Thick Composite Plates Research Articles

Structural optimization of rotating tapered laminated thick composite plates with ply drop-offs

In this study, structural optimization of rotating tapered thick laminated composite plates with ply drop-offs has been investigated numerically. The governing differential equations of motion of the tapered composite plate have been presented including the energy associated with the inertia force, coriolis force, displacement dependent centrifugal force and initial stress resultants due to steady state rotation. Four noded quadrilateral finite element has been formulated based on the first order shear deformation theory. Finite element analysis results are validated with experimental results for natural frequencies of the tapered plate with various configurations. Various cases of optimization problems are formulated with different objective functions in terms of maximization of natural frequencies and damping factors (individually and combined) and solved using genetic algorithm in order to obtain optimal ply sequence and ply orientation. It is shown that the optimization problem with maximization of fundamental modal damping factor without rotating condition yields the optimal layout as 90° for all the layers in the plate. It is also observed that maximization of the fundamental modal damping factor yields identical optimal orientation for uniform and all the configurations of a tapered composite plate.

Vibration analysis of a tapered laminated thick composite plate with ply drop-offs

In this study, vibration characteristics of a tapered laminated thick composite plate have been investigated using finite element method by including the shear deformation and rotary inertia effects. The governing differential equations of motion of a tapered laminated thick composite plate are presented in the finite element formulation based on first-order shear deformation theory for three types of taper configurations. The effectiveness of the developed finite element formulation in identifying the various dynamic properties of a tapered laminated thick composite plate is demonstrated by comparing natural frequencies evaluated using the present FEM with those obtained from the experimental measurements and presented in the available literature. Various parametric studies are also performed to investigate the effect of taper configurations, aspect ratio, taper angle, angle ply orientation and boundary conditions on free and forced vibration responses of the structures. The comparison of the transverse free vibration mode shapes of the uniform and tapered composite plates under various boundary conditions is also presented. The forced vibration response of a composite plate is investigated to study the dynamic response of tapered composite plate under the harmonic force excitation in various tapered configurations. It is concluded that the dynamic properties of laminated thick composite plates could be tailored by dropping off the plies to yield various tapered composite plate.

An element-free IMLS-Ritz framework for buckling analysis of FG–CNT reinforced composite thick plates resting on Winkler foundations

An element-free based improved moving least squares-Ritz (IMLS-Ritz) method is proposed to study the buckling behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) resting on Winkler foundations. The first-order shear deformation theory (FSDT) is employed to account for the effect of shear deformation of plates. The IMLS is used for construction of the two-dimensional displacement field. We derive the energy functional for moderately thick plates. By minimizing the energy functional via the Ritz method, solutions for the critical buckling load of the functionally graded carbon nanotube (FG–CNT) reinforced composite plates on elastic matrix are obtained. Numerical experiments are carried out to examine the effect of the Winkler modulus parameter on the critical buckling loads. The influences of boundary condition, plate thickness-to-width ratio, plate aspect ratio on the critical buckling loads are also investigated. It is found that FG–CNT reinforced composite plates with top and bottom surfaces of CNT-rich have the highest critical buckling loads.

Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method

With very limited literature being available on the nonlinear bending behaviors of functionally graded carbon nanotube (FG-CNT) reinforced composite thick plates, this paper fills the apparent void by providing solutions to this problem based on the first-order shear deformation theory (FSDT). The plate considered rests on elastic foundations under transversely distributed loads. The analysis is carried out using the element-free IMLS-Ritz method. The arc-length iterative algorithm and the modified Newton–Raphson method are employed to obtain the nonlinear responses of FG-CNT reinforced composite plates. Convergence and comparison studies on a few example problems are performed to validate the numerical stability and accuracy of the IMLS-Ritz method. In this study, the characteristics of nonlinear bending influenced by foundation stiffness, transverse shear deformation, CNT distribution, CNT volume fraction and boundary conditions are examined.

Exact refined buckling solutions for laminated plates under uniaxial and biaxial loads

This paper presents a unified Lévy-type solution procedure for the buckling analysis of both thin and thick composite plates under biaxial loads. The plates are simply-supported at two opposite edges, while the two remaining sides are subjected to any combination of simply-supported, clamped and free conditions. The problem is formulated in the context of a variable-kinematic approach, offering the advantage of automatically handling theories of various order. Both layerwise and equivalent single layer theories are considered. The governing equilibrium equations are derived analytically from the Principle of Virtual Displacements (PVD), and are solved exactly referring to the Lévy-type procedure. The accuracy of the predictions is demonstrated by comparison with results available in literature, including exact 3D solutions. A comprehensive set of benchmark results is provided for plates subjected to different loading and boundary conditions and characterized by various width-to-thickness ratios.

A numerical study of bioinspired nacre-like composite plates under blast loading

In this paper, a multi-layered composite inspired by the hierarchical structure of nacre and made of layers of aluminium alloy AA 7075 bonded with toughened epoxy resin is introduced for blast resistant applications. The performance of the proposed nacre-like 3.3-mm and 5.4-mm thick composite plates, made of 1.1-mm thick AA 7075 layers, under localised impulsive loading was numerically studied. The epoxy material was modelled using user-defined interface cohesive elements that properly take into account both strength and toughness enhancements under compression. As compared to bulk plates, the improvement in blast resistance performance was numerically observed in the nacre-like plates, which required larger loads to reach the onset of failure. In addition, a reduction of the peak velocity and maximum deflection of the back face was observed for the nacre-like plates. This improvement is explained by the hierarchical structure facilitating a globalised energy absorption by inter-layer interlocking, delamination and friction.

Delamination-free drilling of thick composite materials

The machining of composite materials is a growing problem in the aeronautical field. In particular, the drilling of these materials, required to assemble different parts, is difficult to control and often leads to delamination at the exit of the laminates. This can affect the strength of the structure. In this paper, the drilling of thick composite plates with a large-diameter drill is studied. An analytical model is developed to determine the critical thrust force at delamination at the hole exit. This analytical model is divided into several zones, along the geometry of the tool active part. A cutting force model, based on the same zones decomposition as the analytical model, is also presented. This model gives the drilling thrust force as a function of the cutting conditions. Finally, the two considered models are used to determine the optimal cutting conditions for delamination-free drilling. The results are validated numerically and experimentally.

A C0 zig-zag model for the analysis of angle-ply composite thick plates

From a theoretical and practical viewpoint, the zig-zag theory is well adopted in the analysis of laminated composite structures. Nevertheless, for the available zig-zag models, artificial constraints in which the first derivatives of transverse displacement are replaced by the assumed variables have to be employed to avoid C1 interpolation functions in the finite element implementation. Such artificial constraints violate continuity conditions of interlaminar transverse stresses at interfaces. To avoid using artificial constraints, a C0-type zig-zag model is proposed in this paper. C0 interpolation functions are only required in the finite element formulation as first derivatives of transverse displacement have all been eliminated from the displacement field based on stress compatibility conditions between plies and on the top and bottom surfaces of the plate. Moreover, the number of variables involved in the proposed zig-zag model is less than that of the existing zig-zag models, yet accurate results are produced comparable to analytical solutions and three-dimensional finite element results. Effects of ply orientations, boundary conditions and length-to-thickness ratio on displacements and stresses of laminated composite plates have been studied.

Computation of vibration solution for functionally graded carbon nanotube-reinforced composite thick plates resting on elastic foundations using the element-free IMLS-Ritz method

This paper explores the element-free IMLS-Ritz method for computation of vibration solution of thick functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates resting on elastic foundations. The shear deformation effect is incorporated through the first-order shear deformation theory (FSDT). The cubic spline weight function and linear basis are utilized in the approximation. Regular node arrangements and cell background meshes are employed in the numerical integration. The penalty method is adopted to impose the essential boundary conditions. Numerical stability and applicability of the IMLS-Ritz method are examined through solving a few numerical example problems. The influence of Winkler modulus parameters on the vibration behavior of FG-CNTRC plates is studied. Besides, the effects of CNT volume fraction, CNT distribution, plate thickness-to-width ratio, plate aspect ratio on FG-CNTRC plates are investigated under different boundary conditions. The vibration frequencies and mode shapes of the FG-CNTRC plates on different Winkler foundations are presented.

Bending of Laminated Composite Plates

In this work, there are presented overviews of theoretical and numerical models for defining the stress-strain state in the cross section of moderately thick and thick composite plates in case of bending. Layered composite plates are constructed by combination of layers of various materials and geometrical characteristics, wherein each of them has got a bearing capacity in previously defined directions. By applying Equivalent Single-layer Laminate Theory (or ESL theory) these layers' problems cannot be solved successfully. That is the reason to apply contemporary theories of plates, in literature known as Layerwise theories. At the end of this work, there are given numeric examples of applying Partial Layerwise Theory.

Analytical solution for the three-dimensional stress fields in anisotropic composite bimaterial corners

The paper presents a theoretical treatise for the three-dimensional elastic stress distributions close to anisotropic bimaterial corners according to which the 3D governing equations are successfully reduced to two uncoupled equations in the two-dimensional space. The former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem. With the new theory an analytical solution for the stress fields for bimaterial corners in thick anisotropic composite plates is presented and its degree of accuracy is discussed comparing theoretical results and numerical data from 3D FE analyses carried out on bimaterial composite plates and joints.

Triangular Differential Quadrature Method in Bending Analysis of Triangular Symmetric Laminated Plates

The main advantage of triangular differential quadrature method in numerical simulations of problems in triangular domain is that it needs very few grid points compared to those of low order methods. In the current work, the method is implemented to analyze the bending behavior of relatively thick triangular composite plates based on the concept of first-order shear deformation theory. A set of triangular symmetric laminated plates with various lay-ups, length to thickness ratios, and boundary conditions is considered. The results are discussed in detail and compared with those obtained from finite element method of analysis using ANSYS package.

A layerwise p-version finite element formulation for free vibration analysis of thick composite laminates with curvilinear fibres

Herein, modes of vibration of a novel type of composite laminates, manufactured by tow-placement machines and which are called Variable Stiffness Composite Laminates (VSCL), are of interest. Layerwise theory is chosen, because it leads to an accurate prediction of displacements through the thickness of laminates, even when these are thick. Furthermore, it naturally has the capability of modelling the bending-membrane coupling that occurs on free vibration of VSCL plates with unsymmetric stacking sequences. The continuity of displacements at layer interfaces is imposed and in-plane displacements vary in a zig-zag fashion along the thickness. The accuracy of the model is confirmed by testing Constant Stiffness Composite Laminates (CSCL) analysed in the literature by others, who employed either Equivalent Single Layer (ESL) or layerwise theories. Abaqus commercial finite element software is as well employed in order to test the present approach. Finally, published natural frequencies of VSCLs, which were studied by an ESL theory, are compared with frequencies resulting from the present layerwise theory. The verification of the proposed model is followed by an investigation on the effect of curvilinear fibre orientation parameters on natural frequencies of thin to thick composite plates, with symmetric and unsymmetric lay-ups.

Drilling of thick composite material with a small-diameter twist drill

Composite materials are increasingly used in aeronautics. The assembly of aircraft structures requires the machining of different parts. The drilling of thick composite plates is a particularly delicate operation because of the fast rise in the temperature of the tool and the material. This causes defects at the hole entry, on the wall of the hole, and at the exit of the plate. These defects reduce the resistance to structural failure, and therefore, it is important to find a solution to minimize and to remove them if possible. The cutting conditions are the main parameters that affect the quality of the machining. This paper focuses on the choice of the feed rate corresponding to the critical case of delamination determined in the case of a twist drill with a small diameter. The feed rate is calculated by means of two models developed in the laboratory. The first model is analytical; it allows determining the critical thrust force at delamination at the exit of the hole as a function of the characteristics of the material and the load applied by the tool. The second allows predicting the drilling thrust force based on the feed rate. The combination of these two models can determine the critical feed rate with respect to the delamination at the exit of the hole.

Isogeometric bending analysis of composite plates based on a higher-order shear deformation theory

This research paper presents an isogeometric plate finite element formulation for analysis of thick composite plates. Isogeometric finite element method which is based on non-uniform rational B-splines (NURBS) basis functions, is a novel numerical procedure developed to bridge the gap between CAD and FEM modeling of structures. In order to investigate the behavior of isogeometric plate elements under static loading, plate kinematics is based on third order shear deformation theory (TSDT) of Reddy, which is free from transverse shear locking. This paper discusses accurate transverse stress recovery procedures for TSDT isogeometric finite elements. Numerical experiments with quadratic, cubic and quartic elements are presented and obtained results are compared to other available ones.

Stress fields at sharp angular corners in thick anisotropic composite plates

A new three-dimensional theory to be applied to thick anisotropic plates is developed, according to which the 3D governing equations of elasticity are successfully reduced to the simultaneous solution of two uncoupled equations in the two-dimensional space. With the new theory an analytical solution for the three-dimensional stress fields in anisotropic composite plates with V-notches is presented and its degree of accuracy is discussed comparing theoretical results and numerical data from 3D FE analyses.

Free vibration of thick composite plates on non-homogeneous elastic foundations by dynamic stiffness method

This research presents a new model for vibration analysis of thick laminated plates on a non-homogeneous elastic foundation by the Dynamic Stiffness Method(DSM). The non-homogeneous foundation consists of multi-segment Winkler-type and Pasternak-type elastic foundation. The Dynamic Stiffness Matrices using the First ShearDeformation Theory (FSDT) are constructed for cross-ply thick composite plates. A computer program is written using the present formulation for calculating natural frequencies and harmonic response of composite plates subjected to various types of boundary conditions. Numerical results are validated by comparison with available results in the literature and with Finite Element Method (FEM). Different test cases make evidence the advantages of the present model: higher precision, less data storage, less computing time and studied frequency range extended.

Dynamic stiffness formulation for vibration analysis of thick composite plates resting on non-homogenous foundations

This research presents new continuous elements for thick laminated plates on a Pasternak or a non-homogeneous foundation using the Dynamic Stiffness Method (DSM). The non-homogeneous foundation consists of multi-section Winkler-type and Pasternak-type elastic foundation. The Dynamic Stiffness Matrices using the First Shear Deformation Theory (FSDT) are constructed based on the exact closed form solutions of the governing differential equations of both cross-ply and angle-ply thick composite plates on non-homogeneous elastic foundations and subjected to various types of boundary conditions. A computer program is written using the present formulation for calculating the natural frequencies and harmonic response of composite plates without contact with elastic foundation and composite plates resting on non-homogenous foundations. The validation is done by comparison of continuous element model with available results in the literature and with Finite Element Method (FEM). Different test cases confirm the advantages of the present model which is supposed to be especially efficient in dynamics analysis.

Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape

This paper investigates the dynamic behavior of moderately thick composite plates of arbitrary shape using the Generalized Differential Quadrature Finite Element Method (GDQFEM), when geometric discontinuities through the thickness are present. In this study a five degrees of freedom structural model, which is also known as the First-order Shear Deformation Theory (FSDT), has been used. GDQFEM is an advanced version of the Generalized Differential Quadrature (GDQ) method which can discretize any derivative of a partial differential system of equations. When the structure under consideration shows an irregular shape, the GDQ method cannot be directly applied. On the contrary, GDQFEM can always be used by subdividing the whole domain into several sub-domains of irregular shape. Each irregular element is mapped on a parent regular domain where the standard GDQ procedure is carried out. The connections among all the GDQFEM elements are only enforced by inter-element compatibility conditions. The equations of motion are written in terms of displacements and solved starting from their strong formulation. The validity of the proposed numerical method is checked up by using Finite Element (FE) results. Comparisons in terms of natural frequencies and mode shapes for all the reported applications have been performed.

Mechanical Buckling of Thick Composite Plates Reinforced with Randomly Oriented, Straight, Single-Walled Carbon Nanotubes Resting on an Elastic Foundation using the Finite Strip Method

AbstractThis paper is devoted to the mechanical buckling analysis of thick composite plates under straight single-walled carbon nanotubes reinforcement with uniform distribution and random orientations resting on an elastic foundation. To develop the fundamental equations, the finite strip method, along with third-order shear deformation theory, is employed, and the total potential energy is minimized, which leads to an eigenvalue problem. The elastic foundation is modeled by classical and two-parameter simulations. For deriving the effective modulus of composite plates reinforced with carbon nanotubes, a method is used in which each straight carbon nanotube is modeled as a fiber with transversely isotropic elastic properties. The results of the numerical experiments, including the critical buckling loads for thick rectangular composite plates reinforced by carbon nanotubes with various boundary conditions and different volume fractions of nanotubes, are provided, and the positive effect of using carbon n...