N.G.R. Iyengar

Natural frequencies of composite plates with random material properties using higher-order shear deformation theory

Composites are known to display a considerable amount of scatter in their material properties due to large number of parameters associated with the manufacturing and fabrication processes. In the present work, the material properties have been taken as random variables for accurate prediction of the system behavior. Higher order shear theory including rotatory inertia effects has been accounted for in the system dynamic equations. A first order perturbation technique has been employed to obtain the solution of the governing equations. An approach has been outlined for obtaining closed form expressions for the variances of eigen solutions. The effects of side to thickness ratio and variation in standard deviation of the material properties have been investigated for cross-ply symmetric and anti-symmetric laminates. The mean and standard deviations of the first five natural frequencies have been worked out for laminated rectangular plates with all edges simply supported. The higher order shear deformation theory results have been validated with Monte Carlo simulation results and compared with the results based on classical laminate and first order shear deformation theories.

Non-linear vibrations of simply supported rectangular cross-ply plates

A method of direct numerical integration of the frequency-ratio expression is proposed to study the non-linear free vibration behaviour of rectangular cross-ply laminates. The proposed method, even with single-term approximations for the admissible functions, yields results that agree very well with the existing perturbation solutions. Non-linear behaviour of the cross-ply laminates is also studied with the harmonic oscillations assumption, by using the conservation of energy and the modal equation. The results are found to be lower and upper bounds to those obtained from the direct numerical integration method. It is also observed that the arithmetic mean of the two solutions with the harmonic oscillations assumption matches very well with that of the direct numerical integration method. Non-linear vibration characteristics are obtained for several configurations of cross-ply plates. Results for orthotropic and isotropic plates are also obtained as special cases.

Optimum design of laminated composite plates with cutouts using a genetic algorithm

Optimum design of the laminated composite plate is attempted in the presence of elliptical cutouts. Orientation of the ellipse with respect to the reference axis, aspect ratio of the cutout, orientation of plies, thickness of plies and material of the plies are used as design parameters with a constraint on natural frequencies. Thus an investigation of the free vibrational response of composite plates with an elliptical cutout is studied, and some results presented. First-order shear deformation theory (FSDT) is used to account for the transverse shear stresses. A nine noded quadrilateral isoparametric element is used in the finite element formulation. A genetic algorithm (GA) is employed to locate the optimum. Numerical results are presented for square plates with simply supported and clamped edge conditions.

Response of composite plates with random material properties using FEM and Monte Carlo simulation

Composite materials have a large number of parameters associated with their manufacturing. It is not physically possible to control all these parameters, and hence variation in the material properties result. In this paper, for a better modeling of the material properties, these are treated as random variables. Static response characteristics of graphite/epoxy composite laminates are obtained with the help of Monte Carlo simulation and the Finite Element Method (FEM) for different boundary conditions, thickness ratio, aspect ratios and fiber orientations. The input material property mean and variance are assumed to be known. From the limited analytical study conducted it is observed that a single design curve can predict normalized characteristics for all the parameters considered.

Thermal Postbuckling Behavior of Laminated Composite Plates

Thermal buckling and postbuckling behavior of shear deformable laminated composite plates is investigated by employing a four-node rectangular C(sup 1) continuous finite element. The investigation reveals that the postbuckling path may not remain stable throughout. It is shown that secondary instabilities coupled with changes in the spatial deformation do take place from the postbuckling path. 15 refs.

Analysis of the Nonlinear Vibrations of Unsymmetrically Laminated Composite Beams

Large-amplitude free vibrations of unsymmetrically laminated beams using von Karman large deflection theory are investigated herein. One-dimensional Finite elements based on classical lamination theory, first-order shear-deformation theory, and higher-order shear-deformation theory having 8, 10, and 12 degrees of freedom per node, respectively, are developed.

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

Initial buckling of composite cylindrical panels with random material properties

Abstract Composites are known to display a considerable amount of scatter in their material properties due to a large number of parameters associated with their fabrication and manufacturing processes. In the present study, the material properties have been modeled as random variables for accurate prediction of the system behavior. Shear deformation effects have been incorporated in the governing equations. First-order perturbation technique has been employed to obtain the second-order buckling load statistics. The results have been presented for composite cylindrical panels with all edges simply supported. These results demonstrate the dependence of scatter in buckling loads on the basic random variables. The effects of side-to-thickness ratio, aspect ratio, curvature-to-side ratio and change in standard deviation of input random variables have been investigated for cross-ply symmetric and anti-symmetric laminates. The approach has been validated by a comparison of the results with those obtained with Monte Carlo simulation. The results for the mean buckling load with different shear deformation theories have also been compared with those available in the literature.

Buckling of antisymmetric cross- and angle-ply laminated plates

Abstract A system of three well-known equations of equilibrium governing the buckling response of arbitrarily laminated composite plates is reduced to a single eighth order partial differential equation in terms of a displacement function. This equation is then solved in closed form to predict the buckling response of antisymmetric cross- and angle-ply plates for different boundary conditions. The effect of various plate parameters including the effect of coupling between inplane extension and out of plane bending upon the buckling response of composite plates is discussed. The results are presented in nondimensional graphical form.

Stability analysis of laminated cylindrical panels with uncertain material properties

Abstract Composite materials experience larger uncertainties in their material properties compared to conventional materials due to a number of parameters involved in their fabrication and manufacturing processes. In the present study, the effect of uncertainty in the material properties on the elastic stability of laminated composite cylindrical panels is attempted. A C 0 finite element has been used for deriving the eigenvalue problem using higher-order shear deformation theory. The uncertain material properties are modeled as random variables. A mean-centered first-order perturbation technique is used to find the probabilistic characteristics of the buckling loads with different boundary conditions.