• Advances in nano research
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• 제9권4호
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• pp.221-235
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• 2020

The following composition establishes a nonlocal strain gradient plate model that is essentially related to mass sensors laying on Winkler-Pasternak medium for the vibrational analysis from graphene sheets. To achieve a seemingly accurate study of graphene sheets, the posited theorem actually accommodates two parameters of scale in relation to the gradient of the strain as well as non-local results. Model graphene sheets are known to have double variant shear deformation plate theory without factors from shear correction. By using the principle of Hamilton, to acquire the governing equations of a non-local strain gradient graphene layer on an elastic substrate, Galerkin's method is therefore used to explicate the equations that govern various partition conditions. The influence of diverse factors like the magnetic field as well as the elastic foundation on graphene sheet's vibration characteristics, the number of nanoparticles, nonlocal parameter, nanoparticle mass as well as the length scale parameter had been evaluated.

• Steel and Composite Structures
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• 제28권1호
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• pp.13-24
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• 2018

A size-dependent novel hyperbolic shear deformation theory of simply supported functionally graded beams is presented in the frame work of the non-local strain gradient theory, in which the stress accounts for only the nonlocal strain gradients stress field. The thickness stretching effect (${\varepsilon}_z{\neq}0$) is also considered here. Elastic coefficients and length scale parameter are assumed to vary in the thickness direction of functionally graded beams according to power-law form. The governing equations are derived using the Hamilton principle. The closed-form solutions for exact critical buckling loads of nonlocal strain gradient functionally graded beams are obtained using Navier's method. The derived results are compared with those of strain gradient theory.

• Steel and Composite Structures
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• 제31권5호
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• pp.469-488
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• 2019

We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials.

• Advances in nano research
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• 제13권4호
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• pp.393-406
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• 2022

In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.

• Steel and Composite Structures
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• 제49권3호
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• pp.293-306
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• 2023

This article focuses on the study of the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity, based on the first shear deformation and higher-order theory of the tube. The nano-scale tube is simulated using the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as a higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. A parametric study is performed to investigate the effects of different parameters, such as axial and radial FG power indices, porosity parameter, and nonlocal gradient strain parameters, on the buckling behavior of the bi-dimensional functionally graded porous tube. Keywords: Nonlocal strain gradient theory; buckling; Zhang-Fu's tube model; Timoshenko theory; Two-dimensional functionally graded materials; Nanotubes; Higher-order theory.

• 한국전산구조공학회논문집
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• 제24권2호
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• pp.185-191
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• 2011

재료의 마이크로 스케일 해석에서 결정의 geometrically necessary dislocation(GND) 효과에 의한 소성 구배(plastic gradient)의 고려는 재료의 소성 거동에 큰 영향을 미칠 수 있다. 본 연구에서는 먼 거리(long range) 전위(dislocation)의 영향(또는 GND 효과)을 고려하여 소성 구배의 영향을 받는 다결정 고체(polycrystalline solids)의 거동을 유한요소해석을 이용하여 살펴보았다. 탄성(elastic)과 소성(plastic) 변형에 추가적으로 먼 거리 변형률(long range strain)을 고려한 항(term)이 포함된 변형 구배(deformation gradient)의 multiplicative decomposition 모델을 기반으로 하여 소성 구배 효과를 해석 모델에 포함하였다. 먼 거리 변형률에 의한 영향을 살펴보기 위해 구배 경화 계수(gradient hardness coefficient)와 먼거리 변형률 길이에 대한 재료 변수(parameter)가 사용되었다. 각각의 계수들이 다결정 고체의 거동에 미치는 영향을 확인하기 위해 두 변수의 적용에 따른 다결정 고체의 거동을 분석하였다. 단결정 및 다결정 재료의 GND 효과에 의한 소성 구배를 고려해서, 고려하지 않은 경우와 비교하여 발생하는 경화(hardening)의 차이를 분석함으로서 GND의 다결정 고체 거동의 영향을 확인하였다.

• 마이크로전자및패키징학회지
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• 제26권4호
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• pp.47-53
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• 2019

Polydimethylsiloxane (PDMS)를 베이스 기판으로 사용하고 이보다 강성도가 높은 polytetrafluoroethylene(PTFE)를 island 기판으로 사용한 soft PDMS/hard PDMS/PTFE 구조의 강성도 경사형 신축 패키지를 형성하고, 이의 신축변형에 따른 저항특성을 분석하였다. PDMS/PTFE 기판패드에 50 ㎛ 직경의 칩 범프들을 anisotropic conductive paste를 사용하여 실장한 플립칩 접속부는 96 mΩ의 평균 접속저항을 나타내었다. Soft PDMS/hard PDMS/PTFE 구조의 신축 패키지를 30% 변형률로 인장시 PTFE의 변형률이 1%로 억제되었으며, PTFE 기판에 형성한 회로저항의 중가는 1%로 무시할 정도였다. 0~30% 범위의 신축변형 싸이클을 2,500회 반복시 회로저항이 1.7% 증가하였다.

• Structural Engineering and Mechanics
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• 제44권2호
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• pp.139-161
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• 2012

In this paper, the static behavior of bi-directional functionally graded (FG) non-uniform thickness circular plate resting on quadratically gradient elastic foundations (Winkler-Pasternak type) subjected to axisymmetric transverse and in-plane shear loads is carried out by using state-space and differential quadrature methods. The governing state equations are derived based on 3D theory of elasticity, and assuming the material properties of the plate except the Poisson's ratio varies continuously throughout the thickness and radius directions in accordance with the exponential and power law distributions. The stresses and displacements distribution are obtained by solving state equations. The effects of foundation stiffnesses, material heterogeneity indices, geometric parameters and loads ratio on the deformation and stress distributions of the FG circular plate are investigated in numerical examples. The results are reported for the first time and the new results can be used as a benchmark solution for future researches.

• 전기화학회지
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• 제8권1호
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• pp.47-54
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• 2005

This article covers the fundamentals of stress-induced diffusion, focusing on the theoretical model for hydrogen transport through self-stressed electrode. First, the relationship between hydrogen diffusion and macroscopic deformation of the electrode specimen was briefly introduced, and then it was classified into the diffusion-elastic and elasto-diffusive phenomena. Next, the transport equation for the flux of hydrogen caused simultaneously by both the concentration gradient and the stress gradient was theoretically derived. Finally, stress-induced diffusion was discussed on the basis of the numerical solutions to the derived transport equation under the permeable and impermeable boundary conditions.

• Advances in nano research
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• 제5권4호
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• pp.393-414
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• 2017

Forced vibration behavior of porous metal foam nanoplates on elastic medium is studied via a 4-variable plate theory. Different porosity distributions called uniform, symmetric and asymmetric are considered. Nonlocal strain gradient theory (NSGT) containing two scale parameters is employed for size-dependent modeling of porous nanoplates. The present plate theory satisfies the shear deformation effect and it has lower field variables compared with first order plate theory. Hamilton's principle is employed to derive the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, dynamic loading, porosity distributions and porosity coefficient on dynamic deflection and resonance frequencies of metal foam nanoscale plates are examined.