D. Yadav

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.

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.

Non-linear free vibration of laminated composite plate with random material properties

Abstract Composite laminates are widely used in construction of mechanical, aerospace, marine and automotive structure. These structures exhibit inherent random dispersion in material properties, as absolute control of production process is neither feasible nor economical. Some composite structures are subjected to large amplitude vibration during their working life that may lead to non-linearity in the response. The present paper analyses the effect of material parameter dispersion on the large amplitude free vibration of especially orthotropic laminated composite plates. The basic formulation of the problem has been developed based on the classical laminate theory and Von-Karman non-linear strain–displacement relation. The system equations have been obtained by using Hamiltons principle and the solution has been found by term wise series integration. Perturbation technique has been used to obtain the second order response statistics. Typical results have been presented for a plate with all edges simply supported. Effects of side-to-thickness ratio, aspect ratio, oscillation amplitude and mode shape along with change in standard deviation of material properties have been investigated for cross-ply symmetric and antisymmetric laminates.

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.

Non-linear response statistics of composite laminates with random material properties under random loading

Abstract Laminated composite plates find extensive use in many engineering applications. Some of these incorporate large deflections that may not be in the linear range. The external loading may be random in nature. The laminate material properties show an inherent dispersion around a mean value. In this paper the static response of laminated composite flat plates to transverse random loading has been studied. The material properties have been taken as random variables for accurate prediction of the system behaviour. The basic formulation of the problem has been developed based on the classical laminate theory and the Von-Karman non-linear strain–displacement relationship. A first order perturbation technique has been used to obtain the second order response statistics. Typical results have been presented for a plate with all edges simply supported. A comparison has been drawn with Monte Carlo simulation results for validation of the proposed approach. The effects of side-to-thickness ratio, aspect ratio and change in standard deviation of input random variables have been investigated for cross-ply symmetric and anti-symmetric laminates.

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.

Buckling Of Laminated Plates with Random Material Characteristics

This paper models the effect of material parameter randomness on the initial buckling load of rectangular, specially orthotropic, composite laminates. The basic formulation for stability analysis is based on classical laminate theory. A perturbation technique is used to obtain the solution of the governing equation. The effects of aspect ratio and change in standard deviation of the input parameters have been investigated for several laminate configurations. The solution has also been checked with the help of Monte Carlo simulation.

Free vibration of composite cylindrical panels with random material properties

Virtually in all structural systems, and in particular composites, there are uncertainties in the system parameters because of practical bounds on the quality control. In the present work the effect of variations in the mechanical properties of laminated composite cylindrical panels on its natural frequency has been obtained by modeling these as random variables. The transverse shear and rotatory inertia effects have been included in the governing equations. A perturbation approach is presented to obtain the mean and variance of the random natural frequencies. The effects of thickness ratios, edge support conditions and standard deviation of material properties on response of shallow square panels have been investigated. Results have been obtained by employing the finite element method. The approach has been validated by comparison of results with other approaches.

Free vibration of composite circular cylindrical shells with random material properties. Part I: General theory

Abstract Composites exhibit inherent random dispersions in material properties. Ignoring this variation during modelling may lead to inaccuracies in structural analysis and would result in erroneous design. Part I presents a general approach for free vibration analysis of composite circular cylindrical shells with the material properties having a random scatter when the random part is small compared with the mean value — a condition commonly met by most engineering materials. An outline has been described for development of the characteristic equation for the random eigen values. First order perturbation has been adopted to split up the characteristic equation and expressions for the mean and the variance of the natural frequencies and mode shapes have been obtained for the shell. Part II presents applications of this scheme to some specific problems.

Buckling of composite circular cylindrical shells with random material properties

Composite materials exhibit a scatter in their properties. This is generally ignored in conventional structural analysis leading to results that may be non-conservative. The present study discusses the critical buckling analysis for circular cylindrical shells of laminated composites incorporating the effects of randomness in the material properties. A perturbation approach has been employed to develop expressions for the mean and variance of the critical buckling load in terms of material property statistics. Working of the approach has been illustrated with an example.