• Smart Structures and Systems
• /
• v.20 no.4
• /
• pp.509-524
• /
• 2017

In this article, a free vibration analysis of functionally graded (FG) plates resting on elastic foundations is presented using a quasi-3D hybrid-type higher order shear deformation theory. Undetermined integral terms are employed in the proposed displacement field and modeled based on a hybrid-type (sinusoidal and parabolic) quasi-3D HSDT with five unknowns in which the stretching effect is taken into account. Thus, it can be said that the significant feature of this theory is that it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The elastic foundation parameters are introduced in the present formulation by following the Pasternak (two-parameter) mathematical model. Equations of motion are obtained via the Hamilton's principles and solved using Navier's method. Accuracy of the proposed theory is confirmed by comparing the results of numerical examples with the ones available in literature.

• Earthquakes and Structures
• /
• v.16 no.5
• /
• pp.547-561
• /
• 2019

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGM plates are studied in detail.

• Advances in materials Research
• /
• v.8 no.4
• /
• pp.313-335
• /
• 2019

The objective of the present paper is to investigate the bending and free vibration behavior of functionally graded material (FGM) sandwich rectangular plates using an efficient and simple higher order shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The most interesting feature of this theory is that it does not require the shear correction factor. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Coupled systems mechanics
• /
• v.13 no.2
• /
• pp.171-186
• /
• 2024

In the present paper, thermal buckling characteristics of functionally graded rectangular plates made of porous material that are integrated with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and constant applied actuator voltage are investigated by utilizing a Navier solution method. The uniform temperature rise loading is considered. Thermomechanical material properties of FGM plates are assumed to be temperature independent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of stability for the piezoelectric FGM plate are derived based on higher order shear deformation plate theory. Influences of several important parameters on the critical thermal buckling temperature are investigated and discussed in detail.

• Steel and Composite Structures
• /
• v.22 no.3
• /
• pp.473-495
• /
• 2016

This work presents a bending, buckling, and vibration analysis of functionally graded plates by employing a novel higher-order shear deformation theory (HSDT). This theory has only four unknowns, which is even less than the first shear deformation theory (FSDT). A shear correction coefficient is, thus, not needed. Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Steel and Composite Structures
• /
• v.20 no.1
• /
• pp.205-225
• /
• 2016

In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.24 no.3
• /
• pp.249-257
• /
• 2011

In this paper, an systematic approach is presented, in which the mixed variational theorem is employed to incorporate independent transverse shear stresses into a classical higher-order shear deformation theory(HSDT). The HSDT displacement field is taken to amplify the benefits of using a classical shear deformation theory such as simple and straightforward calculation and numerical efficiency. Those independent transverse shear stresses are taken from the fifth-order polynomial-based zig-zag theory where the fourth-order transverse shear strains can be obtained. The classical displacement field and independent transverse shear stresses are systematically blended via the mixed variational theorem. Resulting strain energy expressions are named as an enhanced higher-order shear deformation theory via mixed variational theorem(EHSDTM). The EHSDTM possess the same computational advantage as the classical HSDT while allowing for improved through-the-thickness stress and displacement variations via the post-processing procedure. Displacement and stress distributions obtained herein are compared to those of the classical HSDT, three-dimensional elasticity, and available data in literature.

• Structural Engineering and Mechanics
• /
• v.56 no.1
• /
• pp.85-106
• /
• 2015

Postbuckling of thick plates made of functionally graded material (FGM) subjected to in-plane compressive, thermal and thermomechanical loads is investigated in this work. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation. Thermomechanical non-homogeneous properties are considered to be temperature independent, and graded smoothly by the distribution of power law across the thickness in the thickness in terms of the volume fractions of constituents. By employing the higher order shear deformation plate theory together the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect FGM plates are derived. The Galerkin technique is used to determine the buckling loads and postbuckling equilibrium paths for simply supported plates. Numerical examples are presented to show the influences of power law index, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the plates.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.04a
• /
• pp.42-48
• /
• 1997

The dynamic response of symmetric cross-ply and angle-ply composite laminated plates under impact loads is investigated using a higher order shear deformation theory. A modified Hertz law is used to predict the impact loads and a four node finite element is used to model the plate. By using a higher order shear deformation theory, the out-of-plane shear stresses, which can be a crucial factor in the failure of composite plates, are determined with significant accuracy. The results compared with previous investigations showed good agreement. The effect of ply sequence and ply angle on the contact force is also studied.

• International Journal of Aerospace System Engineering
• /
• v.3 no.1
• /
• pp.10-16
• /
• 2016

A trigonometric Layerwise higher order shear deformation theory (TLHSDT) is developed and implemented for free vibration and buckling analysis of laminated composite and sandwich plates by analytical and finite element formulation. The present model assumes parabolic variation of out-plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag model able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. Hence, botheration of shear correction coefficient is neglected. In the case of analytical method, the governing differential equation and boundary conditions are obtained from the principle of virtual work. For the finite element formulation, an efficient eight noded $C^0$ continuous isoparametric serendipity element is established and employed to examine the dynamic analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.