Random System Properties Research Articles

Buckling and Post-Buckling Response of Laminated Composite Plate with Random System Properties

This article addresses the buckling and post-buckling stochastic analysis of a laminated composite plate having random system properties. The transverse shear effects have been included in the system equation in the framework of higher order shear deformation theory. The analysis uses Green Lagrange nonlinear strain displacement equations to model geometric nonlinearity. Direct iteration approach is used to handle deterministic geometric nonlinearity and perturbation approach is presented to handle the randomness in the system properties. Mean and variance of the random buckling and post-buckling strength have been obtained by employing a C 0 isoparametric nonlinear finite element model. Comparisons with the published results show the accuracy of the proposed probabilistic procedure. Results covering various features are presented for a laminated composite plate with different boundary conditions.

Stochastic First-Ply Failure Analysis of Laminated Composite Plates under in Plane Tensile Loading

The present work deals with second order statistics of first-ply failure response of geometrically nonlinear laminated composite plate subjected to in-plane tensile loading with random system properties. System properties such as the material properties and lamina plate thickness are modeled as independent random variables.The mathematical formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear kinematics. An efficient C0 nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is extended successfully and applied for failure problem in random environment and is employed to evaluate the dimensionless mean failure load and variance of failure index by modeling the system properties as basic random variables using Tsai-Wu and Hoffman failure criteria.Typical numerical results are presented to examine the effect of amplitude ratios, boundary conditions, lamination schemes with random system properties for different failure criterion.The results obtained using present solution approach is validated with the results available in the literatures.

Thermomechanical Elastic Post-Buckling of Functionally Graded Materials Plate with Random System Properties

This paper presents the stochastic post-buckling response of elastically supported FGM plate with random system properties subjected to uniform and nonuniform temperature change with temperature-dependent and -independent material properties. The FGMs plate is supported with two parameters of Pasternak foundation with Winkler cubic nonlinearity. The basic formulation is based on higher-order shear deformation theory (HSDT) with von-Karman nonlinearity using modified C0 continuity. A direct iterative-based nonlinear finite element method combined with first-order perturbation technique is used to compute the second-order statistics (mean and coefficient of variation) of post-buckling response of FGM plates.

Geometrically Nonlinear Free Vibration of Laminated Composite Plate Embedded With Piezoelectric Layers Having Uncertain Material Properties

In this paper, the nonlinear free vibration stochastic characteristic of a smart laminated composite plate having random system properties is presented. The transverse shear effects have been included in the system equation in the frame work of higher order shear deformation theory. The analysis uses the Green-Lagrange nonlinear strain displacement relationship to model geometric nonlinearity. The direct iteration approach is used to handle deterministic geometric nonlinearity, and the perturbation approach is employed to handle the randomness in the system properties. Mean and variance of the random natural frequencies have been obtained by employing a C0 isoparametric nonlinear finite element model. Comparisons with the published results show the accuracy of the proposed procedure. A few results covering various features have been presented for a laminated composite plate with different boundary conditions.

Stochastic hygrothermoelectromechanical loaded post buckling analysis of piezoelectric laminated cylindrical shell panel

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient C0 nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

Hygrothermoelastic Buckling Response of Laminated Composite Plates with Random System Properties: Macromechanical and Micromechanical Model

AbstractThe paper deals with the effect of moisture and temperature on the buckling response of a laminated composite plate subjected to hygrothermomechanical loadings. Mechanical loading consists of uniaxial, biaxial, and shear. The distribution of temperature and moisture on the surface is considered to be uniform. The degradation in material properties due to moisture and temperature is taken into account using a micromechanical model. The mathematical formulation is based on higher order shear deformation theory and von Karman’s nonlinear kinematics. A C0 finite-element method based on higher-order shear deformation plate theory is used for deriving the standard Eigenvalue problem. A Taylor series based mean-centered first-order perturbation technique is used to find out the second-order statistics of the hygrothermal buckling loads. The effects of temperature rise, moisture concentration, fiber-volume fraction, and plate parameters on buckling response of the plate are presented.

Nonlinear Flexural Response of Laminated Composite Plates on a Nonlinear Elastic Foundation with Uncertain System Properties under Lateral Pressure and Hygrothermal Loading: Micromechanical Model

This paper investigates the stochastic nonlinear flexural response of laminated composite plates resting on a two-parameter Pasternak elastic foundation with Winkler cubic nonlinearity and random system properties subjected to transverse uniform lateral pressure and hygrothermal loading. System properties, such as the lamina material properties, coefficients of thermal expansion, coefficients of hygroscopic expansion, and lateral load, are modeled as basic random variables using a micromechanical model. A higher-order shear deformation theory in the von Kármán sense is used to model the system behavior of the laminated plate. A direct iterative-based C0 nonlinear FEM, in conjunction with the first-order perturbation technique previously developed by the authors, is extended for the hygrothermal problem to obtain the second-order response statistics, i.e., the mean and variance of the nonlinear transverse deflection of the plate. Typical numerical results for the second-order statistics of the nonlinear transverse central deflection of composite plates subjected to uniform temperature and moisture distribution over the plate surface and through the plate thickness are obtained for various combinations of foundation parameters, uniform lateral pressures, staking sequences, volume fraction, aspect ratio, plate thickness ratio, and boundary conditions under environmental conditions. The approach has been compared with those available in the literature and an independent Monte Carlo simulation (MCS).

STOCHASTIC THERMAL POST-BUCKLING RESPONSE OF LAMINATED COMPOSITE CYLINDRICAL SHELL PANEL WITH SYSTEM RANDOMNESS

The effect of random system properties on thermal post-buckling temperature of laminated composite cylindrical shell panel with temperature independent (TID) and dependent (TD) material properties subjected to uniform temperature distribution is examined in this study. System properties such as material properties, thermal expansion coefficients and lamina plate thickness are modeled as independent basic random variables. The basic formulation is based on higher-order shear deformation (HSDT) theory with von-Karman nonlinearity using modified C0 continuty. A direct iterative-based C0 nonlinear finite element method (FEM) combined with Taylor series-based mean-centered first-order perturbation technique (FOPT) developed by the authors for composite plate is extended for shell panel with reasonable accuracy to compute second-order statistics of post-buckling temperature of cylindrical shell panel. Typical numerical results for second order statistics (mean and coefficient of variance) of thermal post-buckling temperature of laminated cylindrical shell panel are obtained through numerical examples for various support conditions, amplitude ratios, shell thickness ratios, aspect ratios, lamination lay-up sequences, curvature to length ratios, types of material properties with the effect of random system parameters. The performance of outlined approach has been validated with those results available in the literatures and independent MCS.

Stochastic nonlinear bending response of functionally graded material plate with random system properties in thermal environment

This study deals with the stochastic nonlinear bending response of functionally graded materials (FGMs) plate with uncertain system properties subjected to transverse uniformly distributed load in thermal environments. The system properties such as material properties of each constituent’s material, volume fraction index and transverse load are taken as independent random input variables. The material properties are assumed to be temperature independent (TID) and temperature dependent (TD). The basic formulation is based on higher order shear deformation theory with von-Karman nonlinear strain kinematics using modified C0 continuity. A direct iterative based nonlinear finite element method in conjunction with first-order perturbation technique developed by last two authors for the composite plate is extended for the FGM plate to compute the second order statistics (mean and standard deviation) of the nonlinear bending response of the FGM plates. Effects of TD, TID material properties, aspect ratios, volume fraction index and boundary conditions, uniform temperature and non-uniform temperature distribution on the nonlinear bending are presented in detail through parametric studies. The present outlined approach has been validated with the results available in the literature and independent Monte Carlo simulation.

Hygrothermally induced buckling analysis of elastically supported laminated composite plates with random system properties

The article presents hygrothermally induced buckling of geometrically linear laminated composite plates resting on two parameters Pasternak elastic foundation subjected to moisture and temperature-independent and -dependent material properties with random system properties. System properties such as elastic moduli, shear moduli of the constituent materials, hygroscopic contraction coefficients, thermal expansion coefficients, and foundation stiffness parameters are modeled as independent basic random variables. A computationally efficient C 0 finite element method combined with Taylor series based mean-centered first-order perturbation technique via higher order shear deformation plate theory is used to solve the random eigenvalue problem. Typical numerical results for dimensional mean and coefficient of variance of hygrothermally induced buckling load of laminated composite plate subjected to uniform hygrothermal loadings are examined with uniform moisture concentration and temperature rise, plate thickness and aspect ratios, total number of plies, fiber orientations, elastic foundations, and different boundary conditions with random system properties. The numerical results obtained by the present solution approach are validated with those available in the literatures and independent Monte Carlo simulation.

Hygrothermoelastic free vibration response of laminated composite plates resting on elastic foundations with random system properties

This article presents the hygrothermal effects on the free vibration of laminated composite plates resting on a two-parameter Winkler and Pasternak elastic foundations with random system properties using micromechanical model. System properties such as material properties, hygroscopic expansion coefficients, thermal expansion coefficients and foundation stiffness parameters are modeled as independent basic random variables which are affected by the variation in temperature and moisture based on a micromechanical model of a laminate for accurate prediction of system behavior. A C0 finite element method based on higher-order shear deformation theory has been used for deriving the standard eigenvalue problem. A Taylor series-based mean-centered first-order perturbation technique is used to find mean and standard deviation of the natural frequency subjected to uniform moisture concentration and temperature rise, plate aspect ratio, total number of plies, fiber orientations and elastic foundation parameters with different boundary support under hygrothermal environmental conditions. Typical numerical results have been validated with those available in the literature and independent Monte Carlo simulation.

Nonlinear bending response of laminated composite spherical shell panel with system randomness subjected to hygro-thermo-mechanical loading

In the present paper, the effect of random system properties on transverse nonlinear central deflection of laminated composite spherical shell panel subjected to hygro-thermo-mechanical loading is investigated. System properties such as material properties, thermal expansion coefficients, hygro-contraction coefficients, load intensity and lamina plate thickness are taken as independent random variables. The higher order shear deformation theory and von-Karman nonlinear kinematics are used for basic mathematical formulation. The elastic and hygrothermal properties of the composite material, which are considered to be dependent on temperature and moisture concentration, have been obtained based on micromechanical modeling. A direct iterative based C 0 nonlinear finite element method combined with mean centered first-order perturbation technique (FOPT) proposed by present authors for the plate is extended for the spherical shell panel subjected to hygro-thermo-mechanical loading. The influences of random system properties with plate geometry, stacking sequences, support conditions, fiber volume fraction and temperature, and moisture distributions on the response of laminated spherical shell panel are examined in detail. The performance of the proposed approach is validated through comparison with those available in the literature and independent Monte Carlo simulation (MCS).

Stochastic nonlinear free vibration analysis of elastically supported functionally graded materials plate with system randomness in thermal environment

This paper presents the stochastic nonlinear free vibration response of elastically supported functionally graded materials (FGMs) plate resting on two parameter Pasternak foundation having Winkler cubic nonlinearity with random system properties subjected to uniform and nonuniform temperature changes with temperature independent (TID) and dependent (TD) material properties. System properties such as material properties of each constituent’s material, volume fraction index and foundation parameters are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strains using modified C 0 continuity. A direct iterative based nonlinear finite element method in conjunction with first order perturbation technique (FOPT) developed by last two authors for the composite plate is extended for FGM plate to compute the second order statistics (mean and coefficient of variation) of the nonlinear fundamental frequency. The present outlined approach has been validated with those results available in the literature and independent Monte Carlo simulation (MCS).

Effect of random system properties on bending response of thermo-mechanically loaded laminated composite plates

In this paper, effect of random variation in system properties on bending response of geometrically linear laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modeled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behavior of the composite plate. A C 0 finite element method in conjunction with the first order perturbation technique procedure developed earlier by authors for the plate subjected to lateral loading is employed to obtain the second order response statistics (mean and variance) of the transverse deflection of the plate. Typical numerical results for the second order statistics of the transverse central deflection of geometrically linear composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and linearly varying temperature distribution are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The performance of the stochastic laminated composite model is demonstrated through comparison of mean transverse central deflection with those results available in literature and standard deviation of the deflection with an independent Monte Carlo simulation.

Stochastic post buckling analysis of laminated composite cylindrical shell panel subjected to hygrothermomechanical loading

Abstract In this paper, the effect of random system properties on the post buckling load of geometrically nonlinear laminated composite cylindrical shell panel subjected to hygrothermomechanical loading is investigated. System parameters are assumed as independent random variables. The higher order shear deformation theory and von-Karman nonlinear kinematics are used for basic formulation. The elastic and hygrothermal properties of the composite material are considered to be dependent on temperature and moisture concentration using micromechanical approach. A direct iterative based C0 nonlinear finite element method in conjunction with first-order perturbation technique proposed by present author for the plate is extended for shell panel subjected to hygrothermomechanical loading to compute the second-order statistics (mean and variances) of laminated composite cylindrical shell panel. The effect of random system properties, plate geometry, stacking sequences, support conditions, fiber volume fractions and temperature and moisture distributions on hygrothermomechanical post-buckling load of the laminated cylindrical shell panel are presented. The performance of outlined stochastic approach has been validated by comparing the present results with those available in the literature and independent Monte Carlo simulation.

EFFECT OF UNCERTAIN SYSTEM PROPERTIES ON THERMO-ELASTIC STABILITY OF LAMINATED COMPOSITE PLATES UNDER NONUNIFORM TEMPERATURE DISTRIBUTION

Uncertainties in system properties are inherent in all engineering materials. This paper presents the second-order statistics of thermal buckling response of shear deformable laminated composite plate resting on elastic foundation with random system properties under nonuniform tent-like temperature distribution. The mathematical model based on higher-order shear deformation theory [HSDT] is presented. A C0 finite element method in conjunction with first-order perturbation technique is employed to derive the second-order statistics (mean and the standard deviation) of the thermal buckling temperature under nonuniform tent-like temperature distribution. Numerical results have been compared with available results in literatures and independent Monte Carlo simulation.

THERMAL BUCKLING RESPONSE OF LAMINATED COMPOSITE PLATE WITH RANDOM SYSTEM PROPERTIES

This paper deals with second-order statistics of buckling temperature of shear deformable laminated composite plates resting on elastic foundation with random system properties. The temperature field is assumed to be a uniform distribution over the plate surface and through the plate thickness. The material properties are assumed to be independent of temperature. Based on the higher-order deformation theory, C0 finite element in conjunction with mean-centered first-order perturbation technique is proposed and applied to derive the random thermal eigenvalue problems. A detailed parametric study is carried out to highlight the sensitivity of the response. The results are compared with existing and Monte Carlo simulation.

Effects of random system properties on the thermal buckling analysis of laminated composite plates

This paper examines the effect of random system properties on thermal buckling load of laminated composite plates under uniform temperature rise having temperature dependent properties using HSDT. The system properties such as material properties, thermal expansion coefficients and thickness of the laminate are modeled as independent random variables. A C 0 finite element is used for deriving the eigenvalue problem. A Taylor series based first-order perturbation technique is used to handle the randomness in the system properties. Second-order statistics of the thermal buckling load are obtained. The results are validated with those available in the literature and Monte Carlo simulation.

Stochastic nonlinear free vibration of laminated composite plates resting on elastic foundation in thermal environments

This paper presents the nonlinear free vibration analysis of laminated composite plates resting on elastic foundation with random system properties in thermal environments. System parameters are modeled as basic random variables for accurate prediction of system behavior. A C0 nonlinear finite element based on HSDT in von Karman sense is used to descretize the laminate. A direct iterative method in conjunction with first-order perturbation technique is outlined and applied to solve the stochastic nonlinear generalized eigenvalue problem. The developed stochastic procedure is successfully used for thermally induced nonlinear free vibration problem with a reasonable accuracy. Numerical results for various combinations of boundary conditions, geometric parameters, amplitude ratios, foundation parameters and thermal loading have been compared with those available in literature and an independent MCS. Some new results are also presented which clearly demonstrate the importance of the randomness in the system parameters on the response of the structures.

Nonlinear free vibration of laminated composite plates on elastic foundation with random system properties

The present investigation is concerned with free vibration analysis of laminated composite plates resting on elastic foundation undergoing large amplitude oscillation with random system properties. The lamina material properties and foundation stiffness parameters are modeled as basic random variables for accurate prediction of the system behavior. The basic formulation of the problem is based on higher-order shear displacement theory including rotatory inertia effects and von Karman-type nonlinear strain displacement relations. A C 0 finite element is used for descretization of the laminate. A direct iterative method in conjunction with first-order Taylor series based perturbation technique procedure is developed to solve random nonlinear generalized eigenvalue problem. The developed probabilistic procedure is successfully used for the nonlinear free vibration problem with a reasonable accuracy. Typical numerical results (second-order statistics) are obtained for the composite plates resting on Winkler and Pasternak elastic foundations with different support conditions, side-to-thickness ratio, aspect ratio, oscillation amplitude ratio, stacking sequences and foundation parameters for symmetric and anti-symmetric cross-ply and angle-ply laminates. The results are validated with existing available results and independent Monte Carlo simulation.