• Steel and Composite Structures
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• v.43 no.1
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• pp.31-54
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• 2022

This paper is concerned with the buckling behavior of functionally graded graphene reinforced porous nanocomposite beams based on the finite element method (FEM) using two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element, and then the critical buckling load is calculated with different porosity distributions and GPL dispersion patterns. After a convergence and validation study to verify the accuracy of the present model, a comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern of GPL reinforcements on the Buckling behavior of the nanocomposite beam. The effects of various structural parameters such as the dispersion patterns for the graphene and porosity, thickness ratio, boundary conditions, and nonlocal and strain gradient parameters are brought out. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams, and the results allows to identify the most effective way to achieve improved buckling behavior of the porous nanocomposite beam.

• Advances in nano research
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• v.10 no.2
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• pp.175-189
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• 2021

In this article, frequency characteristics, and sensitivity analysis of a size-dependent laminated composite cylindrical nanoshell under bi-directional thermal loading using Nonlocal Strain-stress Gradient Theory (NSGT) are presented. The governing equations of the laminated composite cylindrical nanoshell in thermal environment are developed using Hamilton's principle. The thermodynamic equations of the laminated cylindrical nanoshell are obtained using First-order Shear Deformation Theory (FSDT) and Fourier-expansion based Generalized Differential Quadrature element Method (FGDQM) is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The novelty of the current study is to consider the effects of bi-directional temperature loading and sensitivity parameter on the critical temperature and frequency characteristics of the laminated composite nanostructure. Apart from semi-numerical solution, a finite element model was presented using the finite element package to simulate the response of the laminated cylindrical shell. The results created from finite element simulation illustrates a close agreement with the semi-numerical method results. Finally, the influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature, sensitivity, and frequency of the laminated composite nanostructure are investigated, in details.

• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.141-151
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• 2020

This manuscript tends to investigate influences of nanoscale and surface energy on a static bending and free vibration of piezoelectric perforated nanobeam structural element, for the first time. Nonlocal differential elasticity theory of Eringen is manipulated to depict the long-range atoms interactions, by imposing length scale parameter. Surface energy dominated in nanoscale structure, is included in the proposed model by using Gurtin-Murdoch model. The coupling effect between nonlocal elasticity and surface energy is included in the proposed model. Constitutive and governing equations of nonlocal-surface perforated Euler-Bernoulli nanobeam are derived by Hamilton's principle. The distribution of electric potential for the piezoelectric nanobeam model is assumed to vary as a combination of a cosine and linear variation, which satisfies the Maxwell's equation. The proposed model is solved numerically by using the finite-element method (FEM). The present model is validated by comparing the obtained results with previously published works. The detailed parametric study is presented to examine effects of the number of holes, perforation size, nonlocal parameter, surface energy, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric perforated nanobeams. It is found that the effect of surface stresses becomes more significant as the thickness decreases in the range of nanometers. The effect of number of holes becomes significant in the region 0.2 ≤ α ≤ 0.8. The current model can be used in design of perforated nano-electro-mechanical systems (PNEMS).

• Smart Structures and Systems
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• v.25 no.2
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• pp.219-228
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• 2020

This work presents a modified continuum model to explore and investigate static and vibration behaviors of perforated piezoelectric NEMS structure. The perforated nanostructure is modeled as a thin perforated nanobeam element with Euler-Bernoulli kinematic assumptions. A size scale effect is considered by included a nonlocal constitutive equation of Eringen in differential form. Modifications of geometrical parameters of perforated nanobeams are presented in simplified forms. To satisfy the Maxwell's equation, the distribution of electric potential for the piezoelectric nanobeam model is assumed to be varied as a combination of a cosine and linear functions. Hamilton's principle is exploited to develop mathematical governing equations. Modified numerical finite model is adopted to solve the equation of motion and equilibrium equation. The proposed model is validated with previous respectable work. Numerical investigations are presented to illustrate effects of the number of perforated holes, perforation size, nonlocal parameter, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric nanobeams.

• Advances in nano research
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• v.15 no.5
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• pp.411-422
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• 2023

In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.914-921
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• 2006

To describe the effect of the numerous and various oriented microcracks on the compressive and tensile concrete behaviors, the directional nonlocality is defined. The plasticity model using multiple failure criteria is developed for RC planar members in tension-compression. The crack damages are defined in the pre-determined reference orientations, and then the total crack damage is calculated by integrating multi-oriented crack damages. To describe the effect of directional nonlocality on the anisotropic tensile damage, based on the existing test results, the nonlocal damage factor is defined in each reference orientation. The reduced compressive strength in the cracked concrete is defined by the multi-oriented crack damages defined as excluding the tensile normal plastic strain from the compressive equivalent plastic strain. The proposed model is implemented to finite element analysis, and it is verified by comparisons with various existing panel test results.

• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.89-98
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• 2019

In this study, the mechanical bending behaviors of functionally graded porous nanobeams are investigated. Four types of porosity which are, the classical power porosity function, the symmetric with mid-plane cosine function, bottom surface distribution and top surface distribution are proposed in analysis of nanobeam for the first time. A comparison between four types of porosity are illustrated. The effect of nano-scale is described by the differential nonlocal continuum theory of Eringen by adding the length scale into the constitutive equations as a material parameter comprising information about nanoscopic forces and its interactions. The graded material is designated by a power function through the thickness of nanobeam. The beam is simply-supported and is assumed to be thin, and hence, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Numerical results show effects of porosity type, material graduation, and nanoscale parameters on the static deflection of nanobeam.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.225-228
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• 2008

In case of nonlinear analysis for reinforced concrete structure, the characteristics of the failure, which are depend on loading conditions, such as tension splitting, compression crushing and shear distortion should be considered. On the analytical evaluation for the failure behavior of these, the finite element techniques is the most widely used. After the maximum load, however, an analytical results by finite element technique are depending on the size of the element. In this study, integral nonlocal model which is one of those study for overcoming the element sensitivity and dependancy, used for the failure analysis of box culvert specimen. Comparing on the experimental and analytical results, validity and reliability of integral nonlocal model are investigate.

• Advances in nano research
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• v.9 no.2
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• pp.91-104
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• 2020

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e₀a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

• Journal of the Korea Concrete Institute
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• v.19 no.5
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• pp.655-664
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• 2007

The inherent characteristic of concrete tensile cracks, directional nonlocal crack damage, causes so-called rotating tensile crack damage and softening of compressive strength. In the present study, a plasticity model was developed to describe the behavior of reinforced concrete planar members In tension-compression. To describe the effect of directional nonlocal crack damage, the concept of microplane model was combined with the plasticity model. Unlike existing models, in the proposed model, softening of compressive strength as well as the tensile crack damage were defined by the directional nonlocal crack damage. Once a tensile cracking occurs, the microplanes of concrete are affected by the nonlocal crack damage. In the microplanes, microscopic tension and compression failure surfaces are calculated. By integrating the microscopic failure surfaces, the macroscopic failure surface is calculated. The proposed model was implemented to finite element analysis, and it was verified by comparisons with the results of existing shear panel tests.