• Geomechanics and Engineering
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• v.8 no.3
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• pp.305-321
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• 2015

In this paper, a new hyperbolic shear deformation plate theory based on neutral surface position is developed for the static analysis of functionally graded plates (FGPs). The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present new hyperbolic shear deformation plate theory and the neutral surface concept, the governing equations of equilibrium are derived from the principle of virtual displacements. Numerical illustrations concern flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Advances in nano research
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• v.5 no.2
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• pp.113-126
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• 2017

This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.

• Earthquakes and Structures
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• v.16 no.2
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• pp.177-183
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• 2019

In this paper, a new refined hyperbolic shear deformation beam theory for the bending analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the bending response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equilibrium equations are derived from the principle of virtual work. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG beams.

• Structural Engineering and Mechanics
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• v.84 no.6
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• pp.707-722
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• 2022

In this study, a new refined hyperbolic shear deformation theory (RHSDT) is developed using an equivalent single-layer shell displacement model for the static bending and free vibration response of cross-ply laminated composite spherical shells. It is based on a new kinematic in which the transverse displacement is approximated as a sum of the bending and shear components, leading to a reduction of the number of unknown functions and governing equations. The proposed theory uses the hyperbolic shape function to account for an appropriate distribution of the transverse shear strains through the thickness and satisfies the boundary conditions on the shell surfaces without requiring any shear correction factors. The shell governing equations for this study are derived in terms of displacement from Hamilton's principle and solved via a Navier-type analytical procedure. The validity and high accuracy of the present theory are ascertained by comparing the obtained numerical results of displacements, stresses, and natural frequencies with their counterparts generated by some higher-order shear deformation theories. Further, a parametric study examines in detail the effect of both geometrical parameters (i.e., side-to-thickness ratio and curvature-radius-to-side ratio), on the bending and free vibration response of simply supported laminated spherical shells, which can be very useful for many modern engineering applications and their optimization design.

• 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.

• Steel and Composite Structures
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• v.18 no.6
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• pp.1493-1515
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• 2015

A new refined hyperbolic shear deformation theory (RHSDT), which involves only four unknown functions as against five in case of other shear deformation theories, is presented for the thermoelastic bending analysis of functionally graded sandwich plates. 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 sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson's ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. The influences played by the transverse shear deformation, thermal load, plate aspect ratio and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded metal-ceramic plates are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of functionally graded plates.

• Advances in nano research
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• v.10 no.3
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• pp.281-293
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• 2021

This paper presents a new nonlocal Hyperbolic Shear Deformation Beam Theory (HSDBT) for the free vibration of porous Functionally Graded (FG) nanobeams. A new displacement field containing integrals is proposed which involves only three variables. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect and its account for shear deformation by a hyperbolic variation of all displacements through the thickness without using the shear correction factor. It has been observed that during the manufacture of Functionally Graded Materials (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the free vibration analysis of FG beams taking into account the influence of these imperfections is established. Four different porosity types are considered for FG nanobeam. Material characteristics of the FG beam are supposed to vary continuously within thickness direction according to a power-law scheme which is modified to approximate material characteristics for considering the influence of porosities. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio, and the porosity types on the dynamic responses of the nanobeam are discussed.

• 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.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• Structural Engineering and Mechanics
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• v.69 no.3
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• pp.335-345
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• 2019

In present study, a novel refined hyperbolic shear deformation theory is proposed for the buckling analysis of thick isotropic plates. The new displacement field is constructed with only two unknowns, as against three or more in other higher order shear deformation theories. However, the hyperbolic sine function is assigned according to the shearing stress distribution across the plate thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using any shear correction factors. The equations of motion associated with the present theory are obtained using the principle of virtual work. The analytical solution of the buckling of simply supported plates subjected to uniaxial and biaxial loading conditions was obtained using the Navier method. The critical buckling load results for thick isotropic square plates are compared with various available results in the literature given by other theories. From the present analysis, it can be concluded that the proposed theory is accurate and efficient in predicting the buckling response of isotropic plates.