• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1215-1240
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• 2015

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.407-418
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• 2006

In this paper, an efficient yet accurate stress analysis based on the first-order shear deformation theory (FSDT) is presented. The transverse shear strain energy is modified via the mixed variational theorem, so that the shear correction factors are automatically involved in the formulation. In the mixed variational formulation, the transverse stresses are taken to be functions subject to variations. The transverse shear stresses based on an efficient higher order plate theory (EHOPT, Cho and Parmerter, 1993) are utilized and modified, while the transverse normal stress is assumed to be the third-order polynomial of thickness coordinates, which satisfies both zero transverse shear stresses and prescribed surface fractions in top and bottom surfaces. On the other hand, the displacements are assumed to be those of the FSDT Resulting strain energy expressions are referred to as an EFSDTM3D that stands for an enhanced first-order shear deformation theory based on the mixed formulation for three dimensional elasticity, The developed EFSDTM3D preserves the computational advantage of the classical FSDT while allowing for important local through-the-thickness variations of displacements and stresses through the recovery procedure that is based on the least square minimization of in-plane stresses. Comparisons of displacements and stresses of both laminated and sandwich plates using the present theory are made with the classical FSDT, three-dimensional exact solutions, and available data in the literature.

• Structural Engineering and Mechanics
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• v.72 no.1
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• pp.61-70
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• 2019

The functionally graded materials (FGM) used in plates contain probably a porosity volume fraction which needs taking into account this aspect of imperfection in the mechanical bahavior of such structures. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is developed to study the effect of the distribution shape of porosity on static behavior of FG plates. It was found that the distribution form of porosity significantly influence the mechanical behavior of FG plates, in terms of deflection, normal and shear stress. It can be concluded that the proposed theory is simple and precise for the resolution of the behavior of flexural FGM plates resting on elastic foundations while taking into account the shape of distribution of the porosity.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.11
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• pp.98-109
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• 1995

An investigation was performed to study the inner damage of laminated composite plates subjected to out-of-plane load. During the investigation, inpact velocity and equivalent static load relationship was derived. Reddy's higher-order shear deformation theory(HSDT) and Hashin's failure criteria were used to determine inner stresses and damaged area. And impact testing was carried out on laminated composite plates by air gun type impact testing machine. The CFRP specimens were composed of [ .+-. 45 .deg. ]$_{4}$and [ .+-. 45 .deg. /0 .deg. /90 .deg. ]$_{2}$ stacking sequences with 0.75$^{t}$ * 26$^{w}$ * 100$^{l}$ (mm) dimension. After impact testing. As a result, a relationship holds between damaged area and impact energy, and a matrix cracking was caused by the interlaminar shear stress in the middle ply and was caused by the inplane transverse stress in the bottom ply.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.593-605
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• 2023

This work presents a comparison between analytical and finite element analysis for bending of porous sandwich functionally graded material (FGM) plates. The plate is rectangular and simply supported under static sinusoidal loading. Material properties of FGM are assumed to vary continuously across the face sheets thickness according to a power-law function in terms of the volume fractions of the constituents while the core is homogeneous. Four types of porosity are considered. A refined higher-order shear with normal deformation theory is used. The number of unknowns in this theory is five, as against six or more in other shear and normal deformation theories. This theory assumes the nonlinear variation of transverse shear stresses and satisfies its nullity in the top and bottom surfaces of the plate without the use of a shear correction factor. The governing equations of equilibrium are derived from the virtual work principle. The Navier approach is used to solve equilibrium equations. The constitutive law of the porous FGM sandwich plate is implemented for a 3D finite element through a subroutine in FORTRAN (UMAT) in Abaqus software. Results show good agreement between the finite element model and the analytical method for some results, but the analytical method keeps giving symmetric results even with the thickness stretching effect and load applied to the top surface of the sandwich.

• Structural Engineering and Mechanics
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• v.85 no.6
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• pp.765-780
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• 2023

In this work, a novel combined logarithmic, secant and tangential 2D and quasi-3D refined higher order shear deformation theory is proposed to examine the buckling analysis of simply supported uniform functionally graded plates under uniaxial and biaxial loading. The proposed formulations contain a reduced number of variables compared to others similar solutions. The combined function employed in this study ensures automatically the zero-transverse shear stresses at the free surfaces of the structure. Various models of the material distributions are considered (linear, quadratic, cubic inverse quadratic and power-law). The differentials stability equations are derived via virtual work principle with including the stretching effect. The Navier's approach is applied to solve the governing equations which satisfying the boundary conditions. Several comparative and parametric studies are performed to illustrates the validity and efficacity of the proposed model and the various factors influencing the critical buckling load of thick FG plate.

• Steel and Composite Structures
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• v.22 no.5
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• pp.975-999
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• 2016

This work investigates a thermomechanical bending analysis of functionally graded sandwich plates by proposing a novel quasi-3D type higher order shear deformation theory (HSDT). The mathematical model introduces only 5 variables as the first order shear deformation theory (FSDT). Unlike the conventional HSDT, the present one presents a novel displacement field which includes undetermined integral variables. The mechanical properties of functionally graded layers of the plate are supposed to change in the thickness direction according to a power law distribution. The core layer is still homogeneous and made of an isotropic ceramic material. The governing equations for the thermomechanical bending investigation are obtained through the principle of virtual work and solved via Navier-type method. Interesting results are determined and compared with quasi-3D and 2D HSDTs. The influences of functionally graded material (FGM) layer thickness, power law index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.505-512
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• 2012

In this paper, an efficient yet accurate method for the thermal stress analysis using a first order shear deformation theory(FSDT) is presented. The main objective herein is to systematically modify transverse shear strain energy through the mixed variational theorem(MVT). In the mixed formulation, independent transverse shear stresses are taken from the efficient higher-order zigzag plate theory, and the in-plane displacements are assumed to be those of the FSDT. Moreover, a smooth parabolic distribution through the thickness is assumed in the transverse normal displacement field in order to consider a transverse normal deformation. The resulting strain energy expression is referred to as an enhanced first order shear deformation theory, which is obtained via the mixed variational theorem with transverse normal deformation effect(EFSDTM_TN). The EFSDTM_TN has the same computational advantage as the FSDT_TN(FSDT with transverse normal deformation effect) does, which allows us to improve the through-the-thickness distributions of displacements and stresses via the recovery procedure. The thermal stresses obtained by the present theory are compared with those of the FSDT_TN and three-dimensional elasticity.

• Smart Structures and Systems
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• v.21 no.1
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• pp.75-97
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• 2018

In this paper, a novel higher-order shear deformation theory (HSDT) is proposed for the analysis of the hygro-thermo-mechanical behavior of functionally graded (FG) plates resting on elastic foundations. The developed model uses a novel kinematic by considering undetermined integral terms and only four variables are used in this model. The governing equations are deduced based on the principle of virtual work and the number of unknown functions involved is reduced to only four, which is less than the first shear deformation theory (FSDT) and others HSDTs. The Navier-type exact solutions for static analysis of simply supported FG plates subjected to hygro-thermo-mechanical loads are presented. The accuracy and efficiency of the present model is validated by comparing it with various available solutions in the literature. The influences of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratios and elastic coefficients parameters on deflections and stresses of FG plates are also investigated.

• Advances in materials Research
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• v.7 no.2
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• pp.119-136
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• 2018

In this paper, static and vibration analysis for anti-symmetric cross-ply and angle- ply carbon/glass hybrid laminates rectangular composite plate are presented. In this analysis, the equations of motion for simply supported thick laminated hybrid rectangular plates are derived and obtained through the use of Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle- ply laminates are obtained using Navier solution. The effects of side-to-thickness ratio, aspect ratio, and lamination schemes on the fundamental frequencies loads are investigated. The study concludes that shear deformation laminate theories accurately predict the behavior of composite laminates, whereas the classical laminate theory over predicts natural frequencies. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behaviors of anti-symmetric cross-ply and angle- ply hybrid laminated composite plates.