Arbitrary Lay-ups Research Articles

Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory

Skew fibre-reinforced composite laminates are important structural elements in modern engineering structures, particularly in aero-space industry. Natural frequencies of these skew laminates are of primary significance to structural designers. As far as the author's knowledge is concerned the references on this topic is very limited. Within the context of the first-order shear deformation plate theory (SDPT) [Reissner, The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. ASME, 12, 69–76 (1945); Mindlin, influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech. ASME, 12(18), 1031–1036 (1951).] this paper presents a B-spline Rayleigh-Ritz method (RRM) for free vibration analysis of skew fibre-reinforced composite laminates which may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy. In this approach the displacement field consists of the three mid-surface translational displacements u, v and w and the two through-thickness shear strains γ xz and γ yz instead of the two rotations ψ x and ψ y in order to avoid the shear locking phenomenon. Various numerical applications are presented and the method is shown to be accurate and efficient.

Buckling of thin skew fibre-reinforced composite laminates

This paper presents a B-spline Rayleigh-Ritz method (RRM) based on classical plate theory (CPT) for buckling analysis of thin skew fibre-reinforced composite laminates, which are important structural elements in modern engineering structures, particularly in the aerospace industry. The laminates considered may have arbitrary lay-ups, admitting the possibility of coupling between in plane and out-of-plane behaviour and general anisotropy. Various numerical applications are conducted and comparisons are made wherever possible. All the results are tabulated in a manner of full convergence studies and could be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for similar problems.

VIBRATION OF THIN SKEW FIBRE REINFORCED COMPOSITE LAMINATES

Skew fibre reinforced composite laminates are important structural elements in modern engineering structures, particularly in the aerospace industry. The natural frequencies of these skew laminates are of primary significance to structural designers. As far as the author's knowledge is concerned, the references on this topic are very limited. In this paper a B-spline Rayleigh-Ritz method (RRM) is presented for free vibration analysis of thin skew fibre reinforced composite laminates which may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy. Various numerical applications are presented, and the method is shown to be accurate and efficient.

Stresses and Deformations Induced during Manufacturing. Part I: Theoretical Analysis of Composite Cylinders and Shells

Composite cylinders and cylindrical shells are important structural members. It has been observed that during the manufacture of these components, residual stresses build up. In composite cylinders, the state of residual stresses may lead to defects such as micro-cracking, fibre waviness, delamination, and wrinkling, which might degrade the final mechanical performance of the cylinders. In the case of cylindrical segments, the residual stresses also lead to a reduction in the enclosed angle where the out-of-plane contraction is higher than the in-plane contraction. This phenomenon (of the reduction in the enclosed angle) is referred to as spring-in. In this paper, a simple mechanics-based model is developed using modified shell theory that predicts the degree of spring-in in anisotropic cylindrical shells and determines the residual stresses, strains and displacements in both anisotropic laminated composite cylinders and shells with arbitrary lay-ups subjected to random temperature gradients. The model accounts for the resin shrinkage occurring during curing and also includes the effect of moisture gradients. The effects of various factors such as geometry of the component, the ply stacking sequence, the part thickness and the tool radius are examined. The accuracy of the present analysis is investigated by comparing predicted results with previously published results.

Buckling analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory

This paper presents a B-spline Rayleigh-Ritz method (RRM) based on first-order shear deformation plate theory 1,2 (SDPT) for buckling analysis of skew fibre-reinforced composite laminates which are important structural elements in modern engineering structures, particularly in the aerospace industry. The laminates considered may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy. Various numerical applications are conducted and the method is proved to be accurate and efficient. It is observed that the effect of through-thickness shear deformation is very large for moderately thick skew laminates and increases with the increase of skew angles. The analysis based on the classical plate theory (CPT) could grossly overestimate critical buckling stresses. As far as the author's knowledge is concerned it seems that there is no paper in the open literature, up to now, dealing with the buckling problems of skew fibre-reinforced composite laminates based on SDPT. Therefore, all the present results are presented in a manner of full convergence studies and it is hoped that they could be useful for designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and software for similar problems.

Higher-order shear deformation theory for thin-walled composite beams

A higher-order shear deformation theory for the static and dynamic analysis of thin-walled composite beams of arbitrary lay-ups and cross sections is presented. The method is applicable to beams of open as well as closed cross sections. The formulation includes Euler-Bernoulli and Timoshenko theories as subsets. The bendingand torsion-related warping functions are derived in closed form. The method is validated by comparison with experimental and analytical results for static deflections of composite beams with symmetric and antisymmetric lay-ups. Comparison with experimental results for the vibration of beams exhibiting bending torsion coupling shows that the present method gives better correlations. The significance of the higher-order theory is brought out by validating the results of the analyses against results from other theoretical methods. The results show the importance of the lay-up sequence on the shear lag in thin-walled composite beams.

On Residual Stress Induced Distortions during Fabrication of Composite Shells

Channel or angle components are important structural members. It has been observed that during the manufacture of these components, residual stresses build up. The state of residual stress in these components leads to a reduction in the enclosed angle where the out-of-plane contraction is higher than the in-plane contraction. This phenomenon (of the reduction in the enclosed angle) is referred to as spring-in. The residual stresses, in addition, may lead to defects such as micro-cracking, delamination, etc. The degree of spring-in and the residual stresses may be estimated by analysing the curved portions of these structural components as sectors of circular cylindrical tubes (see Figure 1). In this paper, a simple mechanics-based model is developed using modified shell theory that predicts the degree of spring-in and determines the stresses and strains in cylindrical segments with arbitrary lay-ups subjected to random temperature gradients. The model accounts for the resin shrinkage occurring during curing and also includes the effect of moisture gradients. The accuracy of the present analysis is investigated by comparing predicted results with previously published results.

Static shear correction factor for laminated rectangular beams

Most practical analyses of laminated composite beams, particularly rectangular sections used in civil structures, are based on first order shear deformation theories (FSDT), which generally require shear correction factors to account for shear stiffness and transverse shear stress. Using an energy equivalence principle, a general expression for the shear correction factor of laminated rectangular beams with arbitrary lay-up configurations is derived in this paper. A convenient algebraic form of the solution is presented and validated with existing results for composite beams and plates. An example is given to illustrate the use of the present formulation, and a parametric study is conducted to evaluate the effect of number of layers, elastic moduli ratio, and fiber-angle orientation on the shear correction factor for various laminates.

Effect of transverse shear on aeroelastic stability of a composite rotor blade

A formulation, which considers the effects of transverse shear flexibility, torsion warping, and two dimensional in-plane behavior, is extended to analyze arbitrary lay-up geometry including antisymmetric configuration. Numerical simulations are performed for a specific antisymmetric configuration to identify the transverse shear behavior on the aeroelastic stability of composite rotor

Spline finite strip analysis of the buckling and vibration of rectangular composite laminated plates

A spline finite strip capability is presented for predicting the buckling stresses and natural frequencies of rectangular laminated plates. The plates may have arbitrary lay-ups and general boundary conditions. The spline finite strip method is first developed in the context of first-order shear deformation plate theory and then, by reduction, the method is also developed in the context of classical plate theory. In both approaches the superstrip concept is incorporated into the solution procedure. A considerable range of types of application is described and it is demonstrated that the spline finite strip method is versatile, with good convergence characteristics and accuracy. In these applications, frequent comparison is made with the results of other approaches which comprise a spline Rayleigh-Ritz method, a finite element method, an analytical Rayleigh-Ritz method and a semi-analytical finite strip method.

The use of ‘C’-shaped specimens to investigate the interlaminar fracture of woven composite laminates

‘C’-shaped test specimens have been used to find the interlaminar strength of woven carbon/epoxy composite laminates in tension and in combined tension with minor transverse tractions. An analytical solution for the stress distribution within the “C” specimen, of arbitrary lay-up, is developed to permit a rigorous interpretation of the results, which confirm that the presence of relatively minor through-thickness stresses will have a profound influence on the strength of the component.

Modeling of the electromechanical performance of piezoelectric laminated microactuators

Piezoelectric microactuators may be considered as multilayer laminated composites consisting of alternating layers of piezoelectric and non-piezoelectric materials. A generalized analytical formulation of mechanical deformations as a function of applied electric field is derived for an arbitrary lay-up of such laminates. Based on the generalized theory developed, specific formulae for the electromechanical performance of two cantilever microactuator lay-up geometries. including a single piezo/elastic laminate and a bimorph, are derived. In the modeling of the electromechanical performance of piezoelectric microactuators, the present model incorporates both d211 and d222. Furthermore, the elastic properties of both the piezoelectric and the elastic materials have been considered. The developed model is evaluated based on a comparison with results from experiment.

Free vibration of generally-laminated, shear-deformable, composite rectangular plates using a spline Rayleigh-Ritz method

A Rayleigh-Ritz method is presented for predicting the natural frequencies of flat rectangular laminates which can have arbitrary lay-up. The effects of through-thickness shear deformation are included in the analysis. The displacement field utilises B-spline functions in what has been referred to in earlier work as a B k, k−1 -spline Rayleigh-Ritz method and the approach is versatile in the specification of boundary conditions. The results of a number of applications are presented in the form of studies showing the convergence of frequency values with increase in the number of spline sections used. The analysis procedure is seen to have good convergence characteristics when dealing with laminates of thin and thick geometry.

An analytic model for thermoelastic properties of composite laminates containing transverse matrix cracks

An analytical model for the prediction of the thermoelastic properties of composite laminates containing matrix cracks is presented. In particular, transverse matrix cracks with their crack surfaces parallel to the fibre direction and perpendicular to the laminate plane are treated. Two- and three-dimensional laminates of arbitrary layup configurations are covered by the model. The presented expressions for stiffnesses, thermal expansion coefficients, strain contributions from release of residual stresses and local average ply stresses and strains do solely contain known ply property data and matrix crack densities. The key to the model is the judicious use of a known analytical solution for a row of cracks in an infinite isotropic medium. The model has been verified against numerically determined stiffnesses, thermal expansion coefficients and local average ply stresses for matrix cracked angle-ply and cross-ply laminates. Comparisons to experimental data for cross-ply laminates are also presented. It is shown that the present model to a very good accuracy can predict thermoelastic properties of matrix cracked composite laminates at varying matrix crack densities and layup configurations.

Numerical Verification of a Procedure for Calculation of Elastic Constants in Microcracking Composite Laminates

In two recent papers Gudmundson and Östlund have presented a simple to use theory for calculation of reduced thermoelastic constants in composite laminates with matrix cracks. The theory is valid for two- and three-dimensional laminates of arbitrary layups and is asymptotically exact for dilute and infinite microcrark densities. Further more, the theory is based solely on ply property data and matrix crack densities. No ex perimentally determined or unknown theoretical parameters are required. The theory pre dicts changes in all coefficients of the elastic stiffness and thermal expansion coefficient tensors. In previous papers the accuracy of the present theory has been investigated for cross ply laminates by comparisons to experimental results from the literature and two-dimensional finite element calculations. However, in order to become a powerful tool in the analysis of cracked composite laminates the theory must be verified at intermediate crack densities also for angle ply laminates. Unfortunately no useful experimental results for such lami nates have been found in the literature and numerical methods must be considered for the verification. In the present paper the approximate theory is compared with three- dimensional finite element calculations of cracked thick [⊖, - ⊖ ] M glass fiber reinforced epoxy laminates for a wide range of different matrix crack densities. The finite element calculations can be considered as exact for all crack densities within the present formula tion, and errors are due only to the numerical algorithm. It is found that the dilute theory in combination with the theory for infinite crack densities to a surprisingly good accuracy cover all ranges of crack densities.

Cured Shape of Unsymmetric Laminates with Arbitrary Lay-Up Angles

The warping analysis of the general unsymmetric laminates with arbitrary lay-up angles is still not fully understood whereas the cross-ply laminates have been characterized well. This paper presents the formulation that treats the curvatures and prin cipal direction of curvature of the cured shape in unsymmetrically laminated composites. The effect of spatial dependence of in-place strains on curvatures is significant near the bifurcation point in the case of laminates having the stacking arrangement in which snap- through phenomenon occurs. It is shown that the principal direction of curvature calculated from classical lamination theory agrees with this theory in the limited range of length-to-thickness ratios of laminate. Curvatures and principal direction of curvature ac cording to the length-to-thickness ratios, number of layers, and lay-up angles of the lami nate are presented.

Prediction of thermoelastic properties of composite laminates with matrix cracks

A theory is presented for the determination of changes in the elastic compliance tensor and the thermal expansion coefficients due to matrix cracking. Effects of residual stresses are taken into account. The theory is valid for two- or three-dimensional laminates of arbitrary lay-ups and is asymptotically exact for dilute micro-crack densities. For large micro-crack densities an alternative model is described which is asymptotically exact for large crack densities. Combined, the two models cover to a good approximation the whole range of micro-crack densities. The theory is applied to a micro-cracking cross-ply GFRP laminate for which the stress/strain curve is calculated. Data are also presented for changes in thermomechanical properties of angle ply laminates as functions of the lay-up angle.

On the influence of ply-angle on damping and modulus of elasticity of a metal-matrix composite

The central objective of the classical laminate theory is topredict the properties of a laminate having an arbitrary lay-up, taking as its input themeasured properties of an individual lamina. Whereas a fair amount of work has been done concerning the prediction of the laminate stiffness, relatively little attention has been paid to the prediction of laminate damping. A recent model by Ni and Adams[1] fills this gap. The model is not exact and, of necessity, is based on some simplifying assumptions. The objective of this paper is to compare the predictions of their model with the results of a careful and detailed experimental investigation of the problem as it concerns metal-matrix composites. Flexural modulus and flexural damping of a continuous graphite/ aluminum composite of [±θ]s lay-up were measured forθ = 0, 15, 30, 45, 60, 75, and 90 deg. These were compared with the predictions of a slightly modified form of the Ni and Adams model; the model was modified to include theɛy,σy, andτxy terms which were ignored in the earlier work, where (x, y, z) is the laminate coordinate system. Excellent agreement between the theory and experimental results was observed.

Fabrication of birefringent anisotropic model materials

Widely different techniques have been employed in the fabrication of transparent, birefringent, anisotropic model materials. Some of the techniques reported in the technical literature are briefly reviewed. A simple method of fabricating large plates of arbitrary layup is described.