Modeling Of Composite Plates Research Articles

Numerical modeling of defective hybrid composite plates

Numerical modeling of defective hybrid composite plates

Two‐scale topology optimization for composite plates with in‐plane periodicity

SummaryThis study proposes a two‐scale topology optimization method for a microstructure (an in‐plane unit cell) that maximizes the macroscopic mechanical performance of composite plates. The proposed method is based on the in‐plane homogenization method for a composite plate model in which the macrostructure is modeled using thick plate theory and the microstructures are three‐dimensional solids. Macroscopic plate characteristics such as homogenized plate stiffnesses and generalized thermal strains are evaluated through the application of numerical plate tests applied to an in‐plane unit cell. To handle large rotations of the composite plates, we employ a co‐rotational formulation that facilitates working with the two‐scale plate model formulated within a small strain framework. Two types of objective functions are tested in the presented optimization problems: one minimizes the macroscopic end compliance to maximize the macroscopic plate stiffness, whereas the other maximizes components of a macroscopic nodal displacement vector. Analytical sensitivities are derived based on in‐plane homogenization formulae so that a gradient‐based method can be employed to update the topology of in‐plane unit cells. Several numerical examples are presented to demonstrate the proposed method's capability related to the design of optimal in‐plane unit cells of composite plates. Copyright © 2017 John Wiley & Sons, Ltd.

Erratum to: Electromagnetic modeling of carbon-fiber reinforced composite materials using the wave digital concept

This paper deals with the modeling of the carbon fiber composite thin plate exposed to an external electromagnetic field. The underlying anisotropic partial differential equations are solved using the wave digital concept. After an appropriate change of the dependent variables and a coordinate transformation, a multidimensional passive reference circuit is derived along with its wave digital implementation. Numerical results, predicted using the multidimensional wave digital filtering approach, are compared to those obtained using the finite element method. Some stability related aspects are discussed. Besides, an electrostatic application of the presented wave digital model is outlined.

Impact behaviour of GFRP and Kevlar/epoxy sandwich composite plate: Experimental and FE analyses

In this paper, dynamic response of GFRP composite plate under ballistic impact has been studied by experimental tests and also by an efficient FE model. Material characterization of GFRP composite is performed as required for progressive damage analysis of laminate due to impact. Shock effect of impact is considered in the material modeling of composite plate. The influence of the target thickness on the ballistic performance of the composite plate is also studied by considering 3.12, 6.24 and 9.36 mm thick targets. Moreover, sandwich composite plate consisting of GFRP and Kevlar/epoxy in three different combinations of laminate layers is considered to obtain suitable combination for structural application that offer better penetration resistance. Damage pattern, contact force histories and stresses in composite plate are studied in addition to residual velocity and acceleration of projectile. Numerical results from present FE model in terms of residual velocities and damage patterns in composite plate show good agreement with the experimental results.

Dynamic characterization of tapered laminated composite sandwich plates partially treated with magnetorheological elastomer

This study investigates the dynamic performance of the partially treated magnetorheological elastomer tapered composite sandwich plates. Various partially treated tapered magnetorheological elastomer laminated composite sandwich plate models are formulated by dropping-off the plies longitudinally in top and bottom composite face layers to yield tapered plates as the face layers. The uniform rubber and magnetorheological elastomer materials are considered as the core layer. The governing differential equations of motion of the various partially treated magnetorheological elastomer tapered composite sandwich plate configurations are derived using classical laminated plate theory and solved numerically. Further, silicon-based magnetorheological elastomer and natural rubber are being fabricated and tested to identify the various mechanical properties. The effectiveness of the developed finite element formulation is demonstrated by comparing the results obtained with experimental tests and available literature. Also, various partially treated magnetorheological elastomer tapered laminated composite sandwich plates are considered to the study the effect of location and size of magnetorheological elastomer segment on various dynamic properties under various boundary conditions. The effects of magnetic field on the variation of natural frequencies and loss factors of the various partially treated magnetorheological elastomer tapered laminated composite sandwich plate configurations are analysed at different boundary conditions. Also, the effect of taper angle of top and bottom layers, aspect ratio, ply orientations on the natural frequencies of different configurations are analysed. Further, the transverse vibration responses of three different partially treated magnetorheological elastomer tapered laminated composite sandwich plate configurations under harmonic excitation are analysed at various magnetic fields. This analysis suggests that the location and size of the magnetorheological elastomer segments strongly influence the natural frequency, loss factor and transverse displacements of the partially treated magnetorheological elastomer tapered laminated composite sandwich plates apart from the intensities of the applied magnetic field. This shows the applicability of partial treatment to critical components of a large structure to achieve a more efficient and compact vibration control mechanism with variable damping.

A novel, single-layer model for composite plates using local-global approach

Abstract In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate's normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several layer-wise plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a novel, single-layer theory using local-global Approach: based on a finite element semi-discretization of the normal material line, the two-dimensional plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure. Three-dimensional stresses through the plate's thickness can be recovered accurately from the plate's stress resultants.

Variable kinematic finite element models of multilayered composite plates coupled with acoustic fluid

ABSTRACTThis article presents a novel and advanced finite element formulation of the structural-acoustic problem involving thin and thick multilayered composite plates coupled with a cavity. Exploiting the Carrera's unified formulation, many plate and fluid-structure interface elements based on different kinematic models, including higher-order equivalent single-layer and layerwise theories, are developed within a single mathematical framework. Accordingly, a large number of vibro-acoustic models can be easily obtained and selected according to the accuracy requirements of the application. In particular, it is shown that refined models can be adopted in those cases where models relying on traditional or low-order plate theories fail in providing the correct estimation of the fluid-structure coupling. The proposed formulation is also validated with respect to some reference cases available in the literature.

Modal characterization of composite flat plate models using piezoelectric transducers

This paper aims to estimate the modal parameters of composite flat plate models through Experimental Modal Analysis (EMA) using piezoelectric transducers. The flat plates are composed of three ply carbon-epoxy fibers oriented in the same direction. Five specimens with different unidirectional fiber nominal orientations θk (0o, 30o, 45o, 60o and 90o) were tested. These models were instrumented with one PZT (Lead Zirconate Titanate) actuator and one PVDF (Polyvinylidene Fluoride) sensor and an EMA was performed. The natural frequencies and damping factors estimated using only a single PVDF response were compared with the estimated results using twelve measurement points acquired by laser doppler vibrometry. For comparison purposes, the percentage error of each natural frequency estimation and the percentage error of the damping factor estimations were computed, as well as their averages. Even though the comparison was made between a SISO (Single-Input, Single-Output) and a SIMO (Single-Input, Multiple-Output) techniques, both results are very close. The vibration modes were estimated by means of laser measurements and were used in the modal validation. In order to verify the accuracy of the modal parameters, the Modal Assurance Criterion (MAC) was employed and a high correlation among mode shapes was observed.

Dynamic analysis of tapered laminated composite magnetorheological elastomer (MRE) sandwich plates

In the present study, the dynamic performance of the sandwich plate with magneto rheological elastomer (MRE) as the core layer and tapered laminated composite plates as the face layers is investigated. Various MRE tapered laminated composite sandwich plate models are formulated by dropping-off the plies longitudinally in top and bottom composite layers to yield tapered plates as the face layers and uniform MRE layer as the core layer. The governing equations of motion of tapered composite MRE sandwich plates are derived using classical laminated plate theory and solved numerically. Further, silicon based MRE is being fabricated and tested to obtain the shear and loss moduli using MR rheometer. The efficacy of the finite element formulation is validated by carrying out experiments on the various prototypes of tapered composite silicon based MRE sandwich plates and comparing the results in terms of natural frequencies obtained at various magnetic fields with those obtained numerically and with available literature. Also, the effects of magnetic field, taper angle of the top and bottom layers, aspect ratio, ply orientations and various end conditions on the various dynamic properties of tapered laminated composite MRE sandwich plate are investigated. Further, the transverse vibration responses of three different tapered composite MRE based sandwich plates under harmonic force excitation are analyzed at various magnetic fields.

Size dependent and micromechanical modeling of strain gradient-based nanoparticle composite plates with surface elasticity

The bending and free vibration behaviors of strain gradient-based Kirchhoff plates made of nanoparticle composites are investigated with the incorporation of the plate's surface effects. The modified strain gradient theory is used to capture the first-order deformation of the material structure while the impacts of the surface energy and surface tension are represented according to Gurtin and Murdoch surface elasticity theory. The plate is made of a composite material with nanocrystalline matrix and nanoparticles reinforcement. A size-dependent micromechanical model for multi-phase materials is developed to estimate the elastic moduli of the composite plate. This model has the merit to account for the effects of the surface energy of the inhomogeneities inside the composite structure. In addition, the impacts of the interface, grain size of the nanocrystalline matrix, porosity, and size of the reinforcing particles are incorporated into the micromechanical model. A simply supported composite plate consisting of nanocrystalline-silicon as the matrix and Al2O3-nanoparticles as the reinforcement is considered to study the influences of the size of the Si-grains, Al2O3-particles, voids, strain gradient deformation, and plate surface energy and tension on the deflection and natural frequencies of the plate. The results show that a decrease in the plate's thickness is accompanied with a decrease in the plate's deflection and an increase in the plate's natural frequency. Furthermore, the plate's strain gradient and surface tension contribute to its stiffness through a hardening effect while the interface and porosities inside the material structure affect the plate's stiffness with a softening mechanism. The plate's surface energy could stiffen or soften the plate depending on the values of the surface Lame constants. The surface energy of the inhomogeneities inside the material structure may increase or decrease the plate's stiffness, deflection, and natural frequencies depending on the inhomogeneities' sizes, their bulk material parameters, their surface material parameters, and their volume fractions.

Modeling of composite plates based on Reissner's Mixed Variational Theorem with variables separation

In this work, the modeling of laminated composite plates is performed through a variables separation approach based on a Reissner's Variational Mixed Theorem (RMVT). Both the displacement and transverse stress fields are approximated as a sum of separated functions of the in-plane coordinates x,y and the transverse coordinate z. This choice yields to a non-linear problem that can be solved by an iterative process. That consists of solving a 2D and 1D problem successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element method is used.Numerical examples involving several representative laminates are addressed to show the accuracy of the present LayerWise (LW) method. It is shown that it can provide quasi-3D results less costly than classical LW computations. In particular, the estimation of the transverse stresses which are of major importance for damage analysis is very good.

A layerwise isogeometric approach for NURBS-derived laminate composite shells

Layerwise theories provide an accurate prediction of the three-dimensional stress state of composite structures which is in many cases a prerequisite for a successful prediction of failure mechanism. We focus on such a model for laminate composite plate and shell models in the framework of isogeometric analysis. We apply an exact but dimensionally reduced geometry description based on a computer-aided design (CAD) derived mid-surface NURBS model and a layerwise through-thickness B-spline description. Using the unique and characteristic refinement capabilities of isogeometric analysis we simplify the modeling process while keeping the higher order and higher continuity properties of NURBS. Trimmed geometries, as common in CAD models are efficiently handled by an embedded domain method which treats trimmed areas as a fictitious extension domain in the computational model. We verify our approach with several examples for moderately thick laminate plate and shell models and compare our results to existing 3D solutions.

Analytical Modeling of Hard-Coating Cantilever Composite Plate considering the Material Nonlinearity of Hard Coating

Due to the material nonlinearity of hard coating, the coated structure produces the nonlinear dynamical behaviors of variable stiffness and damping, which make the modeling of hard-coating composite structure become a challenging task. In this study, the polynomial was adopted to characterize this material nonlinearity and an analytical modeling method was developed for the hard-coating composite plate. Firstly, to relate the hard-coating material parameters obtained by test and the analytical model, the expression of equivalent strain of composite plate was derived. Then, the analytical model of hard-coating composite plate was created by energy method considering the material nonlinearity of hard coating. Next, using the Newton-Raphson method to solve the vibration response and resonant frequencies of composite plate and a specific calculation procedure was also proposed. Finally, a cantilever plate coated with MgO + Al2O3hard coating was chosen as study case; the vibration response and resonant frequencies of composite plate were calculated using the proposed method. The calculation results were compared with the experiment and general linear calculation, and the correctness of the created model was verified. The study shows the proposed method can still maintain an acceptable precision when the material nonlinearity of hard coating is stronger.

Assessment of the refined sinus plate finite element: Free edge effect and Meyer-Piening sandwich test

This paper deals with the assessment of a refined sinus model for multilayered composite plates in the framework of severe test cases to highlight the interest and limitations of such an approach. The present sinus model is enriched by higher-order terms for both in-plane and transverse displacements, and layer refinement. This kinematics allows us to exactly ensure both (i) the continuity conditions for displacements and transverse shear stresses at the interfaces between layers of a laminated structure, and (ii) the traction-free conditions at the upper and lower surfaces of the plates. The number of unknowns is independent of the number of layers. A C1 6-node triangular finite element implementation is proposed, which does not suffer any numerical pathologies.First, the present approach is assessed on its capability to capture the steep transverse stress gradients occurring in the vicinity of free edges and is also compared with models available in the literature. Then, a highly anisotropic sandwich structure proposed by Meyer-Piening is also addressed for further comparison.

Second-order two-scale method for bending behavior analysis of composite plate with 3-D periodic configuration and its approximation

This paper considers the bending behaviors of composite plate with 3-D periodic configuration. A second-order two-scale (SOTS) computational method is designed by means of construction way. First, by 3-D elastic composite plate model, the cell functions which are defined on the reference cell are constructed. Then the effective homogenization parameters of composites are calculated, and the homogenized plate problem on original domain is defined. Based on the Reissner-Mindlin deformation pattern, the homogenization solution is obtained. And then the SOTS’s approximate solution is obtained by the cell functions and the homogenization solution. Second, the approximation of the SOTS’s solution in energy norm is analyzed and the residual of SOTS’s solution for 3-D original in the pointwise sense is investigated. Finally, the procedure of SOTS’s method is given. A set of numerical results are demonstrated for predicting the effective parameters and the displacement and strains of composite plate. It shows that SOTS’s method can capture the 3-D local behaviors caused by 3-D micro-structures well.

An Enhanced Reddy's Theory for Composite Plates Subjected to Temperature Load

This article proposes an enhanced Reddy's model for composite plates subjected to temperature load. Compared to the classical Reddy's theory, transverse normal strain is considered in the proposed model. Based on the proposed model, a triangular plate element is presented, in which the interelement C1 continuity conditions are satisfied. For finite element implementation, it is found that although transverse normal deformation is considered, displacement variables have not increased since thermal loads could be included in the generalized force vector. From the results of some classical problems, the proposed model shows a substantial improvement in stresses and displacements over Reddy's model.

Topology optimization of unconstrained damping treatments for plates

A finite element model for composite plates consisting of an elastic isotropic base layer covered with viscoelastic treatment is presented. The composite plate undergoes bending vibrations in the lateral direction. In contrast to many previous publications, the viscoelastic treatment is not constrained from the top in order to better simulate real cases. The objective is to find the optimum distribution of viscoelastic treatment which maximizes the modal damping ratio (MDR) for a certain volume of treatment. Topology optimization is performed with two strategies: optimizing the whole domain of viscoelastic treatment and optimizing a unit cell of the periodic treatment. Numerical examples show that the presented model is able to increase the MDR by an order of magnitude compared to plain treatments.

The effect of a thermo-oxidative environment on the behaviour of multistable [0/90] unsymmetric composite plates

The present paper focuses on the effect of a thermo-oxidative environment (150°C under atmospheric air) on the deformation behaviour of multistable IM7-977-2 [0/90] unsymmetric carbon–epoxy composite plates. Sample curvatures are measured at high temperature as a function of the ageing time by an optical method, by following the displacement of marker points situated on the external side of the plate and by fitting them with an interpolation algorithm. The predictions of a composite plate model taking into account thermo-oxidative affected mechanical properties of the elementary ply and the residual strains produced by thermo-oxidation allow interpreting and understanding the experimental results.

Zeroth-order shear deformation micro-mechanical model for composite plates with in-plane heterogeneity

This article introduces a new model for investigating the mechanical behavior of heterogeneous plates, which are composed of periodically-repeated microstructures along the in-plane directions. We first formulate the original three-dimensional problem in an intrinsic form for implementation into a single unified formulation and application to geometrically nonlinear problem. Taking advantage of smallness of the plate thickness-to-length parameter and heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order plate model, which is similar to a generalized Reissner–Mindlin model (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. This present approach is incorporated into a commercial analysis package for the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level. A few examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

Refined modeling of composite plates with in‐plane heterogeneity

AbstractThis article is concerned with the mechanical behavior of heterogeneous composite plates with elastic moduli and layered geometries varying through the thickness direction and periodically along the in‐plane directions. By using the concept of decomposition of the rotation tensor, we first formulate the three‐dimensional elastic problem in an intrinsic form for application to the geometrically nonlinear problem. The variational asymptotic method is then exercised, leading to simultaneous homogenization and dimensional reduction to construct an effective and simple model suitable for plates with in‐plane periodicity. In particular, having obtained the refinement terms up to the second order, we develop a refined plate model, namely a generalized Reissner‐Mindlin model that is capable of capturing the transverse shear deformations. In order to deal with realistic and complex plate geometries and constituent materials efficiently and conveniently, the proposed model is implemented into a single unified formulation suitable for incorporation into a commercial analysis package. Numerical results computed herein for a few examples are compared to similar results available in the literature to demonstrate the application and performance of the present model.