• Steel and Composite Structures
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• v.13 no.2
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• pp.157-169
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• 2012

Shell structures are very interesting from the design point of view and these are well recognized in the scientific literature. In this paper the analysis of the buckling loads and stability paths of a sandwich conical shell with unsymmetrical faces under combined load based on the assumptions of moderately large deflections (geometrically nonlinear theory) is considered and elastic-plastic properties of the material of the faces are taken into considerations. External load is assumed to be two-parametrical one and it is assumed that the shell deforms into the plastic range before buckling. Constitutive relations in the analysis are those of the Nadai-Hencky deformation theory of plasticity and Prandtl-Reuss plastic flow theory with the H-M-H (Huber-Mises-Hencky) yield condition. The governing stability equations are obtained by strain energy approach and Ritz method is used to solve the equations with the help of analytical-numerical methods using computer.

• Advances in nano research
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• v.7 no.4
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• pp.265-275
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• 2019

In this work, the effect of size on the axial buckling behavior of single-layered graphene sheets embedded in elastic media is studied. We incorporate Eringen's nonlocal elasticity equations into three plate theories of first order shear deformation theory, higher order shear deformation theory, and classical plate theory. The surrounding elastic media are simulated using Pasternak and Winkler foundation models and their differences are evaluated. The results obtained from different nonlocal plate theories include the values of Winkler and Pasternak modulus parameters, mode numbers, nonlocal parameter, and side lengths of square SLGSs. We show here that axial buckling behavior strongly depends on modulus and nonlocal parameters, which have different values for different mode numbers and side lengths. In addition, we show that in different nonlocal plate theories, nonlocality is more influential in first order shear deformation theory, especially in certain range of nonlocal parameters.

• Advances in nano research
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• v.7 no.1
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• pp.1-11
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• 2019

In this article, wave propagation characteristics in magneto-electro-elastic (MEE) nanotube considering shell model is studied in the framework nonlocal theory. To account for the small-scale effects, the Eringen's nonlocal elasticity theory of is applied. Nonlocal governing equations of MEE nanotube have been derived utilizing Hamilton's principle. The results of this investigation have been accredited by comparing them of previous studies. An analytical solution of governing equations is used to obtain phase velocities and wave frequencies. The influences of different parameters, such as different mode, nonlocal parameter, length parameter, geometry, magnetic field and electric field on wave propagation responses of MEE nanotube are expressed in detail.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.833-838
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• 2003

The problem of elastic wave resonance scattering from elastic targets is studied in this paper. A new resonance formalism to extract the elastic resonance information of the target from scattered elastic waves is introduced. The proposed resonance formalism is an extension of the works developed for acoustic wave scattering problems by the author. The classical resonance scattering theory computes reasonable magnitude information of the resonances in each partial wave, but the phase behaves in somewhat irregular way, therefore, is not clearly explainable. The proposed method is developed to obtain physically meaningful magnitude and phase of the resonances. As an example problem, elastic wave scattering from an infinitely-long elastic cylinder was analyzed by the proposed method and compared to the results by RST. In case of no mode conversion, both methods generate identical magnitude. However, the new method computes exact $\pi$ radian phase shills through resonances and anti-resonances while RST produces physically unexplainable phases. In case of mode conversion, in addition to the phase even magnitudes are different. The phase shifts through resonances and antiresonances obtained by the proposed method are not exactly $\pi$ radians due to energy leak by mode conversion. But, the phases by the proposed method show reasonable and intuitively correct behavior compared to those by RST.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.5
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• pp.405-413
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• 2017

In this paper, we study the biaxial buckling analysis of nonlocal MEE(magneto-electro-elastic) nano plates based on the first-order shear deformation theory. The in-plane electric and magnetic fields can be ignored for MEE(magneto-electro-elastic) nano plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the MME plate is determined. In order to reformulate the elastic theory of MEE(magneto-electro-elastic) nano-plate, the nonlocal differential constitutive relations of Eringen is used. Using the variational principle, the governing equations of the nonlocal theory are discussed. The relations between nonlocal and local theories are investigated by computational results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on structural responses are studied. Computational results show the effects of the electric and magnetic potentials. These computational results can be useful in the design and analysis of advanced structures constructed from MEE(magneto-electro-elastic) materials and may be the benchmark test for the future study.

• Advances in materials Research
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• v.5 no.4
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• pp.245-261
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• 2016

Thermo-mechanical buckling problem of functionally graded (FG) nanoplates supported by Pasternak elastic foundation subjected to linearly/non-linearly varying loadings is analyzed via the nonlocal elasticity theory. Two opposite edges of the nanoplate are subjected to the linear and nonlinear varying normal stresses. Elastic properties of nanoplate change in spatial coordinate based on a power-law form. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. The equations of motion for an embedded FG nanoplate are derived by using Hamilton principle and Eringen's nonlocal elasticity theory. Navier's method is presented to explore the influences of elastic foundation parameters, various thermal environments, small scale parameter, material composition and the plate geometrical parameters on buckling characteristics of the FG nanoplate. According to the numerical results, it is revealed that the proposed modeling can provide accurate results of the FG nanoplates as compared some cases in the literature. Numerical examples show that the buckling characteristics of the FG nanoplate are related to the material composition, temperature distribution, elastic foundation parameters, nonlocality effects and the different loading conditions.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.589-604
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• 2005

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analysis. For this, the displacement field is expressed by introducing displacement parameters defined at the centroid and shear center axes, respectively. Next the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are rigorously derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to the solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Smart Structures and Systems
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• v.18 no.4
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• pp.755-786
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• 2016

The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.1033-1039
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• 2006

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analyses. For this, the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to tl1e solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Advances in nano research
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• v.12 no.2
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• pp.117-137
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• 2022

Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.