Antisymmetric Angle-ply Laminates Research Articles

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

New shape function in the free-vibration analysis of antisymmetric angleply composite laminates

The paper analyzes the problem of free vibrations in antisymmetric crossply laminates. A new shape function which is used in higher order shear deformation theories has been introduced. The comparative analysis was performed with the known shape functions. The procedure for obtaining dynamic equations of motion in the Matlab software package has been developed. For theoretical considerations, the module with the symbolic variable has been used. The paper shows which of the existing shape functions are applicable in the free vibration analysis of antisymmetric angleply laminates. The advantages and disadvantages of the newly developed shape function are clearly highlighted. Analytical procedures have been used to obtain the results of partial differential equations, based on Navier's solutions. Numerical integration procedures were used as an integral part of the developed Matlab codes for those shape functions where it was necessary. The results are presented in a table and figures. The procedure itself has been verified by comparison with the reference results from the literature.

A meshless study of antisymmetric angle-ply laminates using high-order shear deformation theories

Composite laminated plates have found several applications in engineering field. For instance, aerospace and automotive industry use these structures in several components of their products due to their exceptional specific properties along the direction of the fibres. There are several two-dimensional plate models that aim to more accurately and more efficiently predict the kinematics of those structures. Unlike the Classical Plate Theory (CLPT), which can only be applied to thin laminates, the First-Order Shear Deformation Theory (FSDT), developed by Reissner and Mindlin, already accounts shear effects and, due to that, it can describe in a satisfactory way the kinematic of a generic thick laminated plate. Nevertheless, the FSDT considers linear shape functions to describe the in-plane displacements through the plate thickness, which results in constant shear strains. Thus, the traction boundary conditions on the top and bottom surface of plate are violated. Additionally, the FSDT needs shear correction factors, which are not easily obtained for a generic problem. Equivalent single layer (ESL) theories following high-order shear deformation theories (HSDTs) have been proposed and more efficiently applied to composite laminated plates. These theories allow to represent the nonlinear variation of transverse shear stresses through thickness of plate because they possess nonlinear shape functions interpolating the in-plane displacements. Thus, the kinematics of these structural elements can be better described and more accurate stress fields can be obtained for problems that cannot be handled with the FSDT.These structures have been analysed for several years using the Finite Element Method (FEM), which is the most popular numerical tool in structural analysis. However, several other advanced numerical techniques, such as meshless methods, can also handle this kind of problems and, in some cases, in a more efficient way. This work makes use of a recently developed meshless method – the Natural Neighbour Radial Point Interpolation Method (NNRPIM) (Belinha, 2014) – to study the bending of antisymmetric angle-ply composite laminates using distinct HSDTs.

Microstructure and twisting ability of an adjusted antisymmetric angle ply laminate

This letter describes an adjusted antisymmetric angle ply laminate that is able to twist as a result of temperature-dependent deformation. A theoretical explanation for this twisting ability is presented and the adjusted architecture of the proposed laminate is described. The effects of fiber and matrix volume fractions, laminate angle, total laminate thickness, and temperature range on the torsion of the laminate are analyzed. A sample of the proposed microlaminate is produced by a microfabrication process and tested as the temperature is increased from room temperature to 80 °C. Microscopy images reveal that the microlaminate twists by more than 180° within a length of 200 μm. The proposed material and its twisting ability show great potential for application in microrobotic actuators.

Buckling analysis of anti-symmetric cross and angle-ply laminated composite plates

This article has for objective to analyze the buckling behavior of the unidirectional laminated plates. In this purpose, we propose an analytically method, based on the theory of classical, orthotropic plate theory. The governing equations are solved using Navier solution for uniform uniaxial loading in longitudinal direction. We were interested to identify the critical buckling load for simply supported antisymmetric cross-ply and antisymmetric angle-ply laminates of rectangular shape. Some important progress has been made on these relatively complicated buckling problems, involving coupling between bending and midplane stretching during a buckling deformation. Effects of different parameters such as fiber orientation angles, aspect ratio, modular ratio and number of layers were examined. Results are presented in the form of plots showing the variation in non-dimensional buckling load.

Influence of mechanical couplings on the buckling behaviour of thin-walled plates made of general laminates under compression

The present paper deals with the buckling and post-buckling behaviour of plates made of coupling laminates (the so-called general laminates). Such laminates consist of a number of layers arranged in an arbitrarily way. Thus, the sequences of laminated layers are non-symmetric. In this case, the coupling between tension, flexure, shearing and twisting takes place. The behaviour of general laminates substantially differs from that of laminates with a symmetric layup or isotropic materials. Therefore, they undergo out-of-plane deformation (i.e., warping, bending and/or twisting) when exposed to in-plane loads. Due to a wide range of application possibilities for general laminates, it is worth focusing on their advantages.The analytical-numerical method (ANM) based on Koiter’s theory was used to determine the static buckling loads and post-buckling equilibrium behaviour. In order to obtain the equations of equilibrium for plates, the classic laminate theory was used. The plate displacements were considered within the nonlinear geometrical relations. For special laminates (i.e., regular anti-symmetric angle-ply laminates), there are closed-form solutions of the equilibrium equations of the plate when displacements are slight. Those results were the same as the results produced with the presented methods. The differences in buckling stresses are very low, amounting to less than 5%.

The Effect of Higher Order Model on the Geometric Nonlinear Analysis of Antisymmetric Angle Ply Laminates

Geometric nonlinear analysis of simply supported antisymmetric angle-ply laminated composite plates are investigated based on first order and higher order displacement models with five degrees of freedom. Analytical formulations and solutions are developed based on Von-Karman nonlinear plate theory and Taylor's series expansion of displacement components. Equations of equilibrium are obtained using Principle of Minimum Potential Energy (PMPE) and closed form solutions using Navier's Solution technique. A four layered square plate is considered for the present study. Parametric studies are performed on both the models to study the behaviour of displacements and stresses in laminated composite plates. Comparative studies are performed on both the models and the effect of geometric nonlinearity is discussed.

Accurate prediction of three-dimensional free edge stress field in composite laminates using mixed-field multiterm extended Kantorovich method

An accurate prediction of the three-dimensional (3D) and often singular stress field at the free edges of composite laminates has been the subject of intense research since the pioneering numerical work of Pipes and Pagano (J. Compos. Mater. 4:538–548, 1970). In this work, we present an accurate 3D elasticity-based solution for determining the free edge stress field in laminates under uniaxial extension, bending, twisting and thermal loading, using the mixed-field multiterm extended Kantorovich method (MMEKM), which is a powerful iterative analytical method, developed recently by the author group. Unlike the existing 3D elasticity-based solutions, the present solution satisfies all the boundary conditions and the interfacial continuity conditions exactly at all points. The results are compared with various existing solutions reported for symmetric cross-ply and angle-ply laminates. New results are presented for the free edge stress field in antisymmetric angle-ply laminates for the four different load cases. The results show a rapid convergence and excellent accuracy of the MMEKM solution in all cases. The solution successfully captures the stress singularity at the free edge by predicting a steadily increasing peak value with increasing number of terms. The presented results will serve as useful benchmarks for assessing the accuracy of other approximate 3D and 2D theory-based solutions.

The transverse shear deformation behaviour of magneto-electro-elastic shell

Compared to the large number of possible magneto-electro-elastic shell theories, very few exact solutions determining the in-plane stresses, electric displacements and magnetic inductions are possible. While, solving the magneto-electro-elastic shell equations in terms of thermo-magneto-electro-elastic generalized field functions on arbitrary domains and for general conditions exactly are not always possible. In the present work, a linear version of magneto-electro-elastic shell with simply supported boundary conditions, solved exactly, provided that the lamination scheme is cross-ply or anti-symmetric angle-ply laminates. The exact solution that introduced herein can measure the in-plane stresses, electric displacements and magnetic inductions. It also allow for an accurate and usually elegant and conclusive investigation of the various sensations in a shell structure. However, it is important for micro-electro-mechanical shell applications to have an approach available that gives the transverse shear deformation Behaviourfor cases that cannot examine experimentally. An investigated examples were accompanied and noteworthy conclusions were drawn which highlight the issues of the implementation of the exact solution, implication of the effects of the material properties, lay-ups of the constituent layers, and shell parameters on the static Behaviour.

Bounds on the natural frequencies of laminated rectangular plates with extension-twisting (and shearing–bending) coupling

Anti-symmetric angle-ply laminates are widely believed to uniquely possess Extension-Twisting (together with Shearing–Bending) coupling behavior. The results in this article serve to dispel this misconception by presenting solutions for both standard laminates, containing combinations of angle plies (±45°) and cross plies (90° and/or 0°), and angle-ply laminates, containing only±45° ply orientations; chosen to reflect current industrial design practice, and also because they serve to produce hygro-thermally curvature-stable properties in some standard laminate configurations, i.e., with immunity to the thermal distortions that generally arise in this class of mechanically coupled laminate as a result of the high temperature curing process.Details of the algorithm used to develop the definitive list of laminate stacking sequences, with up to 21 plies, are given first. Closed form natural frequency solutions for each of these sub-groups are then presented, identifying significant differences in the frequency spectrum bounds across a range of aspect ratios, with respect to the ubiquitous anti-symmetric angle-ply designs.

Analytical solution to bending of stiffened and continuous antisymmetric laminates

Abstract Analytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

Postbuckling of laminated composite plates using NURBS-based isogeometric analysis

In this paper, postbuckling behavior of laminated composite plates is investigated using NURBS-based isogeometric analysis (IGA). A Green strain tensor with small rotations is proposed. Both von-Karman strain tensor and the proposed strain tensor are formulated. Governing equations are derived in the framework of first-order shear deformation theory (FSDT). Finite elements based on NUBRS show the robustness in performing a laminate with intentional imperfections as well as deformed mode shapes. Quadratic NURBS elements (Q9Nurbs) are used to construct physical meshes in C1 continuity. Newton–Raphson scheme is adjusted to geometric imperfections and employed for non-linear analysis procedure. In numerical examples, the postbuckling paths of laminated composite plates in sense of von-Karman strain theory and the proposed strain theory are presented. The obtained results of isotropic, symmetric, antisymmetric angle-ply and cross-ply laminates are verified with those available in literature.

Exact 3D solution for static and damped harmonic response of simply supported general laminates

The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each order, with associated mode shapes.Finite element simulations have been performed to validate most of the results presented in this study. As the boundary conditions needed for the general case are not so straightforward, a specific discussion has been added. It is shown that these boundary conditions also work for the two aforementioned laminate classes.The damped harmonic response of a non-symmetrical isotropic sandwich is studied for different frequencies around the fundamental frequency. The static and undamped dynamic behaviors of the [−15/15], [0/30/0] and [−10/0/40] laminates are studied for various length-to-thickness ratios.

A novel semi energy finite strip method for post-buckling analysis of relatively thick anti-symmetric laminated plates

In the current paper, a novel semi-energy FSM is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for thin and relatively thick anti-symmetric angle-ply composite laminates subjected to uniform end-shortening. The laminated plates are assumed to be simply supported at their boundaries. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results has provided confidence in the validity and capability of the developed FSM in handling the post buckling problem of anti-symmetric angle-ply laminates.

Free Vibration of Delaminated Composite Shallow Conical Shells

This paper presents a finite element method to investigate the effects of delamination on free vibration characteristics of graphite-epoxy pretwisted shallow angle-ply composite conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The theoretical formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain numerical results concerning the effect of twist angle, location of delamination and rotational speed on natural frequencies of delaminated angle-ply composite conical shells. The mode shapes are also depicted for a typical laminate configuration. Parametric studies of symmetric and anti-symmetric angle-ply laminates provide the non-dimensional natural frequencies which are the first known results for the type of analyses carried out here.

Three-dimensional Stability Analysis of Piezoelectric Antisymmetric Angle-Ply Laminates Using Finite Layer Method

The finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates. In this method, the plate is divided into a number of finite layers. Within each finite layer, trigonometric functions are used for the in-plane interpolations of displacements, whereas polynomials are employed for the interpolations in the thickness direction. Thus, the 3D analysis is transformed into a series of 1D analyses, and the efficiency is enhanced significantly. In the present study, the finite layer method is extended to the stability analysis of piezoelectric antisymmetric angle-ply laminates, which may be also combined with some symmetrical cross-plies. Numerical results are presented to verify the proposed method. The effects of side-to-thickness ratio, aspect ratio, number of plies, fiber-orientation, and electrical conditions on stability behaviors of some piezoelectric laminates are investigated.

Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions

The intent of the present study is to employ the extended Kantorovich method for semi-analytical solutions of laminated composite plates with arbitrary lamination and boundary conditions subjected to transverse loads. The method based on separation of spatial variables of displacement field components. Within the displacement field of a first-order shear deformation theory, a laminated plate theory is developed. Using the principle of minimum total potential energy, two systems of coupled ordinary differential equations with constant coefficients are obtained. The equations are solved analytically by using the state-space approach. The results obtained are compared with the Levy-type solutions of cross-ply and antisymmetric angle-ply laminates with various admissible boundary conditions to verify the validity and accuracy of the present theory. Also, for other laminations and boundary conditions that there exist no Levy-type solutions the present results are compared with those obtained by other investigators and finite element method. It is found that the present results have very good agreements with those obtained by other methods.

Three-dimensional thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates using finite layer method

Finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates. Using this method, the 3D analysis is transformed into one dimensional analysis by virtue of the orthogonal properties of trigonometric interpolation functions. In the present study, the finite layer method is extended to the thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates, which may be combined with some symmetrical cross-plies. Full coupling between the thermal, electrical and mechanical fields is taken into consideration. Pre-buckling state is assumed to be steady, and initial thermal stresses are computed accordingly. The geometrical stiffness matrix is then formed, and the critical temperature and buckling mode are obtained. Numerical examples are presented to verify the proposed method. The critical temperature is determined for both the adiabatic and isothermal buckling processes. The thermal buckling behaviours of some piezoelectric laminates and the effects of the thermo-electro-mechanical coupling are investigated.

Semi-energy finite strip post-buckling analysis of laminated plates concerning the effects of mechanical coupling

In composite laminated plates the mechanical coupling is one of the significant properties which dominate the performance of a laminated plate structure in large out-of-plane deformations. Some effects of mechanical coupling on the post-buckling behavior of composite laminated plates have been studied in this paper by implementing a finite strip approach based on the concept of a rigorous post-buckling solution for composite plates and plate structures, namely the semi-energy approach, which has been originally developed by the authors of current paper. Moreover, to check the validity and soundness of presented semi-energy FSM the results obtained from developed approach are compared with those obtained from a fairly conventional and well exploited finite strip technique, namely the full-energy finite strip method as well as the obtained results from ANSYS (i.e. the general purpose finite element method software). In this paper, the post-buckling behavior of an anti-symmetric angle-ply square plate with the stacking sequence configuration as [±45]2 has been studied. Moreover, according to anti-symmetric nature of lamination in the mentioned plate there exists a mechanical coupling between in-plane membrane and out-of-plane twisting curvature; therefore, the results of this analysis have been referred as coupled solution in this paper. In order to evaluate the effects of mechanical coupling on the post-buckling performance of mentioned plates, the uncoupled solution has also been determined by precluding the coupling terms (i.e. B16, B26). The post-buckling load–end shortening and load-maximum out-of-plane deflection paths have been obtained for coupled as well as uncoupled solutions. The comparison between the obtained results by coupled and uncoupled solutions revealed markedly different behaviors due to presence of mechanical coupling in the anti-symmetric angle-ply laminates. The outcome of the paper can help structural designers have a better understanding of the effects of mechanical coupling on the post-buckling behavior of laminated composite plates at the design stage.

Interlaminar hygrothermal stresses in laminated plates

Within the elasticity formulation the most general displacement field for hygrothermal problems of long laminated composite plates is presented. The equivalent single-layer theories are then employed to determine the global deformation parameters appearing in the displacement fields of general cross-ply, symmetric, and antisymmetric angle-ply laminates under thermal and hygroscopic loadings. Reddy’s layerwise theory is subsequently used to determine the local deformation parameters of various displacement fields. An elasticity solution is also developed in order to validate the efficiency and accuracy of the layerwise theory in predicting the interlaminar normal and shear stress distributions. Finally, various numerical results are presented for edge-effect problems of several cross-ply, symmetric, and antisymmetric angle-ply laminates subjected to uniform hygrothermal loads. All results indicate high stress gradients of interlaminar normal and shear stresses near the edges of laminates.