasting with the minor impact on the free vibration response. Conclusion: The results of this paper emphasize the critical role of porosity in structural integrity and provide novel insights into the behaviour of advanced composite materials.

Bend-twist coupling effects on the cavitation behavior and hydroelastic response of composite hydrofoils

The objective of this work is to investigate the influence of bend-twist coupling effects on the cavitation behavior and hydroelastic response of four hydrofoils with identical geometry: one rigid hydrofoil and three composite hydrofoils of carbon-fiber reinforced plastic (CFRP) with the ply angles of 45°, 0°, and -45°, respectively. A synchronized measurement system consisting of a high-speed camera, a hydrodynamic load cell, and a Laser Doppler Vibrometer is applied to obtain the cavity dynamics and hydroelastic response simultaneously. The theoretical cross-sectional effective bending stiffness, twisting stiffness, and bend-twist coupling stiffness are calculated based on a chordwise-rigid laminated plate model. In addition to the primary cavity shedding frequency and natural frequencies, additional modulated frequencies are excited for all the hydrofoils due to time-varying added mass effects, which broadens the frequency response of the hydrofoil. Re-entrant jet and shockwave mechanisms are identified as instabilities causing periodic cloud cavity shedding. The cloud cavity shedding frequency is found to be independent of cavitation number in certain conditions induced by the shockwave mechanism. Bubbly shock induces a secondary shedding of cloud cavities, causing the reduction of the cavity shedding frequency. The CFRP 45 hydrofoil with a positive bend-twist coupling effect promotes the bending and twisting deformations of the hydrofoil, increasing lift and moment, decreasing the cloud cavity shedding frequency due to the increase in cavity length, and accelerating the cavitation regime transition by reducing cavitation number. And the opposite is true for the CFRP -45 hydrofoil with a negative bend-twist coupling effect.

STRESS DISTRIBUTION IN THE HOLLOW STIFFENED HYBRID LAMINATED COMPOSITE PANELS IN SHIP STRUCTURES UNDER SINUSOIDAL LOADING

A simplified hollow stiffened hybrid laminated plate model has been developed for the marine structures. The detailed stress analysis through the thickness of the stiffened plate based on the higher order shear deformation theory has been carried out under sinusoidal loading. The hybrid laminates are made by wrapping the GFRP laminates with CFRP at the outermost layers of the stiffened panel. This hybridization technique can be an optimum solution from the point of view of cost reduction as well as enhancement of strength properties. The layer-wise stresses for the stiffened plate have been calculated in the present paper. A 3D polynomial curve fitting technique has been used to obtain higher accuracy and consistency in the computation of stresses. The computer code has been developed using MATLAB considering the plates as eight noded isoparametric plate bending element and the stiffener has been modeled as three noded isoparametric beam element. The stiffened panel has also been analysed using the ANSYS14.0 software package considering 2D model. The results obtained from the present formulation have been compared with those available in the published literature to validate the present formulation. The stiffened panels made of GFRP, CFRP and GFRP-CFRP hybrid laminates have been studied here. An extensive parametric study has been carried out with varying fibre content in the laminates.

Condition Assessment of a Reinforced Concrete Residential Building using Non-destructive Testing Methods - A Case Study

The present study deals with both experimental and numerical investigation on buckling effects of laminated composite plates subjected to varying temperature and moisture. A simple laminated plate model is developed for the buckling of composite plates subjected to adverse hygrothermal loading. A computer program based on FEM in MATLAB environment is developed to perform all necessary computations. The woven fiber Glass/Epoxy specimens were hygrothermally conditioned in a humidity cabinet where theconditions were maintained at temperatures of 300K-425K and relative humidity (RH) ranging from 0-1% for moisture concentrations. All the investigations are made with a symmetric cross-ply laminates. The present study deals with both experimental and numerical investigation on buckling behavior of laminated composite plates subjected to varying temperature and moisture concentration. Quantitative results are presented to show the effects of geometry, material and lamination parameters of woven fiber laminate onbuckling of composite plates for different temperature and moisture concentrations with simply supported boundary conditions with different aspect and side-to-thickness ratios. Experimental results show that there is reduction in buckling loads in KN with the increase in temperature and moisture concentration for laminates with clamped-free-clamped-free boundary conditions

Effect of high strain rate on tensile response and failure analysis of titanium/glass fiber reinforced polymer composites

The high strain rate tensile response of titanium-based fiber metal laminates (FMLs), consisting of layers of titanium Ti-6Al-4V alloy sheet and glass fiber reinforced composites, is examined. A hand layup method is used to fabricate four different layups of FMLs, exhibiting the same thickness of the total metal layer. A split Hopkinson tensile bar apparatus is used to load titanium and composite under a high strain rate to obtain baseline data. High-speed digital image correlation is used to measure the strain directly on the specimen gage region. The elastic-plastic response of FMLs up to maximum stress is predicted by the classical laminated plate model and orthotropic plasticity model. This is followed by a behavior considering the mechanics of delamination. The results show that the layup sequence of titanium-based FMLs considerably affects the failure behavior of composites following ultimate strength. This strength increases at high strain rates and seems higher for titanium-based FMLs than aluminium-based FMLs. This is primarily caused by the rate-dependent response of the titanium and composite. The failure strain of glass fiber reinforced epoxy (GFRP) constituent, failure strain, and toughness of FMLs are affected by isolating composite layers by metallic layers within FMLs and are found to be rate sensitive. Isolation of composite layers from one another by metallic layers results in more progressive failure of FMLs. The proposed models are validated with experiments of aluminium-based FMLs available in the literature.

The size effect in adhesive contact on a gradient nanostructured coating

The adhesive contact problem between a rigid cylindrical punch and a gradient nanostructured (GNS) coating is investigated by considering the size effect. The laminated plate model is applied to characterize the material properties of a GNS coating in plane strain couple stress elasticity. By using the Fourier integral transform and transfer matrix method, the governing integral equation(s) for the two-dimensional adhesive contact problem are obtained. Numerically calculated results are presented to analyse the effect of characteristic material length, the adhesion parameter and nonhomogeneous parameters on the mechanical response of the GNS coating for the adhesive contact problem. We explore the nanoscale contact of a GNS coating with shear modulus varying as a function of depth according to an exponential function or the power-law function. The present results provide a way to improve the contact deformation and damage to nanoelectromechanical systems by adjusting the gradient index of the GNS coating.

Self-sensing piezoelectric bistable laminates for morphing structures

Bistable laminates offer opportunities for shape morphing, energy harvesting, and flow control devices. Smart materials such as piezoelectric macrofiber composites and shape memory alloys have been embedded in bistable laminates to actuate or harvest energy. However, sensor systems capable of measuring bistable shapes and snap-through events are lacking. In this paper, we present curved bistable laminates layered with piezoelectric PVDF films that can sense smooth shape changes as well as abrupt snap-through transitions. Near-static measurement is facilitated by a drift compensated charge amplifier with a large time constant that converts the sensor’s charge output into a measurable voltage with minimal drift error. The sensing function is demonstrated on mechanically-prestressed bistable laminates. The laminated composites include two sensor layers such that one measures the changes in curvature and the other measures snap-through events. An analytical model is presented in which strains and curvatures calculated using a laminated-plate model are fed into a linear piezoelectric model to calculate voltage. Shapes measured by the sensors correlate well with shapes measured using a 3D motion capture system. A model-based analysis is performed to understand the laminates’ design space.

Thermal vibration of MoS2/Black phosphorus Bi-layered heterostructure

Thermal vibration is extremely crucial to nanostructure-based nanoresonators. In this paper, a laminated plate model (LPM) with the van der Waals (vdW) interactions between MoS2 and black phosphorus (BP) taken into consideration is proposed to explore the thermally induced vibration of a MoS2/BP heterostructure. The vdW coefficient between single-layered MoS2 and single-layered BP is calculated. The natural frequencies and the root-mean-squared (RMS) amplitudes of the MoS2/BP heterostructure are obtained from molecular dynamics (MD) simulations and the LPM. The natural frequencies and the RMS amplitudes of the MoS2/BP heterostructure calculated by the LPM and those obtained from the MD simulations coincide well. The LPM has in-phase vibrational modes and anti-phase vibrational modes. The natural frequencies of the in-phase vibrational modes are much lower than the frequencies of the anti-phase vibrational modes of the same order. In the thermal vibration of the MoS2/BP heterostructure, the RMS amplitudes of MoS2 and BP are obviously different. Compared with the natural frequencies and RMS amplitudes of the MoS2/BP heterostructure obtained from the MD simulations, the LPM can provide an accurate prediction of the thermal vibration of the MoS2/BP heterostructure.

A family of higher-order single layer plate models meeting [formula omitted]-requirements for arbitrary laminates

In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic…) to a multilayer Cz0 higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order Cz1 function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are considered. The coefficients of these four warping functions are determined in such a manner that the interlaminar continuity as well as the homogeneity conditions at the plate’s top and bottom surfaces are a priori exactly verified by the transverse shear stress field. These Cz0 ESL models all have the same number of DOF as the original basis HSDT. Numerical assessments are presented by referring to a strong-form Navier-type solution for laminates with arbitrary stacking sequences as well for a sandwich plate. In all practically relevant configurations for which laminated plate models are usually applied, the results obtained in terms of deflection, fundamental frequency and local stress response show that the proposed zig-zag models give better results than the basis models they are issued from.

Free vibration analysis of bilayered circular micro-plate including surface effects

• A new size-dependent Kirchhoff bilayered micro-plate model is developed. • A displacement field is proposed for the bilayered micro-plate. • Natural frequency is larger or smaller than those predicted by existing models. • Larger normalized effective flexural rigidity is predicted. • Transition region is expanded for stiffened surface and reduced for softened surface. Based on the Kirchhoff plate theory and the continuum surface elasticity theory, a novel model of bilayered circular micro-plates including surface effects is developed. Furthermore, the governing equation is derived, and the Galerkin method is employed to obtain approximate results. The influence of surface effects on the natural frequency of bilayered circular micro-plate is investigated. Besides, the effect of residual stresses on the transition behavior of the bilayered circular micro-plate from plate to membrane is predicted. The results are compared with the single-layer model and the modified laminated plate model. It is found that the natural frequency predicted by the present model is obviously different from that of the existing models. For different thickness ratios, the natural frequency obtained by the new model will be larger or smaller than the results of the single-layer model. The transition region from plate to membrane is expanded for stiffened surface and reduced for softened surface. The results of the novel model can provide effective guidance for the design of bilayered circular micro-plate in MEMS devices.

Evaluation of cross-ply laminate stiffness with a non-uniform distribution of transverse matrix cracks by means of a computational meso-mechanic model

This work addresses the evaluation of the stiffness of fiber-reinforced composite laminates, by means of a computational meso-mechanic model, considering two non-uniformly spaced transverse matrix cracks. Laminates with [0n/908]S and [908/0n]S, with n = 1 and 8, have been studied. The meso-mechanic model includes a three dimensional Finite Element continuum model at meso-scale and the macro-scale contains a classical thin laminated plate model. Periodic boundary conditions were used and the stress resultants were evaluated accounting for the equivalence of mechanical power between scales (Hill-Mandel principle). The results obtained with the present model showed good agreement with numerical and experimental data reported in the literature. A parametric analysis allowed identifying the stiffness components which are more influenced by a non-uniform crack distribution. The results suggest that the model with uniformly distributed cracks underestimates the in-plane and bending stiffness, while the bending-extension coupling stiffness components are overestimated.

Bending, free vibration and buckling analyses of anisotropic layered micro-plates based on a new size-dependent model

A new size-dependent composite laminated plate model is proposed in this study based on a re-modified couple stress theory (RMCST) and a zigzag theory. In contrast to the published size-dependent models for composite laminated plates, present model a priori satisfies the continuity conditions of transverse shear stresses (TSSs) at the interfaces. In the present formulation, the discontinuous TSSs obtained from the constitutive relations are replaced by the new continuous TSSs by using the Reissner’s Mixed Variational Theorem (RMVT). In addition, the RMVT is utilized to obtain the governing equations and corresponding boundary conditions. Subsequently, the deflections, stresses, frequencies and critical loads of cross-ply simply supported plates are considered to verify the present formulation. The results prove that the scale effects of present size-dependent models are effectively investigated. Moreover, the results predicted by present size-independent models are in accordance with the exact solutions. Eventually, the differences of the mechanical performance among the following three models, i.e. present, Mindlin and Reddy for composite laminated plates are discussed in different modulus and span-to-thickness ratios.

Graphene oxide-reinforced thermo-sensitive hydrogel consistently release alendronate for enhanced cranial defect repair

A new size-dependent composite laminated plate model is proposed in this study based on a re-modified couple stress theory (RMCST) and a zigzag theory. In contrast to the published size-dependent models for composite laminated plates, present model a priori satisfies the continuity conditions of transverse shear stresses (TSSs) at the interfaces. In the present formulation, the discontinuous TSSs obtained from the constitutive relations are replaced by the new continuous TSSs by using the Reissner’s Mixed Variational Theorem (RMVT). In addition, the RMVT is utilized to obtain the governing equations and corresponding boundary conditions. Subsequently, the deflections, stresses, frequencies and critical loads of cross-ply simply supported plates are considered to verify the present formulation. The results prove that the scale effects of present size-dependent models are effectively investigated. Moreover, the results predicted by present size-independent models are in accordance with the exact solutions. Eventually, the differences of the mechanical performance among the following three models, i.e. present, Mindlin and Reddy for composite laminated plates are discussed in different modulus and span-to-thickness ratios.

Asymptotical modeling of thermopiezoelastic laminates

A general anisotropic laminated plate model with thermal deformation and two-way coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change and external loads. The feature of small thickness and large in-plane dimension of plate structures helps to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. Several numerical examples are studied. The present model is validated by the excellent agreement between the results from 3D finite element analyses and the present model.

Parametric Instability of Square Laminated Plates in Hygrothermal Environment

The present paper investigates the parametric instability of square laminated plates subjected to periodic dynamic loadings in hygrothermal environment. The effects of various parameters like the increase in static load factor and the degree of orthotropy of simply supported composite plates at elevated temperatures and moisture concentrations on the principal instability regions are investigated using finite element method. The effects of transverse shear deformation and rotary inertia are used to study the antisymmetric angle-ply square plates. A simple laminated plate model is developed for the parametric instability of square laminated plates subjected to hygrothermal loading. A computer program based on FEM in MATLAB environment is developed to perform all necessary computations. The results show that instability of square laminated plates occurs for different parameters with an increase in temperature and moisture environment. The onset of instability occurs earlier, and the width of dynamic instability regions increases with a rise in temperature and moisture for different parameters. The effect of damping shows that there is a finite critical value of dynamic load factor for each instability region below which the square laminated plates cannot become unstable.

Assessment of plate theories for free-edge effects

This paper deals with a comparative study of several laminated plate theories with respect to their capability to capture the steep transverse stress gradients occurring in vicinity of free edges. The considered laminated plate theories pertain to the family of Equivalent Single Layer (ESL) as well as Layer-Wise (LW) descriptions. Reference is made to the classical displacement-based approach as well as to a partially mixed variational formulation, which allows to introduce independent assumptions for the transverse stresses and the displacements. Finite element solutions are obtained for free-edge effects that arise in several representative laminates subjected to uniaxial tension. An equivalent stress measure is proposed for assessing the three-dimensional (3D) stress fields predicted by the various theories. It is shown that refined LW models can provide quasi-3D results that compare well with full 3D FEM computations, whereas ESL models fail to capture the free-edge effects. Present results indicate that free-edge effects induced by a ±45° interface are most critical for the accuracy of laminated plate models.

Vibration of woven fiber laminated composite plates in hygrothermal environment

The present study deals with both experimental and numerical investigation on the free vibration behavior of laminated composite plates subjected to varying temperature and moisture. A simple laminated plate model is developed for the vibration of composite plates subjected to hygrothermal loading. A computer program based on finite element method in the MATLAB environment is developed to perform all necessary computations. The woven fiber glass/epoxy specimens were hygrothermally conditioned in a humidity cabinet where the conditions were maintained at temperatures of 300–425 K and relative humidity ranging from 0% to 1.0% for moisture concentrations. Quantitative results are presented to show the effects of geometry, material and lamination parameters of woven fiber laminate on the free vibration of composite plates for different temperature and moisture concentrations. The numerical and experimental results show that there is reduction in natural frequency in Hz with the increase in temperature and moisture concentration for laminates with simply supported and clamped boundary conditions with different aspect ratio and side-to-thickness ratios.