Antisymmetric Cross-ply Research Articles

Analytical Solutions for Bending of Clamped Layered Composite Plates Using a Higher-Order Theory

Analytical solutions are presented for the bending of clamped laminated plates using a higher-order shear deformation theory. Unlike the first-order shear deformation theory, the higher-order theory does not require a shear correction factor. The displacement field of the higher-order theory contains the same number of dependent variables as in the first-order shear deformation theory, and also accounts for the cubic variation of the in-plane displacements through the thickness. Closed-form solutions are not tractable for clamped composite plates due to the boundary conditions and anisotropy of the plate and hence approximate methods are required. In the present work, a method based on Lagrange multipliers is used to enforce the boundary conditions not satisfied by the assumed series. Results are presented for antisymmetric cross-ply and angle-ply plates to study the influence of anisotropy, aspect ratio, and loadings on the deflections and stresses of clamped plates.

Chaotic response of a composite plate

The chaotic response of a six-layered anti-symmetric cross-ply ( 0 ° 90 ° ) 3 rectangular plate with immovable edges is studied. The plate is assumed to be damped and acted upon by a harmonic force f 0 sin T. For a value of f 0 = 97, it is shown that chaos occurs.

Three-dimensional stability analysis of laminated anisotropic circular cylinders

Linear bifurcation stability of laminated anisotropic circular cylinders is investigated on the basis of three-dimensional elasticity using Biot's incremental deformation theory. A finite element code employing radial discretization is formulated for the calculations. By this approach, the laminate's thickness profile may be composed of an arbitrary number of bonded elastic anisotropic layers, each of which may have its own mechanical properties, thickness and initial stress state. Using a solution that is periodic axially and circumferentially in the variationally derived equilibrium equations yields an algebraic eigenvalue problem, where the critical (lowest) eigenvalue is sought. It represents the ratio of the buckling stress state to initial stress state and its associated eigenvector contains the radial distribution of the displacements. A parametric study on a series of regular symmetric and antisymmetric cross-ply and angle-ply laminated composite cylinders under axial compression and torsion was conducted, where the data can be used to assess the accuracy and range of validity of stability predictions based on shell theories. An example of the axial compression of a thick-walled laminated composite cylinder is presented to illustrate an instability phenomenon where internal and surface deformations are present.

Modal Interaction in the Response of Antisymmetric Cross-Ply Laminated Rectangular Plates

A higher-order shear-deformation theory is used to analyze the interaction of two modes in the response of thick laminated rectangular plates to transverse harmonic loads. The case of a two-to-one au toparametric resonance is considered. Four first-order ordinary differential equations describing the modula tion of the amplitudes and phases of the internally resonant modes are derived using the averaged Lagrangian when the higher mode is excited by a primary resonance. The fixed-point solutions are determined, and their stability is analyzed. It is shown that besides the single-mode solution, two-mode solutions exist for a certain range of parameters. It is further shown that, in the multimode case, the lower mode, which is indirectly excited through the internal resonance, may dominate the response. For a certain range of parameters, the fixed points lose stability via a Hopf bifurcation, thereby giving rise to limit-cycle solutions. It is shown that these limit cycles undergo a series of period-doubling bifurcations, culminating in chaos.

Improvement of mechanical properties of HIP aluminium alloy by extrusion : K. Hanada et al (University of Electro-Communication, Tsukuba Ibaraki, Japan.)

Metal matrix composites provide new materials with superior properties. They give high strength and stiffness. In this study, a stainless steel fiber reinforced aluminum metal matrix laminated simple supported plate is loaded transversely. Elasto-plastic stress analysis is carried out in the laminated plate by using finite element technique. The expansion of plastic zone and residual stresses are determined in the symmetric and/or antisymmetric cross-ply and angle-ply laminated plates for small deformations. Iteration numbers are chosen as 100, 150 and 200. The yield points in symmetric laminates are higher than those in antisymmetric laminates.

Thermoelastic analysis of laminated plates including transverse shear deformation effects

In this paper a discrete-layer shear deformation laminated plate theory is used to analyse steady-state thermal stresses in laminated plates. Both the in-plane displacements and the temperature rise are assumed to be piecewise linear across the thickness. By the assumption that the transverse shear strains across any two layers are linearly dependent on each other, the theory contains the same dependent variables as first-order shear deformation theory. The set of governing differential equations is of the twelfth order which does not depend on the number of layers. No shear correction factors are required. The thermal bending of simply supported, symmetric and antisymmetric cross-ply plates is calculated. Numerical results of the present theory for thermal stresses and deflections are compared with those obtained using the classical, first-order and higher-order shear deformation plate theories.

Vibration of clamped right triangular thin plates - Accurate simplified solutions

Numerical Results and Discussion The numerical applications are carried out for cross-ply spherical shells whose geometrical and material properties are the same for all layers. The transverse deflection presented in the figures is evaluated at (*i,jc2, f) = (0, b/2, ?). Zero initial conditions are assumed. The variations of center deflection with time for antisymmetric cross-ply (0/90) and symmetric cross-ply (0/90/0) laminated spherical caps are shown in Figs. 1 and 2, respectively, for various boundary conditions. It is interesting to note that for SSSS, SSCS, and SSCC boundary conditions the amplitudes are smaller for symmetric cross-ply than for antisymmetric cross-ply laminates, whereas for SSFF, SSFS, and SSFC the amplitudes are higher. Moreover, the first-order (FSDT) and the third-order (HSDT) theories predict almost the same response, whereas the classical theory (CST) differs both in amplitude and phase.

Vibration Analysis Of Laminated Plates Using A Refined Shear Deformation Theory

A previously published discrete-layer shear deformation theory is used to analyze free vibration of laminated plates. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first order shear deformation theory, but the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of simply supported symmetric and antisymmetric cross-ply plates is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.

Fracture Behavior of Continuous Alumina Fiber Reinforced Epoxy

This work investigates fracture behavior of a continuous alumina fiber (FP) reinforced epoxy under compression at two different temperatures. Effects of fiber orientation, stacking sequence, and temperature on failure mechanisms of the composite material are analyzed through a scanning electron microscope (SEM). Fiber orientation is found to affect the failure mechanisms of the FP/epoxy. While the failure of the 00 laminae is mainly caused by fiber breakage, that of the 90° laminae by sheared epoxy matrix. The [02/902]s laminates not only have the combined failure modes of the 00 and 900 laminae but also show fiber micro-buckling in the 0° plies and ply delamination at the interfaces of the 0° and 900 plies. Failure mechanisms are found to be different between the symmetric and antisymmetric crossply laminates. In addition, the composites fractured at 77 K display more fiber-matrix debonding, smoother fractured surfaces of fiber and matrix, and cleaner ply delamination at the interfaces of the 00 and 900 plies than the composites fractured at 295 K.

IMPROVED HIGH-ORDER THERMOELASTIC RESPONSE THEORY FOR ANALYZING THERMAL BENDING OF LAMINATED COMPOSITE PLATES

A new high-order laminated plate thermoelastic responses theory, which is based on a new mixed variational principle proposed by Reissner (1984) and accounts for transverse shear and transverse normal strains, is developed to study the thermoelastic behavior of a laminated composite plate. To this end, a zig-zag-shaped Co function and Legendre polynomials are introduced into the approximate displacement distributions across the plate thickness. The thickness variation of temperature is considered to be linear. The theory is examined by applying it to the thermal bending problem of cross-ply rectangular plates. The numerical results of central deflection and thickness variation of in-plane and transverse thermal stresses are obtained for symmetric and antisymmetric cross-ply plates.

Thermal post buckling behavior of rectangular antisymmetric cross-ply composite plates

The thermal post buckling behavior of simply-supported, antisymmetric cross-ply plates with immovable edges is investigated in this paper. For this purpose, a one term approximation for the inplane and transverse displacements is assumed and Rayleigh-Ritz method is used to obtain the equations of equilibrium. The question, whether the true thermal buckling (bifurcation buckling under thermal loads) exists for such plates is also addressed to. The conditions under which the thermal buckling in the classical sense occurs are derived. It is shown that nonlinear bending stiffness for such plates is direction dependent, because of an extra quadratic nonlinear term in addition to the usual cubic nonlinear term in the governing equilibrium equation. Results are presented for various plate configurations.

Bending analysis of laminated plates using a refined shear deformation theory

In this paper the refinement of a previously published discrete-layer shear deformation laminated plate theory by the assumption that the transverse shear strains across any two layers are linearly dependent on each other is briefly described. The theory contains the same dependent variables as first-order shear deformation theory, but the set of governing differential equations is of the twelfth order. No shear correction factors are required. Solutions for simply-supported symmetric and antisymmetric cross-ply plates are discussed. The numerical results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory gives a better estimate of the deflections and stresses even for fairly thick laminates. For laminates of the same thickness, it is shown that the solution accuracy improves as the number of layers increases.

Vibration of clamped moderately thick general cross-ply plates using a generalized Navier approach

A hitherto unavailable analytical solution to the free vibration problem of general cross-ply laminated rigidly clamped rectangular plates, incorporating first-order shear deformation, and rotatory and in-plane inertias into the formulation, is presented. A recently developed boundary continuous displacement-based generalized Navier solution technique is used to solve the five highly coupled linear second-order partial differential equations with constant coefficients, and the associated geometric boundary conditions. The assumed solution functions are in the form of double Fourier series, which satisfy the rigidly clamped boundary conditions a priori in a manner similar to the conventional Navier method. Convergence characteristics of the natural frequencies of both symmetric and antisymmetric cross-ply plates are numerically established. Other numerical results presented herein include (i) comparison with the corresponding available first-order shear deformation theory-based Galerkin and classical lamination theory-based boundary-discontinuous analytical solutions, and (ii) study of the effects of thickness and aspect ratio on the natural frequencies.

Nonlinear Analysis of Thick Antisymmetric Cross-Ply Laminated Plates in Cylindrical Bending

The large deflection analysis (in the von Karman sense) is used to assess the effects of transverse shear deformation and bending-extension coupling on the behavior of antisymmetrically laminated, cross-ply plates under cylindrical bending. Solutions are presented for uniformly loaded simply supported and clamped plates.

Non-linear forced vibrations of antisymmetric rectangular cross-ply plates

A method of direct numerical integration of the frequency/time period expression is proposed to study the non-linear forced/free vibration behaviour of rectangular, antisymmetric cross-ply plates. The presence of bending-extension coupling in such plates results in a cubic non-linear term in addition to a fourth power term in the energy balance equation. The existence of this term does not allow two real and opposite roots at a maximum amplitude position unlike in isotropic, orthotropic, symmetric cross-ply, square antisymmetric cross-ply and symmetric and antisymmetric angle-ply plates, but such an energy balance equation definitely has two real roots, which are unequal in magnitude and different in sign. The extensively used perturbation method fails to predict the response of such plates, depending on the severity of the bending-extension coupling. The proposed direct integration method, even with single-term approximations for in-plane and transverse displacements, yields consistently accurate results. Response curves for several configurations of antisymmetric, simply supported rectangular cross-ply plates are presented.

Large amplitude free vibration of simply supported antisymmetric cross-ply plates

The presence of bending-extension coupling in antisymmetric cross-ply plates results in the cubic nonlinear term in addition to the fourth-power term in the energy balance equation. A direct numerical integration method has been proposed to study the large amplitude free vibrations of such plates

Some observations on the large deflection bending of rectangular antisymmetric cross-ply plates

Large deflection bending analysis of antisymmetric rectangular cross-ply plates based on Von-Karman plate theory is investigated in this paper, with one-term approximation for the in-plane and transverse displacements, under sinusoidal loading. The presence of bending-stretching coupling in such plates results in an additional square nonlinear term which makes the solution (for example, displacements) load direction dependent, unlike isotropic, orthotropic, symmetric, square antisymmetric cross-ply and symmetric and antisymmetric angle-ply plates. The effect of this term on large deflection response, based on the Rayleigh-Ritz method is presented for various configurations and modular ratios of such plates. It is shown that the presence of this square term could alter the very nature of nonlinearity i.e. hardening or softening for certain values of the load parameter.

Non-linear bending of antisymmetric cross-ply plates

Non-linear bending of antisymmetric cross-ply plates

Non-linear bending of antisymmetric cross-ply plates

The bending of antisymmetric cross-ply plates, based on Von-Karman plate theory, is investigated in this paper with one term approximations for the in-plane and transverse displacements. Rayleigh-Ritz solutions are presented for the non-linear response of cross-ply laminates with various modular and aspect ratios and subjected to sinusoidal transverse loading.

Bending of cross-ply laminated clamped plates using lagrange multipliers

The application of the Lagrange multiplier method to the bending analysis of laminated cross-ply clamped plates is described. Transverse shear deformation effects are incorporated in the energy functional. Boundary conditions not satisfied by the assumed series expressions are enforced by Lagrange multipliers. A variety of results are presented for symmetric and antisymmetric cross-ply plates with clamped boundary conditions to demonstrate the effect of anisotropy, plate geometry and span-to-depth ratios on the deflections. Closed form solutions are not tractable for laminated clamped plates and the results of the present methodology can be used as a reference for other approximate solutions.