• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.191-213
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• 2011

This paper presents an improved 8-node shell element for the analysis of plates and shells. The finite element, based on a refined first-order shear deformation theory, is further improved by the combined use of assumed natural strain method. We analyze the influence of the shell element with the different patterns of sampling points for interpolating different components of strains. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Further, a refined first-order shear deformation theory, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. Numerical examples demonstrate that the present element perform better in comparison with other shell elements.

• Structural Engineering and Mechanics
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• v.10 no.4
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• pp.337-357
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• 2000

Analytical formulations and solutions for the first time, to the stability analysis of a simply supported composite and sandwich plates based on a higher order refined theory, developed by the first author and already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of inplane displacements with respect to the thickness coordinate - thus modelling the warping of transverse cross sections more accurately and eliminating the need for shear correction coefficients. The equations of equilibrium are obtained using the Principle of Minimum Potential Energy (PMPE). The comparison of the results using this higher order refined theory with the available elasticity solutions and the results computed independently using the first order and the other higher order theories developed by other investigators and available in the literature shows that this refined theory predicts the critical buckling load more accurately than all other theories considered in this paper. New results for sandwich laminates are also presented which may serve as a benchmark for future investigations.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.725-734
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• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Geomechanics and Engineering
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• v.13 no.3
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• pp.385-410
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• 2017

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Steel and Composite Structures
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• v.22 no.4
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• pp.713-732
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• 2016

A novel four variable refined plate theory is proposed in this work for laminated composite plates. The theory considers a parabolic distribution of the transverse shear strains, and respects the zero traction boundary conditions on the surfaces of the plate without employing shear correction coefficient. The displacement field is based on a novel kinematic in which the undetermined integral terms are used, and only four unknowns are involved. The analytical solutions of antisymmetric cross-ply and angle-ply laminates are determined via Navier technique. The obtained results from the present model are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories reported in the literature. It can be concluded that the developed theory is accurate and simple in investigating the bending and buckling responses of laminated composite plates.

• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.4
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• pp.107-114
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• 2004

In this paper, a simple improved 8-node finite element for the finite element analysis of fibrous composite plates is presented by using the direct modification. We drive explicit expressions of shape functions for the 8-node element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian coordinates. The refined first-order shear deformation theory is proposed, which results in parabolic through-thickness distribution of the transverse shear strains and stresses from the formulation based on the third-order shear deformation theory. It eliminates the need for shear correction factors in the first-order theory. This finite element is further improved by combined use of assumed strain, modified shape function, and refined first-order theory. To show the effectiveness of our simple modification on the 8-node finite elements, numerical studies are carried out the static, buckling and free vibration analysis of fibrous composite plates.

• Smart Structures and Systems
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• v.25 no.4
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• pp.409-422
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• 2020

This article deals with the flexural analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal loading using a refined plate theory with four variables. In this theory, the undetermined integral terms are used and the number of variables is reduced to four, instead of five or more in other higher-order theories. The boundary conditions on the top and the bottom surfaces of the plate are satisfied; hence the use of the transverse shear correction factors is avoided. The principle of virtual work is used to obtain governing equations and boundary conditions. Navier solution for simply supported plates is used to derive analytical solutions. For the validation of the present theory, numerical results for displacements and stresses are compared with those of classical, first-order, higher-order and trigonometric shear theories reported in the literature.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1287-1306
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• 2016

The current research presents a buckling analysis of isotropic and orthotropic plates by proposing a new four variable refined plate theory. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only four variables. The governing equations for buckling analysis are deduced by utilizing the principle of virtual works. The analytical solution of a simply supported rectangular plate under the axial loading has been determined via the Navier method. Numerical investigations are performed by using the proposed model and the obtained results are compared with CPT solutions, FSDT solutions, and the existing exact solutions in the literature. It can be concluded that the developed four variable refined plate theory, which does not use shear correction coefficient, is not only simple but also comparable to the FSDT.

• Structural Engineering and Mechanics
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• v.83 no.5
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• pp.617-625
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• 2022

A novel three variable refined plate theory (TVRPT) is developed in this article for laminated composite plates for the first time. The theory takes into account the nonlinear variation of transverse shear deformations, and satisfies the boundary conditions of zero traction on the plate surfaces without considering the "shear correction factor". The important characteristic of this new kinematic is that the unknowns numbers is only 3 as is employed in "classical plate theory" (CPT). The numerical results of the current theory are compared with 3D-elasticity solutions and the calculations of "first order theories" and other higher order models found in the literature.

• Advances in materials Research
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• v.12 no.2
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• pp.133-159
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• 2023

In this paper, a size-dependent dynamic investigation of a porous metal foams microbeamsis presented. The novelty of this study is to use a metal foam microbeam that contain porosities based on the refined high order shear deformation beam model, with sinusoidal shear strain function, and the modified strain gradient theory (MSGT) for the first time. The Lagrange's principle combined with differential quadrature hierarchicalfinite element method (DQHFEM) are used to obtain the porous microbeam governing equations. The solutions are presented for the natural frequencies of the porous and homogeneoustype microbeam. The obtained results are validated with the analytical methods found in the literature, in order to confirm the accuracy of the presented resolution method. The influences of the shape of porosity distribution, slenderness ratio, microbeam thickness, and porosity coefficient on the free vibration of the porous microbeams are explored in detail. The results of this paper can be used in various design formetallic foammicro-structuresin engineering.