• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.311-324
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• 2017

In this paper a new eight-unknown higher order shear deformation theory is proposed for functionally graded (FG) material plates. The theory based on full twelve-unknown higher order shear deformation theory, simultaneously satisfy zeros transverse stresses at top and bottom surface of FG plates. Equations of motion are derived from principle of virtual displacement. Exact closed-form solutions are obtained for simply supported rectangular FG plates under uniform loading. The accuracy of present numerical results has been verified by comparing it with generalized shear deformation theory. The effect of power law index of functionally graded material, side-to-thickness ratio, and aspect ratio on static behavior of FG plates is investigated.

• Proceeding of KASS Symposium
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• 2008.05a
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• pp.95-100
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• 2008

A 4-node assumed strain finite element based on higher order shear deformation theory is developed to investigate the behaviours of symmetric and unsymmetric laminated composite plates. The present element is based on Reddy's higher order shear deformation theory so that it can consider the parabolic distribution of shear deformation through plate thickness direction. In particular, assumed strain method is adopted to alleviate the shear locking phenomena inherited plate elements based on higher order shear deformation theory. The present finite element has seven degrees of freedom per node and denoted as HSA4. Numerical examples are carried out for symmetric and unsymmetric laminated composite plate with various thickness values. Numerical results are compared with reference solutions produced by other higher order shear deformation theories.

• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.49-63
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• 2017

This paper presents an original hyperbolic (first present model) and parabolic (second present model) shear and normal deformation theory for the bending analysis to account for the effect of thickness stretching in functionally graded sandwich plates. Indeed, the number of unknown functions involved in these presents theories is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. It is evident from the present analyses; the thickness stretching effect is more pronounced for thick plates and it needs to be taken into consideration in more physically realistic simulations. The numerical results are compared with 3D exact solution, quasi-3-dimensional solutions and with other higher-order shear deformation theories, and the superiority of the present theory can be noticed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.65-76
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• 1994

A higher-oder laminated plate theory including the effect of transverse shear deformation is developed to calculate the gross response and the detailed stress distribution. The theory satisfies the continuity condition of transverse shear stress, and accounts for parabolic variation of the transverse shear stresses through the thickness of each layer. Exact closed-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and a simple higher-order theory solutions. The results of the present work exhibit acceptable accuracy when compared to the three-dimensional elasticity solutions.

• Smart Structures and Systems
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• v.5 no.5
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• pp.531-546
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• 2009

In the present analysis, the spline finite strip with higher-order shear deformation is formulated for the static analysis of piezoelectric composite plates. The proposed method incorporates Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model, Cho's higher-order zigzag laminate theory, as well as the classic plate theory and the first-order plate theory. Thus, the analysis can be conducted based on any of the above-mentioned theories. The selection of a specific method is done by simply changing a few terms in a 2 by 2 square matrix and the results, obtained according to different plate theories, can be compared to each other. Numerical examples are presented for piezoelectric composite plates subjected to mechanical loading. The results based on different shear deformation theories are compared with the three-dimensional solutions. The behaviours of piezoelectric composite plates with different length-to-thickness ratios, fibre orientations, and boundary conditions are also investigated in these examples.

• Smart Structures and Systems
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• v.26 no.2
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• pp.253-262
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• 2020

In this paper, a new higher order shear deformation model is developed for static analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. The model account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG beam. Based on the present higher-order shear deformation model, the equations of motion are derived by the principle of virtual works. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, and geometry on the bending of imperfect FG beams. It can be concluded that the proposed model is simple and precise for the resolution of the behavior of flexural FGM beams while taking into account the shape of distribution of the porosity.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.761-769
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• 2018

In this paper, we study the Carbon/Glass hybrid laminated composite plates, where the buckling behavior is examined using an accurate and simple refined higher order shear deformation theory. This theory takes account the shear effect, where shear deformation and shear stresses will be considered in determination of critical buckling load under different boundary conditions. The most interesting feature of this new kind of hybrid laminated composite plates is that the possibility of varying components percentages, which allows us for a variety of plates with different materials combinations in order to overcome the most difficult obstacles faced in traditional laminated composite plates like (cost and strength). Numerical results of the present study are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories issue from the literature. It can be concluded that the proposed theory is accurate and simple in solving the buckling behavior of hybrid laminated composite plates and allows to industrials the possibility to adjust the component of this new kind of plates in the most efficient way (reducing time and cost) according to their specific needs.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.601-609
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• 1997

Bending and vibration results for a laminated plate base on a simplified higher-order plate theory with four variables are presented. Assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order shear deformation theory it is shown that a simpler higher-order theory can be obtained with the reduction of one variable without significant loss in the accuracy. This simple higher-order shear deformation theory is then used for predicting the natural frequencies and deflection of simply-supported laminated composite plates. The results obtained for antisymmetrical laminated composite plates compare favorably with third-order and first-order shear deformation theory. The information presented should be useful to composite-structure designers, to researchers seeking to obtain better correlation between theory and experiment and to numerical analysts in checking out their programs.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.49-60
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• 1995

In the present study, a finite strip method for the vibration and stability analyses of anisotropic laminated composite plates is developed according to the higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. In comparison with the finite strip method based on the first-order shear deformation theory, the present method gives improved results for very thick plates while using approximately the same number of degrees of freedom. It also eliminates the need for shear correction factors in calculating the transverse shear stiffness. A number of numerical examples are presented to show the effect of aspect ratio, length-to-thickness ratio, number of plies, fibre orientation and stacking sequence on the natural frequencies and critical buckling loads of simply supported rectangular cross-ply and arbitrary angle-ply composite laminates.

• Journal of KSNVE
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• v.8 no.1
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• pp.132-138
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• 1998

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 higer 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. This is accomplished by using a stress recovery technique using the in-plane stresses. The results compared with previous investigations showed good agreement. It can be seen that this method of analyzing impact problems is more efficient than current three dimensional methods in terms of time and expense.