B.N. Singh

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.

New Nonpolynomial Shear-Deformation Theories for Structural Behavior of Laminated-Composite and Sandwich Plates

In the present study, new nonpolynomial shear-deformation theories are proposed and implemented for structural responses of laminated-composite and sandwich plates. The theories assume nonlinear distribution of transverse shear stresses, and also satisfy the traction-free boundary conditions at the top and bottom layers of the laminates. The governing differential equations are derived for a generalized shear-deformation theory by implementing the dynamic version of principle of virtual work and calculus of variations. A generalized closed-form solution methodology of the Navier type is implemented to ensure the validity and efficiency of the present theories for bending, buckling, and free-vibration responses of the laminated-composite and sandwich plates. It is observed that the proposed formulation in conjunction with the solution methodology is capable of handling all existing five-degree-of-freedom-based shear-deformation theories. The comparison of results also shows that the adequate choice of shea...

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.

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.

Analysis of Laminated Sandwich Plates Based on an Improved Higher Order Zigzag Theory

A finite element model based on an improved higher order zigzag plate theory developed by the authors is refined in this study and applied to bending and vibration response of soft core sandwich plates. The theory satisfies interlayer transverse shear stress continuity including transverse shear stress free condition at the plate top and bottom surfaces and transverse normal compressibility of the core. The in-plane displacements vary cubically through the entire thickness, while transverse displacement is assumed to vary quadratically within the core. In order to have a better computational benefit, a C0 finite element formulation is adopted. This is refined through satisfaction of certain constrains variationally using a penalty function approach. The performance of the model is demonstrated by comparing the present results with 3D elasticity solutions and other available results.

THERMO-MECHANICAL BUCKLING ANALYSIS OF FINITE ELEMENT MODELED FUNCTIONALLY GRADED CERAMIC-METAL PLATES

In the present investigation, buckling analysis of functionally graded ceramic-metal (FGM) plates subjected to thermo-mechanical load is presented. The effective material properties of FGM plates are assumed to be temperature-dependent and vary in the thickness direction according to the power-law distribution of the volume fractions of the constituents. An improved higher-order shear deformation plate theory is employed to account for the transverse shear strains by maintaining stress-free top and bottom faces of the plate. An efficient C0 finite element is proposed for the model, and the variational approach is utilized to derive the fundamental equations for the FGM plates. Convergence and comparison studies have been performed to describe the efficiency of the present model. The numerical results are highlighted with different system parameters and boundary conditions.

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.

Thermo-mechanical induced vibration characteristics of shear deformable functionally graded ceramic—metal plates using finite element method

This paper deals with the thermomechanical-induced vibration characteristics of shear deformable functionally graded material (FGM) plates. Theoretical formulations are based on higher-order shear deformation theory with a significant improvement in the transverse displacement using finite-element method. The mechanical properties of the plate are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The temperature field is ascertained to be a uniform distribution over the plate surface and varied in the thickness direction only. The fundamental equations for FGM plates are derived using variational approach by considering traction-free boundary conditions on the top and bottom faces of the plate. A C 0 continuous isoparametric Lagrangian finite-element with 13 degrees of freedom (DOF) per node have been used to accomplish the results. Convergence and comparison studies have been performed for square plates to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index, and temperature rise with different boundary conditions. The results reveal that the temperature field and the gradient in the material properties have significant effect on the vibration characteristics of the FGM plates.

Static Response of Laminated Composite Plates Resting on Elastic Foundation with Uncertain System Properties

Virtually, in all structural systems, there are uncertainties in the system parameters because of real bounds on the quality control and modeling. This paper presents an investigation of the stochastic bending static response of laminated composite plates resting on elastic foundation with uncertain system parameters subjected to static distributed loading. The transverse shear effects have been included in the system equation using higher order shear deformation theory. The interaction between the plate and foundation is included in the formulation with a two-parameter Pasternak model. System parameters such as material properties and foundation stiffness parameters are modeled as independent random variables. A C0 finite element method in conjunction with mean centered first-order perturbation technique is outlined to obtain the second-order response statistics of the bending deflection of the plate supported on with and without elastic foundation. The approach has been validated with independent Monte Carlo simulation and other approaches.

Stochastic Response of Laminated Composite Shell Panel in Hygrothermal Environment

In this article, the effect of random system properties is accounted to estimate the free vibration of multilayered composite shell panel in hygrothermal environment, instead the majority of previous investigations assumed that the material properties are independent of temperature and moisture. Establishing margin on material properties for design, analysis, and conceptualizing the material is highly difficult and uncertain. To perturb that, a first-order perturbation technique is adopted to obtain the response statistics of the structure by obtaining the mean and variance of the random natural frequencies. The higher-order shear deformation theory with nine degrees of freedom (DOFs) per node with von-Karman sense of nonlinear kinematics is employed for generating basic formulation. The analysis is carried out by using quadratic C°eight-noded isoparametric element. The governing equation for free vibration of laminated composite panel is derived using variational principle, which is generalization of the principle of virtual displacement. The solution methodology is validated with published results. Mean and variance is obtained for different cross-ply of spherical and cylindrical laminates with different stacking sequence and boundary conditions.