Unsymmetric Composite Laminates Research Articles

Environmental effects on thermally induced multistability in unsymmetric composite laminates

The principles involved in the generation of thermal induced multistability in carbon fibre epoxy laminates have received much interest in the published literature. This work examines the effects of moisture absorption on the mechanical properties of these plates focussing on geometry and ‘snap-through’ loadings. Samples were monitored from a dry state until moisture equilibrium was achieved. It was observed that substantial changes in geometry and snap-through performance occurred as moisture content increased. As part of this work, a first order strain energy analysis was modified to incorporate a hygrothermal strain term to enable prediction of the laminate shape due to moisture content.

Distortion Simulation of Unsymmetrical Composite Laminates Using the Finite Element Analysis Method

Unsymmetric composite laminates were benefit to reducing the structure weight of some aircrafts. However, the cured unsymmetric laminates showed distortion at room temperature. Therefore, predicting the deformation before using the unsymmetrical composite is very important. In this study an attempt was made to predict the shapes of some unsymmetric cross-ply laminates using the finite element analysis (FEA). The bilinear shell-element was adopted in the process. Then the simulation results were compared with the experimental data. The studies we had performed showed that the theoretical calculation agreed well with the experimental results, the predicted shapes were similar to the real laminates, and the difference between the calculated maximum deflections and the experimental data were less than 5%. Hence the FEA method was suitable for predicting the warpage of unsymmetric laminates. The error analysis showed that the simulation results were very sensitive to the lamina thickness, 2 α and (T.

Numerical and Experimental Studies on Cured Shape of Thin Unsymmetric Carbon/Epoxy Laminates

An analytical model was established by means of Ritz method to calculate the cured shape of cross-ply unsymmetric composite laminates. A number of experiments of Carbon/Epoxy laminates were conducted. It was found in the experiment that the warped surface could be a multiple-value function, which should be studied further. The result of calculation correlates well with the experimental result except the regions very near the laminate edge. The conclusion is instructive to manufacture of composite laminates.

Cracks in Laminates Subjected to Concentrated Forces and Moments

The crack problems are important not only in macromechanics but also in micromechanics. Because of its importance a lot of analytical, numerical and experimental studies have been published in journals and books. Among them, the study of Green’s function attracts many researchers’ attention because analytically it may provide solutions for arbitrary loading through superposition and numerically it can be employed as the fundamental solutions for boundary element method and as the kernel functions of integral equations to consider crack interaction problems. Although a lot of Green’s functions have been presented in the literature, due to mathematical infeasibility most of them are restricted to two-dimensional problems and very few of them consider possible coupled stretching-bending analysis which may occur for general unsymmetric composite laminates subjected inplane and/or out-of-plane forces and moments. In this paper we consider an infinite composite laminate containing a traction-free crack subjected to concentrated forces and moments at an arbitrary point of the laminate. By employing Stroh-like formalism for the coupled stretching-bending analysis, recently the Green’s functions for the infinite laminates (without holes) were obtained in closed-form. Based upon the non-hole Green’s functions, through the use of analytical continuation method the Green’s functions for cracks are now obtained in explicit closed-form and are valid for the full fields. By proper differentiation, the associated stress intensity factors are also solved explicitly.

Stacking-sequence optimization using fractal branch-and-bound method for unsymmetrical laminates

The fractal branch-and-bound method has been developed by the authors for stacking-sequence optimizations of symmetric and balanced composite laminates comprise of two in-plane and two out-of-plane lamination parameters. Cylindrical structures such as tanks or pipes, however, are usually made from balanced laminates. In the present study, therefore, we focus on the stacking-sequence optimizations of unsymmetrical composite laminates. In the unsymmetrical laminates, nine lamination parameters including three coupling-lamination parameters exist, and its feasible design region of fractal pattern is unrevealed. The paper clarifies the feasible region in which the in-plane, out-of-plane and coupling lamination parameters create fractal patterns of tetrahedrons or tetradecahedrons. Using the fractal patterns of lamination parameters, the improved fractal branch-and-bound method is proposed for unsymmetrical laminates including coupling lamination parameters. This new method is applied to stacking-sequence optimization problems of maximization of buckling load of cylindrical laminated shells. As a result, the method is successfully applied, and a practical optimal stacking sequence is obtained with low computational cost.

Green’s Functions for Holes/Cracks in Laminates With Stretching-Bending Coupling

Consider an infinite composite laminate containing a traction-free elliptical hole subjected to concentrated forces and moments at an arbitrary point outside the hole. This problem for two-dimensional deformation has been solved analytically in the literature, while for the general unsymmetric composite laminates stretching and bending coupling may occur and due to the mathematical complexity the associated Green’s functions have never been found for complete loading cases. Recently, by employing Stroh-like formalism for coupled stretching-bending analysis, the Green’s functions for the infinite laminates (without holes) were obtained in closed-form. Based upon the nonhole Green’s functions, through the use of analytical continuation method the Green’s functions for holes are now obtained in explicit closed-form for complete loading cases and are valid for the full fields. The Green’s functions for cracks are then obtained by letting the minor axis of ellipse be zero. By proper differentiation, the stress resultants and moments along the hole boundary and the stress intensity factors of cracks are also solved explicitly. Like the Green’s functions for the infinite laminates, only the solutions associated with the in-plane concentrated forces f^1,f^2 and out-of-plane concentrated moments m^1,m^2 have exactly the same form as those of the corresponding two-dimensional problems. For the cases under the concentrated force f^3 and torsion m^3, new types of solutions are obtained.

SMA-induced snap-through of unsymmetric fiber-reinforced composite laminates

A theory is developed and experiments designed to study the concept of using shape memory alloy (SMA) wires to effect the snap-through of unsymmetric composite laminates. The concept is presented in the context of structural morphing, that is, a structure changing shape to adjust to changing conditions or to change operating characteristics. While the specific problem studied is a simplification, the overall concept is to potentially take advantage of structures which have multiple equilibrium configurations and expend power only to change the structure from one configuration to another rather than to continuously expend power to hold the structure in the changed configuration. The unsymmetric laminate could be the structure itself, or simply part of a structure. Specifically, a theory is presented which allows for the prediction of the moment levels needed to effect the snap-through event. The moment is generated by a force and support arrangement attached to the laminate. A heated SMA wire attached to the supports provides the force. The necessary SMA constitutive behavior and laminate mechanics are presented. To avoid dealing with the heat transfer aspects of the SMA wire, the theory is used to predict snap-through as a function of SMA wire temperature, which can be measured directly. The geometry and force level considerations of the experiment are discussed, and the results of testing four unsymmetric laminates are compared with predictions. Laminate strain levels vs. temperature and the snap-through temperatures are measured for the these laminates. Repeatability of the experimental results is generally good, and the predictions are in reasonable agreement with the measurements.

Stress resultants and moments around holes in unsymmetrical composite laminates subjected to remote uniform loading

Stress resultants and moments around the holes of infinite unsymmetrical composite laminates under remote uniform loading are analyzed using the complex potential approach developed by Chen and Shen [Mech. Res. Commun. 28 (4) (2001) 423; 28 (5) (2001) 513]. In the analysis, the authors’ previous work has been modified to determine the complex constants B k appeared in the complex potential functions of Chen and Shen [Mech. Res. Commun. 28 (5) (2001) 513]. Herein B k are the unknown quantities related to the remote loading conditions. The effect of bending extension coupling has been discussed for several laminates such as [0/90] T, [45/−45] T and [0/90/45/−45] nT . Results indicates that the coupling between bending and extension significantly affects the stresses around the hole of an unsymmetrical laminate containing one sub-laminate only. Such the effect rapidly decreases as the number of the sub-laminates increases. The results confirm the validity of the developed complex potential approach.

논문 : 비대칭 직교적층 복합재료 적층판의 성형시 및 성형후 광섬유 센서를 이용한 변형률 및 온도의 동시 모니터링

광섬유 브래그 격자/외부 패브리-페로 간섭 (FBG/EFPI) 센서를 이용하여 비대칭 적층판의 성형시 및 성형후 변형률과 온도를 동시에 모니터링 하였따. 본 논문에서는 광섬유 센서의 출력에 대한 변형률 및 온도의 관계를 수치적으로 유도하였으며 이를 통해 센서의 특성 행렬을 구하였다. 따라서 각각의 센서에 대해 특성 행렬을 구하기 위해 센서의 보정실험을 수행할 필요가 없다. 광원으로는 파장 이동 광섬유 레이저를 사용하였다. 두 개의 FBG/EFPI 센서를 Gr/Ep 비대칭 직교적층 복합적층판에 방향과 위치를 달리하여 삽입하고 오토클레이브 내에서 성형하는 동안 두 지점에서의 성형변형률과 온도를 실시간으로 모니터링 하였다. 또한 열챔버 내에서 제작된 적층판의 열변형률과 온도를 측정하였다. 이러한 실험들을 통해 복합재료의 효울적인 스마트 프로세싱에 대한 기초를 마련할 수 있으며 비대칭 직교적층 복합적층판의 열적 거동에 대해 알 수 있을 것이다. In this paper, we present the simulation monitoring of strain and temperature during and after the cure of unsymmetric composite laminate using fiber optic sensors. Fiber Bragg grating/extrinsic Fabry-Perot interferometric (FBG/EFPI) hybrid sensors are used to measure those measurands. The characteristic matrix of the sensor is analytically derived and measurements can be done without sensor calibration. A wavelength-swept fiber laser is utilised as a lighr source. Two FBG/EFPI sensors are embedded in a graphite/epoxy unsymmetric cross-ply composite laminate in different directions and different locations. We perform a real time monitoring of fabrication strains and temperatures at two points of the composite laminate during cure process in an autoclave. Also, the thermal strains and temperatures of the fabricated laminate are measured in a thermal chamber. Through these experiments, we can provide a basis for the efficient smart processing of composite and know the thermal behavior of unsymmetric cross-ply composite laminate.

General solution for an infinite unsymmetric composite laminate containing an elliptic hole

General solution for an infinite unsymmetric composite laminate containing an elliptic hole

Extension of lekhnitskii's complex potential approach to unsymmetric composite laminates

Extension of lekhnitskii's complex potential approach to unsymmetric composite laminates

Unsymmetric composite laminate with a discontinuity of the in-plane displacement or of the slope

A discontinuity of the in-plane displacements and slopes in an infinitely extended anisotropic laminate is considered under coupled bending and stretching. The laminate is supposed to the thin with arbitrary anisotropy of the constitutive plies. Using the classical 2-D theory of laminates and techniques of complex potentials, a family of exact solutions is obtained for the case of a static problem. As it follows from the analysis, the energy of dislocations does not depend on their orientation. A few numerical results for real laminates are considered.

A {3,2}-order bending theory for laminated composite and sandwich beams

A higher-order bending theory is derived for laminated composite and sandwich beams thus extending the recent {1,2}-order theory to include third-order axial effects without introducing additional kinematic variables. The present theory is of order {3,2} and includes both transverse shear and transverse normal deformations. A closed-form solution to the cylindrical bending problem is derived and compared with the corresponding exact elasticity solution. The numerical comparisons are focused on the most challenging material systems and beam aspect ratios which include moderate-to-thick unsymmetric composite and sandwich laminates. Advantages and limitations of the theory are discussed.

A Study on the Room-Temperature Curvature Shapes of Unsymmetric Laminates Including Slippage Effects

The room-temperature shapes of cured unsymmetric composite laminates have out-of-plane warping after autoclave processing. In addition, they exhibit two stable room-temperature configurations due to snap-through phenomena when the side length of laminates exceed a critical value. The cured shape of unsymmetric laminates are influenced by many factors. Experiments show that the effect of tool-plate cannot be ignored and has significant influence on the cured shape. This study examines slippage effects resulting from the interaction between the laminates and the tool-plate which are ignored in the previous researches. By introducing a dimensionless slippage coefficient and correlating the corresponding value with experimental results, the influence of processing parameters is investigated. Modeling is extended to predict curvatures of general lamination layup configurations.

Vibratory characteristics of general laminates

Abstract This paper presents Part I of investigations of free flexural vibration of multi-layered symmetric and unsymmetric composite laminates with symmetric trapezoidal planform of arbitrary combinations of edge conditions. The Ritz procedure withpb−2shape functions as the admissible functions is used to arrive at the governing eivenvalue equation. The set ofpb−2shape functions is intrinsically a product of a class of orthogonally generated two-dimensional polynomial functions and a basic function which ensures the satisfaction of geometric boundary conditions at the outset. Different boundary conditions, with various combinations of in-plane constraints, are considered. The effects of wide ranges of chord ratios, angles of fibre orientation and stacking sequences on the vibration response are investigated. With the aim of increasing the existing database, sets of previously unavailable vibration frequencies and mode shapes are presented as benchmarks for future reference.

Advanced calculation of the room-temperature shapes of thin unsymmetric composite laminates

It is well known that the room-temperature shapes of unsymmetric laminates do not always conform to the predictions of classical lamination theory. Instead of being saddle shaped, as classical lamination theory predicts, the room-temperature shapes of unsymmetrically laminated composites are often cylindrical in nature. In addition, a second cylindrical shape can sometimes be obtained from the first by a simple snap-through action. Hyer developed for the class of all square unsymmetric cross-ply laminates which can be fabricated from four layers i.e., [ 0 3 90 ], [0 2/90/0], [0/90/0/90], [ 0 2 90 2 ], an extended classical lamination theory to predict whether these laminates have a saddle shape or one or two cylindrical shapes. The Finite Element Analysis (FEA) has just recently been used for the calculation of the room-temperature shapes of unsymmetric laminates, because more sophisticated finite element codes are now available and the calculations can be made in an acceptable time. The hope is to get more accurate results for the shape and the stresses and forces that occur during the snap through action. These results are needed for the development of active deformable composite structures based on unsymmetric laminates and incorporated shape memory alloy wires [Schlecht M. & Schulte K., Development of active deformable structures due to thermal residual stresses and incorporating shape memory alloys. In Proc. ECCM Smart Composites Workshop, ECCM6, Bordeaux, 1993, pp. 20–115.] Results for different lay-ups are presented and compared.

Different Numerical Techniques for the Estimation of Multiaxial Stresses in Symmetric/Unsymmetric Composite and Sandwich Beams with Refined Theories

A set of simple but efficient and accurate higher-order displacement models are used to evaluate the multiaxial stress behavior in symmetric and unsymmetric composite and sandwich laminates. These theories incorporate a more realistic non-linear variation of displacements through the beam thickness, thus eliminating the use of shear correction coefficient(s). Constitutive relations are used to evaluate inplane stresses. The computer program developed incorporates the realistic prediction of transverse stresses from equilibrium equations. The integration of the equilibrium equations is attempted through direct integration method, forward and central direct finite difference technique and a new approach called an exact curve fitting method. The versatility of the present higher-order theories is demonstrated by comparing the results with the available elasticity and other closed-form solutions for cross-ply and sandwich laminates. The results show that the exact curve fitting method gives good estimates of multiaxial stresses compared to finite difference and direct integration methods.

Environmental Effects on Unsymmetric Composite Laminates

In order to take full advantage of the tailorability of composite materials, the response of unsymmetric composite laminates is studied in an integrated analytical/ex perimental program. The laminates tested include a symmetric and an unsymmetric layup, [0 2/452] s and [04/454] I , constructed of the IM7/977-2 graphite epoxy material system pro duced by Fiberite. The test conditions simulated mclude both ambient and hot/wet condi tions in addition to tension and torsion. A quasi three-dimensional finite element program is used to evaluate the stress-strain response of these laminates. These responses are com pared with experimental observations.