Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation

Buckling and free vibration analysis of simply supported symmetric and antisymmetric cross-ply thick composite plates on elastic foundation are examined by a new hyperbolic displacement model in this paper. In this new model, inplane displacements vary as a hyperbolic function across the plate thickness, so account for parabolic distributions of transverse shear stresses and satisfy zero shear stress conditions at the top and bottom surfaces of the plate. In the analysis, the foundation is modeled as two parameter Pasternak type foundation, and Winkler type if the second foundation parameter is zero. The equation of motion for thick laminated rectangular plates resting on elastic foundation and subjected to inplane loads is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then buckling loads and fundamental frequencies are found by solving the results of eigenvalue problems. The numerical results obtained through the present analysis for free vibration and buckling of cross-ply laminated plates on elastic foundation are presented, and compared with the ones available in the literature

Analysis of thick laminated composite plates on an elastic foundation with the use of various plate theories

In this study, various theories of composite laminated plates are extended to rectangular composite laminates resting on an elastic foundation. First, an analysis based on the classical theory of laminated plates is employed. Then the first-order Reissner-Mindlin theory is used for analyzing the laminates. At last, the Reddy shear deformation theory, which allows for the transverse shear strains, is applied to the bending analysis of the laminates. In the analysis, the two-parameter Pasternak and Winkler foundations are considered. The accuracy of the present analysis is demonstrated by solving problems numerical results for which are available in the literature. Some numerical examples are presented to compare the three methods and to illustrate the effects of parameters of the elastic foundations on the bending of shear-deformable laminated plates. © 2005 Springer Science+Business Media, Inc

Thermal buckling analysis of functionally graded plates on an elastic foundation according to a hyperbolic shear deformation theory

A thermal buckling analysis of functionally graded thick rectangular plates on an elastic foundation is presented. The foundation is described by the Pasternak model. The formulation is based on a higher-order hyperbolic shear deformation theory. Two types of thermal loading, uniform temperature rise and graded temperature change across the thickness of the plates are considered, and their equilibrium and stability equations are obtained. The accuracy of the formulation presented is verified by comparing the results of numerical examples with data available in the literature. © 2014 Springer Science+Business Media New York

Analysis of shear deformable symmetrically laminated composite plates on elastic foundation

In this study, a shear deformable theory which accounts for the transverse shear strains is employed to the bending analysis of symmetrically laminated crossply composite plates resting on elastic foundation. The displacement equations of laminated plates based on the classical laminated plate theory and including the effect of transverse shear deformation are presented. The theory accounts for parabolic distribution of the transverse shear strains. In the analysis, the foundation is modeled as two parameter Pasternak-type foundation and Winkler-type, also, if the second foundation paramater is zero. The accuracy of the present analysis is demonstrated by solving problems which the exact solutions and numerical results are available in literature. Some numerical examples are presented to illustrate the effects of fiber orientation and elastic foundation parameter on the bending of shear deformable laminated plates. © Freund Publishing House Ltd

An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation

Free vibration analysis of plates made of functionally graded materials and resting on elastic foundation is presented by taking into account the effect of transverse shear deformations. The foundation is described by the Pasternak (two-parameter) model. The material properties of the plate are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. The formulation is based on a higher order hyperbolic shear deformation theory. The equation of motion for thick functionally graded plates is obtained through the Hamilton's principle. The closed form solutions are obtained by using Navier technique and then fundamental frequencies are found by solving the results of eigenvalue problems. Accuracy of the present formulation is shown by comparing the results of numerical examples with the ones available in literature. © 2013 Elsevier Ltd

Nonlinear analysis of semi-rigid frames with rigid end sections

This work presents a computer-based analysis of semi-rigid steel frames. The geometric nonlinearity of the structure and the material nonlinearity of the connections are considered in the analysis. The critical load has been searched as a suitable load parameter for the loss of stability of the system. Several examples are presented to demonstrate the validity of the analysis procedure. © Shiraz University

Mechanical behavior of functionally graded sandwich plates on elastic foundation

A new hyperbolic shear and normal deformation plate theory, presented in this paper, is used to study the static, free vibration and buckling analysis of the simply supported functionally graded sandwich plates on elastic foundation. This theory accounts for the realistic variations of the displacements through the thickness. In the analysis, two common types of FGM sandwich plates, namely, homogeneous face sheets with FGM core and FGM face sheets with homogeneous core are considered. The elastic foundation is described by the Pasternak model. The equations of motion are derived from Hamilton's principle. The closed form solutions are obtained by using Navier technique. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is simple and efficient in predicting the mechanical behavior of functionally graded sandwich plates. © 2016 Elsevier Ltd. All rights reserved

Two new hyperbolic shear displacement models for orthotropic laminated composite plates

Two hyperbolic displacement models, HPSDT1 and HPSDlz, are developed for a bending analysis of orthotropic laminated composite plates. These models take into account the parabolic distribution of transverse shear stresses and satisfy the condition of zero shear stresses on the top and bottom surfaces of the plates. The accuracy of the analysis presented is demonstrated by comparing the results with solutions derived from other higher-order models and with data found in the literature. It is established that the HPSDT1 model is more accurate than some theories of laminates developed previously, and therefore the analysis can be expanded to laminated composite shells. © 2010 Springer Science+Business Media, Inc

Buckling and free vibration analyses of laminated composite plates by using two new hyperbolic shear-deformation theories

Two new hyperbolic displacement models, HPSDT1 and HPSDT2, are used for the buckling and free vibration analyses of simply supported orthotropic laminated composite plates. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The equation of motion for thick laminated rectangular plates subjected to in-plane loads is deduced through the use of Hamilton's principle. Closed-form solutions are obtained by using the Navier technique, and then the buckling loads and the fundamental frequencies are found by solving eigenvalue problems. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other higher-order models given in the literature. It is found that the theories proposed can predict the fundamental frequencies and buckling loads of cross-ply laminated composite plates rather accurately. © 2008 Springer Science+Business Media, Inc

Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories

In this study, two dimensional (2D) and quasi three-dimensional (quasi-3D) shear deformation theories are presented for static and free vibration analysis of single-layer functionally graded (FG) plates using a new hyperbolic shape function. The material of the plate is inhomogeneous and the material properties assumed to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The fundamental governing equations which take into account the effects of both transverse shear and normal stresses are derived through the Hamilton's principle. The closed form solutions are obtained by using Navier technique and then fundamental frequencies are found by solving the results of eigenvalue problems. In-plane stress components have been obtained by the constitutive equations of composite plates. The transverse stress components have been obtained by integrating the three-dimensional stress equilibrium equations in the thickness direction of the plate. The accuracy of the present method is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature. © 2015 Elsevier Ltd. All rights reserved