• Journal of Korean Society of Steel Construction
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• v.23 no.4
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• pp.475-481
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• 2011

In this study, a simplified method of improving not only transverse shear stress but also shear strain based on the first-order shear deformation theory was developed. Unlike many established methods, such as the higher-order shear deformation and layerwise theories, this method can easily apply to finite elements as only $C^0$ continuity is necessary and the formulation of equations is very simple. The basic concept in this method, however, must be corrected:the distribution of the transverse shear stresses and shear strains through the thickness from the formulation based on the higher-order shear deformation theory. Therefore, the shear correction factors are no longer required, based on the first-order shear deformation theory. Numerical analyses were conducted to verify the validity of the proposed formulations. The solutions based on the simplified method were in very good agreement with the results considering the higher-order shear deformation theory.

• Advances in materials Research
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• v.5 no.4
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• pp.223-244
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• 2016

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory 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. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

• 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.

• Steel and Composite Structures
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• v.32 no.2
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• pp.157-171
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• 2019

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

• Structural Engineering and Mechanics
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• v.72 no.5
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• pp.653-673
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• 2019

This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.

• 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.

• 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.

• Advances in aircraft and spacecraft science
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• v.7 no.2
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• pp.115-134
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• 2020

This paper proposes a bending analysis for a functionally graded piezoelectric (FGP) plate through utilizing a two-variable shear deformation plate theory under simply-supported edge conditions. The number of unknown functions used in this theory is only four. The electric potential distribution is assumed to be a combination of a cosine function along the cartesian coordinate. Applying the analytical solutions of FGP plate by using Navier's approach and the principle of virtual work, the equilibrium equations are derived. The paper also discusses thoroughly the impact of applied electric voltage, plate's aspect ratio, thickness ratio and inhomogeneity parameter. Results are compared with the analytical solution obtained by classical plate theory, first-order-shear deformation theory, higher-order shear deformation plate theories and quasi-three-dimensional sinusoidal shear deformation plate theory.

• Smart Structures and Systems
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• v.21 no.4
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• pp.397-405
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• 2018

In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the rectangular nano-plate. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The results are verified with the known results in the literature. The influences played by Effects of nonlocal parameter, length, thickness of the graphene sheets and shear deformation effect on the critical buckling load are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.121-128
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• 2007

Enhanced lower order shear deformation theory is developed in this study. Generally, lower order theories are not adequate to predict accurate deformation and stress distribution through the thickness of laminated plate. For the accurate prediction of detailed stress and deformation distributions through the thickness, higher order zigzag theories have been proposed. However, in most cases, simplified zigzag higher order theory requires $C_1$, shape functions in finite element implementation. In commercial FE softwares, $C_1$, shape functions are not so common in plate and shell analysis. Thus zigzag theories are useful for the highly accurate prediction of thick composite behaviors but they are not practical in the sense that they cannot be used conveniently in the commercial package. In practice, iso-parametric $C_0$ plate model is the standard model for the analysis and design of composite laminated plates and shells. Thus in the present study, an enhanced lower order shear deformation theory is developed. The proposed theory requires only $C_0$ shape function in FE implementation. The least-squared energy error between the lower order theory and higher order theory is minimized. An enhanced lower order shear deformation theory(ELSDT) in this paper is proposed for smart structure under complex loadings. The ELSDT is constructed by the strain energy transformation and fully coupled mechanical, electric loading cases are studied. In order to obtain accurate prediction, zigzag in-plane displacement and transverse normal deformation are considered in the deformation Held. In the electric behavior, open-circuit condition as well as closed-circuit condition is considered. Through the numerous examples, the accuracy and robustness of present theory are demonstrated.