• Wind and Structures
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• v.22 no.4
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• pp.429-454
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• 2016

In this paper, a shear deformation plate theory based on neutral surface position is developed for free vibration analysis of functionally graded material (FGM) plates. The material properties of the FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. During manufacture, defects such as porosities can appear. It is therefore necessary to consider the vibration behavior of FG plates having porosities in this investigation. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The equation of motion for FG rectangular plates is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Numerical results are presented and the influences of the volume fraction index and porosity volume fraction on frequencies of FGM plates are clearly discussed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.3A
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• pp.447-455
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• 2006

A general purpose of 4-node co-rotational resultant shell element is developed for the solution of nonlinear problems of reinforced concrete, steel and fiber-reinforced composite structures. The formulation of the geometrical stiffness presented here is defined on the mid-surface by using the second order kinematic relations and is efficient for analyzing thick plates and shells by incorporating bending moment and transverse shear resultant forces. The present element is free of shear locking behavior by using the ANS (Assumed Natural Strain) method such that the element performs very well as thin shells. Inelastic behaviour of concrete material is based on the plasticity with strain hardening and elasto-plastic fracture model. The plasticity of steel is based on Von-Mises Yield and Ivanov Yield criteria with strain hardening. The transverse shear stiffness of laminate composite is defined by an equilibrium approach instead of using the shear correction factor. The proposed formulation is computationally efficient and versitile for most civil engineering application and the test results showed good agreement.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.93-103
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• 1994

Two beam/column elements are developed in order to analyze the geometric nonlinear plane irames including the effects of internal hinge and transverse shear deformation. In the case of the first element (finite segment method), tangent stiffness matrix is derived by directly integrating the equilibrium equations whereas in the case of the second element (finite element method) elastic and goemetric stiffness matrices are calculated by using the hermitian polynomials including the effects of internal hinge and shear deformation as the shape function. Numerical results are presented for the selected test problems which demonstrate that both elements represent reliable and highly accurate tools.

• Smart Structures and Systems
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• v.22 no.1
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• pp.27-40
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• 2018

The governing equations of motion are derived for analysis of a sandwich microbeam in this paper. The sandwich microbeam is including an elastic micro-core and two piezoelectric micro-face-sheets. The microbeam is subjected to transverse loads and two-dimensional electric potential. Higher-order sinusoidal shear deformation beam theory is used for description of displacement field. To account size dependency in governing equations of motion, strain gradient theory is used to mention higher-order stress and strains. An analytical approach for simply-supported sandwich microbeam with short-circuited electric potential is proposed. The numerical results indicate that various types of parameters such as foundation and material length scales have significant effects on the free vibration responses and dynamic results. Investigation on the influence of material length scales indicates that increase of both dimensionless material length scale parameters leads to significant changes of vibration and dynamic responses of microbeam.

• Journal of Korean Society of Steel Construction
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• v.9 no.1 s.30
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• pp.65-79
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• 1997

Composite materials are consist of two or more different materials to produce desirable properties for structural strength. Because of their superiority in strength, corrosion resistance, and weight reduction, they are used extensively as structural members. The objective of this study is to present the effectivness of the laminated composite elements by analyzing in-plane displacement and stress of the anisotropic laminated annular elements. Anisotropic laminated structures are very difficult to analyze and apply, compared with isotropic and orthotropic cases for arbitrary boundaries and fiber angle -ply. Boundary conditions for the examples used in this study consist of two opposite edges clamped and the other two edges free, and finite difference method is used in this study for numerical analysis. From the numerical result, it is found that the program used in this study can be used to obtain the displacement of the straight beams considering it's transverse shear deformation as well as anisotropic laminated elements. Several numerical examples show the advantages of the stiffness increase when the angle-ply composite materials are used. Therefore it gives a guide in deciding how to make use of fiber's angle for the subtended angle, load cases, and boundary conditions.

• Advances in nano research
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• v.1 no.1
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• pp.1-11
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• 2013

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.641-654
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• 2004

This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

• Structural Engineering and Mechanics
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• v.40 no.6
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• pp.783-800
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• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• Composites Research
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• v.33 no.6
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• pp.377-382
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• 2020

The free vibration characteristics of corrugated laminated composite plates with axial stiffeners is investigated using the Rayleigh-Ritz method. The plate is stiffened by beams with open cross-section area. The equivalent homogenization model is used for the corrugated laminated composite plates. This homogenization model is treated a corrugated plate as an orthotropic plate that has different material properties in two perpendicular directions. The motion of equivalent plate is represented on the basis of the first order shear deformation theory (FSDT) to account for the effect of rotary inertia and transverse shear deformation. Stiffeners are considered as discrete elements to predict the local vibration mode to be generated by the presence of stiffeners. To validate the proposed analytical approach, natural frequencies and vibration mode shapes from the analytical method are compared with those from the FEA by ANSYS.

• Coupled systems mechanics
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• v.9 no.6
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• pp.499-519
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• 2020

The effect of porosity on the thermo-mechanical behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper using new refined hyperbolic shear deformation plate theory. Both even and uneven distribution of porosity are taken into account and the effective properties of FG plates with porosity are defined by theoretical formula with an additional term of porosity. The present formulation is based on a refined higher order shear deformation theory, which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the FG plate and takes into account the various distribution shape of porosity. The elastic foundation is described by the Winkler-Pasternak model. Anew modified power-law formulation is used to describe the material properties of FGM plates in the thickness direction. The closed form solutions are obtained by using Navier technique. The present results are verified in comparison with the published ones in the literature. The results show that the dimensionless and stresses are affected by the porosity volume fraction, constituent volume fraction, and thermal load.