Antisymmetric Angle-ply Plates Research Articles

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.

Deflections and Stresses of Antisymmetric Angle-Ply Clamped Plates Under Transverse Loading

Closed-form solutions are not tractable for clamped composite plates due to the boundary conditions and anisotropy of the plate. In the present work, a method based on Lagrange multipliers is developed for the bending analysis of antisymmetric angle-ply clamped plates. The transverse shear flexibility is incorporated in the energy functional. Boundary conditions not satisfied by the assumed series are enforced using Lagrange multipliers. Results are presented to study the influence of shear deformation, anisotropy, aspect ratio and loadings on the deflections and stresses of clamped 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.

Dynamic stability of laminated composite plates by the finite element method

The dynamic stability of laminated composite plates due to periodic in-plane loads is investigated. The Galerkin finite element model, including the effects of transverse shear deformation and rotary inertia, is used to study the antisymmetric angle-ply plates subjected to the combination of a periodic bending stress and a periodic uniform compressive stress. The effects of various parameters and boundary conditions on dynamic stability are studied.

Response of laminated plates to non-stationary random excitation

The response of composite laminated plates subjected to non-stationary random excitation is determined. First-order shear deformation theory is used for the analysis of symmetric cross-ply and antisymmetric angle-ply plates. The time-dependent component of the forcing function is taken as a product of a well-defined, slowly varying envelope function, and a noise function, assumed to be white or narrow-band random excitation.

On boundary-discontinuous double Fourier series solution to a system of completely coupled P.D.E.'s

A heretofore unavailable boundary-discontinuous double Fourier series based approach for solution to a system of completely coupled linear second-order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions is presented. This method facilitates the selection of the unknown Fourier coefficients, contributing to the complete solution and also takes into account the possible discontinuities of the assumed solution functions and/or their first derivatives at the boundaries. Dirichlet and Neumann types of boundary conditions can be treated as two special cases. The method is applied to obtain solutions of the hitherto unsolved class of problems, pertaining to arbitrarily laminated anisotropic (constant)-shear-flexible doubly-curved shells of rectangular planform, with arbitrary admissible boundary conditions and subjected to general transverse loading. Such specific cases of lamination as anti-symmetric angle-ply, symmetric angle-ply and general cross-ply, such particular case of loading as uniformly distributed transverse load and such specific case of geometry as a rectangular plate, can be obtained as special cases of the above. In addition, this method is shown to reproduce the available boundary-continuous solutions for unsymmetric cross-ply plates and doubly-curved shells with SS3 type simply-supported boundary conditions and anti-symmetric angle-ply plates with SS2 type simply-supported boundary conditions.

Postbuckling response of antisymmetric angle-ply laminates to uniform temperature loading

The postbuckling behavior of antisymmetric angle-ply plates, resting on simple supports and subjected to a gradually increasing uniform temperature field is investigated. Stable equilibrium configurations are determined through a direct application of the principle of minimum potential energy. Since nonunique equilibrium states may exist, a method of incremental loading is employed to identify the particular state associated with a given thermal loading path. Numerical results for fiber-reinforced laminates illustrate the effects of ply orientation, number of layers and aspect ratio on the postbuckling behavior. The phenomena of secondary buckling is examined in detail.

LARGE DEFORMATION OF ANTISYMMETRIC ANGLE-PLY LAMINATES RESULTING FROM NONUNIFORM TEMPERATURE LOADINGS

A recently proposed incremental-loading procedure [1] is used to obtain approximate solutions for the moderately large deflections of antisymmetric angle-ply plates under nonuniform temperature fields. A parabolic in-plane variation and a linearly varying transverse distribution of temperature are considered. The analysis predicts the existence of a bifurcation along the thermal load-deflection path for certain laminate configurations and loadings. Results based on the large-deflection theory are compared with exact solutions to the classical small-deformation formulation for various fiber-reinforced laminates.

Dynamic instability of shear deformable antisymmetric angle-ply plates

The effect of shear deformation on dynamic instability of simply supported antisymmetric angle-ply rectangular plates is considered. The boundaries of the principal instability region are conveniently represented in the plane “non-dimensional excitation frequency squared-non-dimensional load amplitude”. The effects of the magnitude of the shear correction coefficients, number of layers, plate aspect ratio, and thickness-to-edge length ratio are illustrated in numerical examples.

Application of diverging motions to calculate loads for oscillating motions

ply composite plates. For these cases, the El/E2 ratio is varied while the aspect ratio is held constant. The results are in good agreement to those obtained by Noor as shown in Fig. 1. Figure 2 displays buckling loads of antisymmetric angle-ply plates with simply supported/clamped boundary conditions for different ply orientation angles 9. These are compared to those obtained by Sharma. As can be observed, the present formulation yields an upper bound to the elasticity model. However, the overall results are good and the formulation is much less cumbersome than a three-dimensional approach.

Initial flexural failure of square, simply supported, angle-ply plates

The Tsai-Hill stress failure criterion is combined with an exact equilibrium solution to analyse the initial flexural failure of square, simply supported, antisymmetric angle-ply plates subjected to either uniform or uniform, square patch loading at the plate centre. Dimensionless initial failure loads and associated plate centre deflections are presented for a range of angle-ply lay-ups in GFRP and CFRP plates.