Multilayered Composite Plates Research Articles

A fast and efficient pseudo-direct identification method for orthotropic elastic properties of multi-layered composite plates

New types of laminated composites are continuously being developed to meet various requirements involved in engineering applications. Before mass production of these new composite materials can take place, it is necessary to identify their elastic properties. Although current identification methods based on vibration tests and optimization algorithms are highly accurate, their high computation cost is a drawback. To address this issue, this paper proposes a new method to identify orthotropic elastic properties of multi-layered composite plates. The proposed method is based on the Modal Stability Procedure, using the experimental vibration frequencies and corresponding numerical mode shapes of structures. It converges after only two or three iterations without requiring an optimization algorithm. Therefore, the computational cost of the proposed method is significantly lower than that of optimization-based methods. The effectiveness and robustness of this method are demonstrated through three examples with different material, stacking sequences, and geometries including curved plate.

Homogenised strength criterion for natural fibre-reinforced composite

A representative model for multilayer natural fibre composite (NFC) plates is introduced to investigate its homogenised strength criterion. A three-layer NFC plate model is used to analyse the local stress–strain characteristics in multi-layered NFC. Finite element analysis (FEA) is performed on the representative volume element (RVE) under various boundary conditions to investigate stress and strain at macroscopic and microscopic levels. The explicit assessment of homogenised strength requires calculating stress tensors and equivalent stresses to determine parameter values. The precise specification of homogenised strength requirements assists in comprehending the material's behaviour under various loading conditions, which affects composite application design and optimisation techniques. The study examined the effect of fibre orientation angles on NFC's mechanical behaviour. The results demonstrate that flax fibres have comparatively higher stress levels than coir fibres. This study improves the understanding of natural fibre laminate composites’ macroscopic and microscopic behaviours, that is, the material's response under different loadings. The definition of homogenised strength criterion on NFC improves their design evaluations.

Solver-free reduced order homogenization for nonlinear periodic heterogeneous media

Reduced-order homogenization (ROH) and related methods are important computational tools for simulating the material behavior of composites. These methods generally sacrifice accuracy in exchange for superior computational efficiency, relative to methods such as classical computational homogenization (CCH). In this study, building on the recently developed solver-free CCH, we propose a fine-scale solver-free reduced order homogenization approach that avoids solving the fine-scale equilibrium equations and approximates the phase-average eigenstrains by sampling the fine-scale eigenstrain at a small number of points. The proposed method, which we call solver-free ROH, works by pre-computing history-dependent eigenstrain influence function tensors and sampling point contribution factors based on training data from a small set of CCH simulations. Then, during the online stage of the computation, phase-average eigenstrains are computed from sampling point eigenstrains and used to compute homogenized stresses and strains. Focusing on small-deformation problems, this paper formulates and verifies the solver-free ROH approach for nonlinear periodic heterogeneous media. First, in the formulation, we delineate a sampling point approximation of the phase eigenstrains and describe the use of this approximation within the coarse-scale stress update. Next, we verify the solver-free ROH using loading cases outside the training data set. Finally, we use the proposed method to simulate a multilayer composite plate in three point bending (3pt-bend) and open hole tension (OHT), demonstrating the method’s efficiency and accuracy relative to the CCH.

Natural Frequency Characteristics of Stiffened FG Multilayer Graphene-Reinforced Composite Plate with Circular Cutout Resting on Elastic Foundation

In this research, natural frequency response of functionally-graded multilayer graphene-reinforced composite plate with circular cutout reinforced by orthogonal stiffeners is investigated for the first time. The structure is surrounded by Winkler-type elastic support. The plate is composed of polymethyl methacrylate (PMMA) as matrix material and reinforced by graphene platelets (GPLs). The material of the orthogonal stiffeners is the same as that for the matrix. Rule of mixtures and Halpin–Tsai approach are applied to estimate the effective material properties of the composite plate. Third-order shear deformation plate theory and finite element procedure is employed to obtain the element matrices of the structure. Natural frequencies and mode shapes of the stiffened plate are reported for different variables such as nanofillers dispersion patterns, width and height of the stiffeners, aspect ratio of plate, plate thickness ratio, weight fraction of nanofillers, number of stiffeners, boundary conditions, elastic foundation stiffness parameter and size of circular cutout. The obtained results denote that with the addition of a set of stiffeners, fundamental frequency enhanced up to 32.3% with just about 10% increase of mass.

Nonlinear free vibration analysis of internal thickness-tapered multi-layered composite rectangular plates undergoing moderately large deflections

Thickness-tapering in multi-layered composites is achieved by terminating the plies at discrete locations. This allows for effective material utilization and significant weight savings and is adopted in applications involving multi-layered composites that demand variation in thickness such as helicopter yokes, flexbeams and rotor blades, aircraft wing-skin structures and turbine blades. In the present work, the nonlinear free vibration of such tapered composites undergoing moderately large deflections is investigated for the first time. A general nonlinear finite element formulation for tapered multi-layered composite plates based on Reddy's higher-order shear deformation theory and considering Von Karman nonlinearity is developed. Newton–Raphson scheme in conjunction with Newmark time-integration technique is employed to obtain the time response. The developed model is validated against available results in the literature and through experimentally obtained linear natural frequencies of a honeycomb sandwich plate with tapered face sheets. Parametric studies are conducted to deeply understand the nonlinear dynamic behaviour of tapered composite structures. The investigation reveals that tapered multi-layered composite plates exhibit higher nonlinearity compared to uniform plates thus necessitating the consideration of nonlinear effects in the analysis of such structures.

Solver‐free classical computational homogenization for nonlinear periodic heterogeneous media

AbstractModeling the behavior of composite materials is an important application of computational homogenization methods. Classical computational homogenization (CCH), based on asymptotic analysis, is such a method. In CCH, equilibrium equations are separated into two length scales and solved numerically. Solving the fine‐scale equilibrium equations at every coarse‐scale Gauss point, in every iteration of a Newton–Raphson loop, is often too computationally expensive for real engineering applications. In this study, we propose a modified CCH approach that avoids solving the fine‐scale equilibrium equations. The proposed method, which we call solver‐free CCH, works by pre‐computing a set of eigenstrain influence function tensors based on data from a small number of numerical experiments. Then, during the online stage of the computation, these eigenstrain influence tensors are used in the fine‐scale problem to evaluate and homogenize strains and stresses. This article begins by formulating the solver‐free CCH approach for small‐deformation problems involving composites with nonlinear constituent phase material models, including computation of the eigenstrain influence tensors and their application within the online stage. To verify the proposed approach, we consider loading cases outside the training set used to derive the eigenstrain influence tensors. The combinational efficiency and accuracy of the solver‐free CCH in comparison to the conventional CCH is studied on a multilayer composite plate in three point bending (3pt‐bend) and open hole tension.

Buckling response of functionally graded multilayer graphene platelet-reinforced composite plates with circular/elliptical cutouts supporting on an elastic foundation under normal and shear loads

The present article deals with the buckling response of functionally graded multilayer graphene platelet-reinforced composite (FG-GPL RC) rectangular plates with circular/elliptical cutouts resting on a Winkler-type elastic foundation under uniaxial and biaxial normal and shear loads. Rule of mixtures and the Halpin–Tsai approach are applied to obtain the effective Poisson’s ratio, mass density, and elastic modulus of the reinforced composite. The governing equations are developed by applying the third-order shear deformation plate theory. Then, the finite element procedure is used to solve the problem. Four different types of graphene platelet distributions, namely, UD, FG-X, FG-V, and FG-O, are considered. A broad range of factors such as plate aspect ratio, plate slenderness ratio, applying uniaxial and biaxial normal and shear loads to the plate, several Winkler elastic foundation stiffness parameters, different displacement boundary conditions, the effect of size of the circular cutout and orientation of the elliptical cutout, and the influence of GPL weight fraction are discussed in several tabular and graphical data in detail.

Determination of elastic characteristics for a package of monolayers thin-walled plates from composite fibrous materials

An analytical method for calculating the equivalent elastic characteristics of anisotropic multilayer plates made of composite fibrous materials is laid out. The main assumptions taken into consideration when calculating elastic moduli and Pousson's coefficients are that fibers are elastic materials with orthotropic mechanical characteristics that deform together when multilayer plates are loaded. Analytical methods for calculating effective modulus of elasticity most common in practical applications of applied mechanics are laid out in the list of cited publications. These include the rules of the mixture, the model proposed by Hill and Khashin, the model of Kilchinsky, the methods of Vanin and L.P. Khoroshun. Numerical methods for determining the elastic mechanical properties of reinforced unidirectional and layered composite materials are based on information technologies of finite-element modeling of representative volumes of composite materials and solving a number of boundary value problems for them. For the constructions of thin-walled plates with composite fibrous materials, traditional calculation schemes are used, for which the plane stress state is typical. The stress-strain relationship for a monolayer of plates loaded at an arbitrary angle is presented in the form of Hooke's law for aniotropic materials. Deformations of a package of monolayers with composite fibrous materials in a plane elastic-deformed state are determined, as for a monolayer, by four independent elastic constants. With the use of a universal calculation model based on the equations of applied mechanics, the results of the calculations of elastic moduli and Poisson's coefficients were obtained for a package of monolayers of thin-walled plates with composite fibrous materials made of carbon fiber and carbon fiber. Research results are presented in an analytical and graphic form. The influence of the construction structure of composite fibrous materials of thin-walled plates on its mechanical properties and their dependence on the angle of the force load vector is presented. The research results can be used to determine the rational mechanical properties of multilayer composite plates, taking into account their structural and technological purpose in various industries.

A new and efficient zigzag theory for laminated composite plates

This paper develops a new and efficient zigzag theory named as C-311 for laminated composite plates. The new local zigzag displacement model of C-311 nonlinearly distributes through the thickness coordinate and satisfies the piece-wise continuity at the layer surface, and combines three-order displacement model to form the initial displacement field of the present theory. By enforcing the inter-laminar transverse stress continuity and the free surface conditions, the local displacement unknown variables can be eliminated, and the final displacement field of C-311 is expressed by a fixed number of unknown variables. In addition, the equilibrium equations and boundary conditions of the present theory can be obtained from the virtual work principle. To test the prediction accuracy of C-311, a simple-supported cross-ply square plate is investigated under mechanical loading. Numerical results show that compared to several classical laminated plates theories, the present theory can predict accurately mechanical behaviors of thick multilayered composite plates and heterogeneous laminated plates. Especially the C-311 can give an acceptable accuracy of the transverse shear stress derived from the constitutive equations directly, and that is benefit for practical engineering applications in the finite element method.

A discontinuous Galerkin formulation for nonlinear analysis of multilayered shells refined theories

A novel pure penalty discontinuous Galerkin method is proposed for the geometrically nonlinear analysis of multilayered composite plates and shells, modelled via high-order refined theories. The approach allows to build different two-dimensional equivalent single layer structural models, which are obtained by expressing the covariant components of the displacement field through-the-thickness via Taylor’s polynomial expansion of different order. The problem governing equations are deduced starting from the geometrically nonlinear principle of virtual displacements in a total Lagrangian formulation. They are addressed with a pure penalty discontinuous Galerkin method using Legendre polynomials trial functions. The resulting nonlinear algebraic system is solved by a Newton–Raphson arc-length linearization scheme. Numerical tests involving plates and shells are proposed to validate the method, by comparison with literature benchmark problems and finite element solutions, and to assess its features. The obtained results demonstrate the accuracy of the method as well as the effectiveness of high-order elements.

A new mixed model based on the enhanced-Refined Zigzag Theory for the analysis of thick multilayered composite plates

In this paper, a new mixed model based on the enhanced Refined Zigzag Theory for thick multilayered composite plates is formulated. The kinematics is assumed cubic for the in-plane displacements and parabolic for the transverse one. The set of kinematic variables are reduced by using a partial constraint on the transverse shear stress, and a new set of enhanced cubic zigzag functions are obtained. The transverse normal stress is assumed as a smeared cubic function along the laminate thickness. The assumed transverse shear stresses profile is derived from the integration of local three-dimensional equilibrium equations involving a new set of strain variables. The entire formulation is developed by involving the Hellinger-Reissner functional and a penalty term for the strains compatibility; the governing equations and the consistent boundary conditions are derived. Finally, to assess the proposed model's predictive capabilities for general multilayered laminated and sandwich plates, results are compared with exact three-dimensional solutions available in the literature.

Modeling and prediction of short/long term mechanical behavior of FRP-strengthened slabs using innovative composite finite elements

The analysis of plates or slabs strengthened with fiber reinforced polymer (FRP), especially when it comes to geometric irregularity and the time-varying characteristics of adhesive, presents multi-faceted simulation, modeling and computational challenges. In this paper, two new multilayer composite plate elements are proposed to model and analyze FRP-strengthened slabs, aiming at meeting these challenges with efficiency. The novelty relies on that the innovative elements realize the modeling of substrate, adhesive layer and FRP sheet in one “macroscopic” element rather than modeling each component by separate elements. One of them is capable of emulating geometric irregular structures while the other has better accuracy, and the flexible combination of them can be used to achieve accurate simulation and calculation of various strengthening systems. Another novelty is the extension of the study from elastic to viscoelastic by introducing an appropriate rheological interface and correspondence principle. The consistency with literature verifies the correctness of the proposed elements, subsequently, they were used to investigate the influence of the FRP tapering ends and strengthening forms on the reinforcement effectiveness. It is found that the proposed method is convenient to predict the short/long term mechanical behavior of FRP strengthened slabs with accuracy and computational efficiency, thus contributing to the design and optimization of the strengthening system.

Finite element modeling of the bending and vibration behavior of three-layer composite plates with a crack in the core layer

For multi-layered composite plates made up of different types of material components, each layer commonly has a different reinforcement angle (angle-ply). In the working process, cracking defects may appear, which also due to there being numerous layers, cracks can appear only in a certain inner layer without the surface layers being cracked. This necessitates considerable research. Therefore, this study uses the third-order shear deformation theory in conjunction with the phase-field theory to model the free vibration response and static bending of laminated composite plates with just a core layer fracture. Additionally, this is the first investigation to integrate the finite element method with phase-field theory in order to model the appearance of a fracture in a portion of the plate thickness. The phase-field variable is utilized to convert the crack to a continuous domain, which simplifies calculation; this is also a property that other computational theories lack. The results of the calculations show some surprising things that have never been seen before. For example, the length of the crack changes, but the natural frequency and maximum deflection of the plate don't change much, which makes it hard to find this kind of fault.

Modeling of aeroelastic composite plates vibrations based on asymptotic theory

The paper is devoted to solving the problem of aeroelastic deformation of multilayer thin composite plates. A theory of aeroelastic deformations of composite plates based on the application of the asymptotic averaging method and piston theory for modeling pressure on the body surface is proposed. The averaged equations of aeroelastic vibrations of composite plates are derived. An example of a numerical solution of the problem of one-dimensional bending vibrations of a composite plate based on the developed theory is given.

Beam element resonance-based prediction and parametric analysis of sound transmission of laminated plates

Laminated plates are complex structures important to practical applications, so it is essential and valuable to develop efficient and accurate models for predicting their sound transmission loss. An efficient and unified approach based on the frequency-dependent bending stiffness of a beam element taken from a laminated plate is proposed to predict the sound transmission loss of the laminated plate. First, the finite element method is used to calculate the resonant frequencies of the multilayer beam under different boundary conditions, based on which the apparent bending stiffness of the corresponding multilayer plate is estimated. Next, with the aid of the so obtained apparent bending stiffness, the dynamic behavior of a multilayer composite plate is described by a simplified fourth-order governing equation. Finally, the sound transmission loss is conveniently calculated with the modal superposition method. In this approach, the influences can be conveniently and accurately simulated of the plate size, shear modulus of the core, loss factor and boundary conditions. Furthermore, the predicted sound transmission loss is validated through comparisons with the measured values of typical laminated plates. Finally, based on calculations with the proposed approach, the influence is revealed of the shear modulus on the coincidence region and sound transmission loss, and the relationship is discussed between the weighted sound reduction index and the shear modulus. These results suggest that to achieve good acoustic performance of a designed laminated plate, the coincidence region should be narrow and located at frequencies as high as possible.

A computationally efficient C0 continuous finite element model for thermo-mechanical analysis of cross-ply and angle-ply composite plates in non-polynomial axiomatic framework

In the present article, the thermo-mechanical bending response of multi-layered composite plates is investigated in the framework of inverse-hyperbolic shear deformation theory using a generalized finite element model. The mathematical development is carried out under the assumptions of linear structural kinematics for the materials following generalized Hooke’s law. Energy-based finite element formulation and the principle of minimum potential energy are employed to develop the finite element governing equations. A computationally efficient C0 continuous finite element formulation is developed to examine the response of laminated composites subjected to constant, linear, and non-linear temperature change. Numerical analyses are carried out for composite laminates considering various lamination sequences (cross-ply as well as angle-ply), boundary conditions, loading conditions, span-thickness ratio, etc. The present results are compared with the existing analytical and numerical results and their agreement is observed. The effect of fiber orientation angle on bending response is analyzed to enable the optimal design of laminated composite structures under thermo-mechanical loading.

3D progressive damage analysis of a unidirectional multi-layered composite for mechanical joints

ABSTRACT Due to the presence of holes in composite mechanical joints, stresses around the holes are increased, and they may cause failure in the composites. Analysis of the composite behaviour after damage initiation around the holes is important, complex, and mostly three-dimensional. In order to achieve accurate results about the composite failure modes, damage analysis using a modern criterion is needed. In this research, to investigate the damage behaviour of a unidirectional multi-layered composite plate of a mechanical joint under pure tension, three codes are prepared in the USDFLD, VUSDFLD and VUMAT subroutines based on the Hashin criterion and implemented in ABAQUS software. These codes, using the methods of suddenly and gradually degradation in composite properties, progressively simulate the three-dimensional damage behaviour of the composite plate after damage initiation. The results show that, when a mechanical joint is under pure tension, the adequate distance from the edge of a hole to the edge of a composite plate is about two times the hole diameter. Furthermore, it is found that to rapidly investigate and analyse a mechanical joint in the composite structures, the USDFLD subroutine, which uses suddenly decreased material properties after damage initiation, is reasonable and more efficient.

3D hygro-elastic shell model for the analysis of composite and sandwich structures

The present work proposes the study of the hygrometric loading effects in the static analysis of multilayered composite and sandwich plates and shells. The employed model is based on a general exact 3D shell theory valid for one-layered and multilayered sandwich and composite plates, cylinders and cylindrical/spherical shell panels. The employed 3D equilibrium equations are developed in an orthogonal mixed curvilinear coordinate system for spherical shells in order to obtain the other simpler geometries as particular cases. A layer-wise approach is employed and equilibrium equations are solved in the thickness direction via the exponential matrix method. The partial derivatives in the in-plane directions are exactly calculated by assuming simply-supported edges and harmonic forms for the variables. The presented 3D shell model is extended to hygro-elastic cases by considering moisture content amplitudes imposed at the external surfaces of the structures in steady-state conditions. The moisture content profile through the thickness of the structures can be included in the 3D shell model using three different methodologies: it can be calculated by solving the steady-state 3D or 1D version of the Fick diffusion law, or it can be “a priori” assumed as linear through the thickness. Therefore, the developed system includes three non-homogeneous second order differential equilibrium equations that are solved after the introduction of opportune mathematical layers to consider the curvature effects through the thickness. The reduction to a first order differential equation system is obtained by redoubling the number of variables. The exponential matrix method is employed to accurately define both general and particular solutions. The implemented 3D hygro-elastic shell model is firstly validated and then it is employed with confidence for new benchmarks where the effects of thickness ratio, geometry, lamination scheme, material, thickness layer and imposed moisture content values at the external surfaces are investigated for composite and sandwich plates and shells. Showed results demonstrate the importance of an accurate developing of the elastic part of the 3D shell model combined with an appropriate evaluation of the moisture content profile through the thickness. Assumed linear moisture content profiles are correct only for thin one-layered isotropic structures, the use of the 1D Fick diffusion law allows only the correct definition of the material layer effect, the use of its 3D version allows the correct definition of both material and thickness layer effects.

Static and dynamic NURBS-based isogeometric analysis of composite plates under hygrothermal environment

In this paper, a computationally efficient isogeometric plate model, employing nonpolynomial shear deformation theory (NPSDT), for static and dynamic analysis of laminated and sandwich composite plates under hygrothermal environment is presented. Transient and steady-state response using Rayleigh damping model and fast Fourier transformation of transient response have also been obtained for the hygrothermal environment. The non-uniform rational B-splines (NURBS) based formulation has been considered, which attribute only five-degree of freedom and satisfies the stringent continuity requirement of the NPSDT model (C1-continuity) without any additional variables. A total Lagrangian approach in conjunction with Hamilton’s principle is utilized to formulate the governing equations for thermal bending and subsequent dynamic analysis of multilayered composite plates. To model stress stiffening effect due to hygrothermal load, both von Kármán and Green–Lagrange strain displacement relations are incorporated and obtained solutions are compared. It has been shown that at higher temperature (around one fourth of the critical buckling temperature), the consideration of Green–Lagrange strain relationship for modeling stiffening effect due to hygrothermal load is important for better accuracy. Further, it has been shown that bending strip is essential in case of higher-order shear deformation theory (HSDT) to get more accurate solution. In addition, the obtained transient damped/undamped solutions may be used to get the natural frequency from their FFT solution.

DESIGNING THE STRUCTURE OF HINGED FASTENING OF THE MULTILAYER COMPOSITE BOARD TO A VEHICLE TRAILER BODY

Steel sides of dump tractor trailers used in the transportation of bulk and semi-liquid agricultural goods are subject to active abrasive wear and corrosion. The article proposes replacing the existing design of the sides, instead of steel sheets to use multilayer composite plates, which will increase the reliability and service life of the machine as a whole. (Research purpose) The research purpose is developing a design and methodology for calculating the hinge fastening of a composite side to the agricultural vehicle. (Materials and methods) The article analyses the existing metalcomposite compounds. When using multilayer sandwich-structured composites, all layers do not adhere to the metal base. We have developed a design of a pivotally movable side support of the trailer, which provides a tight connection due to the introduction of a metal steel element into the prepreg, consisting of a plate with studs and an axle welded to it. Additional tightening of the support due to threaded connections made it possible to connect a multilayer composite with metal plates. (Results and discussion). The article presents the equation of node loading to determine the maximum force acting on the fastener. The calculation of the most loaded part, the fastener, was carried out according to the permissible stresses of the cut of its cylindrical part. (Conclusions) The expediency of using power structures of vehicles of the agro-industrial complex exposed to abrasive wear and corrosion made of polymer composite materials is confirmed. A new design of a detachable swivel joint of a multilayer composite side with a metal frame was created.