• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.707-720
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• 2005

The bending stress formula that taking into account the transverse deformation is developed for plane-curved, untwisted isotropic beams subjected to loadings that result in deformations in the plane of curvature. In order to account the transverse Poisson contraction effect, a new constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved plate is derived in a $6{\times}6$ matrix form. This constitutive relation will provide the fundamental basis to the analyses of curved structures composing of isotropic or anisotropic materials. Then, the bending stress formula of a curved isotropic beam can be deduced from this newly developed curved plate theory. The stress predictions by the present analysis are compared to those by the analysis that neglected the Poisson contraction effect. The results show that the Poisson effect becomes more significant as the Poisson ratio and the curvature are getting larger.

• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.145-153
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• 2019

Modified couple stress formulation and first order shear deformation theory are used for magneto-electro-elastic bending analysis of three-layered curved size-dependent beam subjected to mechanical, magnetic and electrical loads. The governing equations are derived using a displacement field including radial and transverse displacements of middle surface and a rotation component. Size dependency is accounted based on modified couple stress theory by employing a small scale parameter. The numerical results are presented to study the influence of small scale parameter, initial electric and magnetic potentials and opening angle on the magneto-electro-elastic bending results of curved micro beam.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09b
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• pp.1146-1147
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• 2006

Diamond segments were fabricated by cold pressing and sintering under pressure at the temperature up to $750^{\circ}C$. Based on the results of this investigation, it can be concluded that the segments containing 39wt.% cobalt in the matrix material have the highest bending strength at a fracture probability of 50 % due to the weibull distribution method. According to the weibull statistics, it was also determined that the transverse rupture strength was the best for 39 wt.% cobalt ratio in the matrix material for the fracture probability when the other variables are the same.

• Smart Structures and Systems
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• v.29 no.3
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• pp.395-420
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• 2022

A new hybrid quasi-3D and 2D high-order shear deformation theory is studied in this mathematical formulation, for an investigation of the bending, free vibrations and buckling influences on a functionally graded material plate. The theoretical formulation has been begun by a displacement field of five unknowns, governing the transverse displacement across the thickness of the plate by bending, shearing and stretching. The transverse shear deformation effect has been taken into consideration, satisfying the stress-free boundary conditions, especially on plate free surfaces as parabolic variation through its thickness. Thus, the mechanical properties of the functionally graded plate vary across the plate thickness, following three distributions forms: the power law, exponential form and the Mori-Tanaka scheme. The mechanical properties are used to develop the equations of motion, obtained from the Hamilton principle, and solved by applying the Navier-type solution for simply supported boundary conditions. The results obtained are compared with other solutions of 2D, 3D and quasi-3D plate theories have been found in the literature.

• 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.

• Advances in aircraft and spacecraft science
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• v.3 no.2
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• pp.113-148
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• 2016

In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

• Progress in Superconductivity and Cryogenics
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• v.20 no.4
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• pp.31-35
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• 2018

When REBCO coated conductors (CCs) are applied to superconducting devices such as coils and magnets, they are subjected to deformation in various modes such as compression/tension bending, uniaxial/transverse tension and torsion. Despite outstanding performances by REBCO CC tapes, their electromechanical properties have been evaluated primarily under uniaxial tension, therefore data about the critical current ($I_c$) response in the compressive strain region are lacking. In this study, the characteristic responses of $I_c$ in REBCO CC tapes under bending strains in the range from tensile to compressive were evaluated. The springboard bending beam was used, wherein the CC tape sample was soldered onto the surface of the springboard. A Goldacker-type bending test rig, which lacks a support holding the sample during testing, was used as a comparator. Degradation in $I_c$ behaviors, including strain sensitivity, in differently processed REBCO CC tapes were examined based on the test rig used.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.10
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• pp.687-694
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• 2019

A circular composite spar in the wing of ultra-light aircraft is subjected to both bending moment and transverse shear loads. However, the beam being used in the aircraft may be inefficient because the design would not take into account the characteristics of the circular tube that supports the bending moment in top and bottom arc parts and the transverse load in left and right ones. Therefore, it is necessary to efficiently fabricate the circular tube beam by properly selecting the stacking sequences or the laminated composite structure. In order to increase both bending and transverse shear strengths of the beams, in this study, a cross-section of circular tube is divided into four arcs: top, bottom, left and right ones. The commercial program, MSC/NASTRAN is used to calculate vertical displacement and the normal and shear strains with variation of parameters such as division angle of arc and fiber orientation. Based on the results, the effective parameters for the new circular composite beam are presented to increase its bending and shear strengths.

• Steel and Composite Structures
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• v.44 no.5
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• pp.707-720
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• 2022

In the present work, bending and free vibration analyses of multilayered functionally graded (FG) graphene platelet (GPL) and fiber-reinforced hybrid composite beams are carried out using the parabolic function based shear deformation theory. Parabolic variation of transverse shear stress across the thickness of beam and transverse shear stress-free conditions at top and bottom surfaces of the beam are considered, and the proposed formulation incorporates a transverse displacement field. The present theory works only with four unknowns and is computationally efficient. Hamilton's principle has been employed for deriving the governing equations. Analytical solutions are obtained for both the bending and free vibration problems in the present work considering different variations of GPLs and fibers distribution, namely, FG-X, FG-U, FG-Λ, and FG-O for beams having simply-supported boundary condition. First, the matrix is assumed to be strengthened using GPLs, and then the fibers are embedded. Multiscale modeling for material properties of functionally graded graphene platelet/fiber hybrid composites (FG-GPL/FHRC) is performed using Halpin-Tsai micromechanical model. The study reveals that the distributions of GPLs and fibers have significant impacts on the stresses, deflections, and natural frequencies of the beam. The number of layers and shape factors widely affect the behavior of FG-GPL-FHRC beams. The multilayered FG-GPL-FHRC beams turn out to be a good approximation to the FG beams without exhibiting the stress-channeling effects.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2005.07a
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• pp.298-299
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• 2005

Differently from the tensile, transverse compression and torsion cases, the bending test of HTS tapes requires a lot of time and efforts, since the sample should be mounted successively onto bent sample holders in the order of decreasing radius and measuring the $I_c$ at each step. The influence of repeated cooling and warming experienced during these processes on the $I_c$ degradation can not be ignored. As a result, in this study, particularly. a new one-body type sample holder which provides continuous bending strains at 77K was devised. And, $I_c$ degradation behavior of Bi-2223 tapes under easy bending condition was investigated and compared that with other cases using Goldacker-type bending tester or respective sample holder.