• Earthquakes and Structures
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• v.17 no.3
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• pp.257-270
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• 2019

The purpose of this work is to analyze the bending behavior of laminated composite plates using the refined fourvariable theory and the finite element method approach using an ANSYS 12 computational code. The analytical model is based on the multilayer plate theory of shear deformation of the nth-order proposed by Xiang et al 2011 using the theory principle developed by Shimpi and Patel 2006. Unlike other theories, the number of unknown functions in the present theory is only four, while five or more in the case of other theories of shear deformation. The formulation of the present theory is based on the principle of virtual works, it has a strong similarity with the classical theory of plates in many aspects, it does not require shear correction factor and gives a parabolic description of the shear stress across the thickness while filling the condition of zero shear stress on the free edges. The analysis is validated by comparing results with those in the literature.

• Coupled systems mechanics
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• v.13 no.4
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• pp.277-291
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• 2024

The objective of this work is to study the effects of the modification of material properties on the vibration of the FGM beam using an integral shear strain model. In the present theory, the rotational displacement is replaced by an integral term in the displacement fields. The use of a shear correction factor is not necessary because our model gives a parabolic description of shear stress through the thickness while satisfying the conditions of zero shear stresses on the bottom and top surfaces of the beam. The FGM beam is assumed that the beam is a mixture of metal and ceramic, and that its properties change depending on the power functions of the thickness of the beam such as: linear, quadratic, cubic and inverse quadratic. By applying Hamilton's principle, general formulas were obtained to obtain the frequencies of the FGM beam. The effects of changing compositional characteristics of materials presented by volume fraction of FGM beams with simply supported edges on free vibration and some mode shapes are investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.5
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• pp.489-495
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• 2009

A novel technique to measuret of viscoelastic properties of polymers is proposed to investigate complex Poisson's ratio as a function of frequency. The forced vibration responses for the samples under the normal and the shear deformation are to be measured with varying load masses. The measured data were used to obtain the viscoelastic properties of the material based on an accurate 2D numerical deformation model of the sample. The 2D model enabled us to exclude data correction by the empirical form factor used in 1D model. Comprehensive measurements of viscoelastic properties of two slightly varied silicone RTV rubber ($Silastic^{(R)}$ S2) compositions were performed. Standard composition (90% PDMS polymer + 10% catalyst) and modified composition (92.5% polymer + 7.5% catalyst) were tested in temperature range from $30^{\circ}C$ to $70^{\circ}C$. Shear modulus, modulus of elasticity, loss factor, and both the real and the imaginary parts of the Poisson's ratio were determined for frequencies from 50 to 400Hz in the linear deformation regime (at relative deformations $10^{-4}{\sim}10^{-3}$).

• Steel and Composite Structures
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• v.17 no.1
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• pp.21-46
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• 2014

This paper presents a simple n-order four variable refined theory for the bending and vibration analyses of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

• Steel and Composite Structures
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• v.15 no.4
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• pp.399-423
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• 2013

In the present study, the thermal buckling behavior of functionally graded sandwich plates is studied using a new hyperbolic displacement model. Unlike any other theory, the theory is variationally consistent and gives four governing equations. Number of unknown functions involved in displacement field is only four, as against five in case of other shear deformation theories. This present model takes into account the parabolic distribution of transverse shear stresses and satisfies the condition of zero shear stresses on the top and bottom surfaces without using shear correction factor. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates.

• Steel and Composite Structures
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• v.13 no.1
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• pp.91-107
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• 2012

In this research, mechanical buckling of hybrid functionally graded plates is considered using a new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. The effectiveness of the theories is brought out through illustrative examples.

• Structural Engineering and Mechanics
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• v.56 no.2
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• pp.223-240
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• 2015

In this work, a nonlocal quasi-3D trigonometric plate theory for micro/nanoscale plates is proposed. In order to introduce the size influences, the Eringen's nonlocal elasticity theory is utilized. In addition, the theory considers both shear deformation and thickness stretching effects by a trigonometric variation of all displacements within the thickness, and respects the stress-free boundary conditions on the top and bottom surfaces of the plate without considering the shear correction factor. The advantage of this theory is that, in addition to considering the small scale and thickness stretching effects (${\varepsilon}_z{\neq}0$), the displacement field is modelled with only 5 unknowns as the first order shear deformation theory (FSDT). Analytical solutions for vibration of simply supported micro/nanoscale plates are illustrated, and the computed results are compared with the available solutions in the literature and finite element model using ABAQUS software package. The influences of the nonlocal parameter, shear deformation and thickness stretching on the vibration behaviors of the micro/nanoscale plates are examined.

• Advances in aircraft and spacecraft science
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• v.6 no.5
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• pp.409-426
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• 2019

The aim of the present work is to study the nonlinear behavior of the laminated composite plates under transverse sinusoidal loading using a new inverse trigonometric shear deformation theory, where geometric nonlinearity in the Von-Karman sense is taken into account. In the present theory, in-plane displacements use an inverse trigonometric shape function to account the effect of transverse shear deformation. The theory satisfies the traction free boundary conditions and violates the need of shear correction factor. The governing equations of equilibrium and boundary conditions associated with present theory are obtained by using the principle of minimum potential energy. These governing equations are solved by eight nodded serendipity element having five degree of freedom per node. A square laminated composite plate is considered for the geometrically linear and nonlinear formulation. The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses. Finite element Codes are developed using MATLAB. The present results are compared with previously published results. It is concluded that the geometrically linear and nonlinear response of laminated composite plates predicted by using the present inverse trigonometric shape function is in excellent agreement with previously published results.

• Computers and Concrete
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• v.27 no.1
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• pp.73-83
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• 2021

In this article, the mechanical buckling analysis of simply-supported functionally graded plates is carried out using a higher shear deformation theory (HSDT) in conjunction with the stress function method. The proposed formulation is variationally consistent, does not use a shear correction factor and gives rise to a variation of transverse shear stress such that the transverse shear stresses vary parabolically through the thickness satisfying the surface conditions without stress of shear. The properties of the plate are supposed to vary across the thickness according to a simple power law variation in terms of volume fraction of the constituents of the material. Numerical results are obtained to study the influences of the power law index and the geometric ratio on the critical buckling load.

• 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.