• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.663-668
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• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.2
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• pp.25-32
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• 1988

A formulation of an isoparametric quadrilateral higher-order plate bending finite element is presented. The 8-noded 28-d.o.f. plate element has been degenerated from the three-dimensional continuum by introducing the plate assumptions and considering higher-order in-plane displacement profile. The element characteristics have been derived by the Galerkin's weighted residual method and computed by using the selective reduced integration technique to avoid shear-locking phenomenon. Several numerical examples are given to demonstrate the accuracy and versatility of the proposed quadrilateral higher-order plate bending element over the other existing plate finite elements in both static and dynamic analyses.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.3
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• pp.1-10
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• 1988

A higher order plate bending finite element using cubic in-plane displacement profiles is proposed for geometrically nonlinear analysis of thin and thick plates. The higher order plate bending element has been derived from the three dimensional plate-like continuum by discretization of the equations of motion by Galerkin weighted residual method, together with enforcing higher order plate assumptions. Total Lagrangian formulation has been used for geometrically nonlinear analysis of plates and consistent linearization by Newton-Raphson method has been performed to solve the nonlinear equations. The element characteristics have been computed by, selective reduced integration technique using Gauss quadrature to avoid shear locking phenomenon in case of extremely thin plates. Several numerical examples were solved with FEAP macro program to demonstrate versatility and accuracy of the present higher order plate bending element.

• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1143-1165
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• 2015

In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and porosity volume fraction on wave propagation of functionally graded plate are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.259-269
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• 2020

In this paper, bending-stretching analysis of thick functionally graded piezoelectric rectangular plates is studied using the higher-order shear and normal deformable plate theory. On the basis of this theory, Legendre polynomials are used for approximating the components of displacement field. Also, the effects of both normal and shear deformations are encountered in the theory. The governing equations are derived using the principle of virtual work and variational approach. It is assumed that plate is made of piezoelectric materials with functionally graded distribution of material properties. Hence, exponential function is used to modify mechanical and electrical properties through the thickness of the plate. Finally, the effect of material properties, electrical boundary conditions and dimensions are investigated on the static response of plate. Also, it is shown that results of the presented model are close to the three dimensional elasticity solutions.

• Steel and Composite Structures
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• v.45 no.3
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• pp.305-330
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• 2022

This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.1
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• pp.65-73
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• 1987

An efficient plate bending finite element has been developed using higher-order inplane displacement profiles of the plate. The 6-noded, 21-d.o.f. triangular element including shear deformation effect has been derived from the plate-like continuum by the Galerkin's weighted residual method. Square plate examples were tested with selected element meshes and several aspect ratios for their static behavior under uniformly distributed load. The result of the example tests indicated consistently good performance of the present higher-order plate bending element in comparison with the thin and thick plate solution and other existing finite element solutions.

• Journal of Korean Association for Spatial Structures
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• v.5 no.3 s.17
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• pp.65-74
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• 2005

An analytical model was developed to investigate the flexural behavior of a pultruded fiber-reinforced plastic deck of rectangular unit module. The model is based on first-order shea. deformable plate theory (FSDT), and capable of predicting deflection of the deck of arbitrary laminate stacking sequences. To formulate tile problem, two-dimensional plate finite element method is employed. Numerical results are obtained for FRP decks under uniformly-distributed loading, addressing the effects of fiber angle and span-to-height ratio. It is found that the present analytical model is accurate and efficient for solving flexural behavior of FRP decks. Also, as the height of FRP deck plate is higher, the necessity of higher order Shear deformable plate theory(HSDT) is announced, not the FSDT in the plate analysis theory.