• Steel and Composite Structures
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• 제24권6호
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• pp.727-740
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• 2017

The present paper studies the stability analysis of the continuously graded CNT-Reinforced Composite (CNTRC) panel stiffened by rings and stringers. The Stiffened Panel (SP) subjected to axial and lateral loads is reinforced by agglomerated CNTs smoothly graded through the thickness. A two-parameter Eshelby-Mori-Tanaka (EMT) model is adopted to derive the effective material moduli of the CNTRC. The stability equations of the CNRTC SP are obtained by means of the adjacent equilibrium criterion. Notwithstanding most available literature in which the stiffener effects were smeared out over the respective stiffener spacing, in the present work, the stiffeners are modeled as Euler-Bernoulli beams. The Generalized Differential Quadrature Method (GDQM) is employed to discretize the stability equations. A numerical study is performed to investigate the influences of different types of parameters involved on the critical buckling of the SP reinforced by agglomerated CNTs. The results achieved reveal that continuously distributing of CNTs adjacent to the inner and outer panel's surface results in improving the stiffness of the SP and, as a consequence, inclining the critical buckling load. Furthermore, it has been concluded that the decline rate of buckling load intensity factor owing to the increase of the panel angle is significantly more sensible for the smaller values of panel angle.

• 한국안전학회지
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• 제9권3호
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• pp.3-12
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• 1994

This study employed the Eshelby's equivalent inclusion method incorporated with mean field theory to investigate the Internal stress of short fiber-reinforced metal matrix composites during static loading and the dynamic finite element analysis by using alternative unit cell model to investigate the impact behaviors during the impact loading. Using the 2124 Al-SiC system as an example, the general effects of parameters such as fiber's aspect ratio, content and modulus were examined.

• Steel and Composite Structures
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• 제20권3호
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• pp.623-649
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• 2016

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.56-59
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• 2008

This paper presents results of a parametric study for a constitutive model (Lee et ai, 1989) for particle-reinforced composites considering weakened interfaces and crack nucleation. Eshelby's tensors for particles with imperfect interfaces (Ju and Chen, 1994) and microcracks (Sun and Ju, 2004) are incorporated into a micromechanical formulation. A parametric study for the microcrack nucleation parameter ${\phi}_{{\upsilon}0}$ and ${\epsilon}^{th}$ is conducted to investigate the sensitivity of the parameter to the constitutive model.

• Composites Research
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• 제36권1호
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• pp.16-24
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• 2023

본 논문에서는 복합재료의 섬유와 기지사이의 경계면 손상을 고려한 멀티스케일 점진적 피로 손상 모델을 제안한다. 먼저 점진적인 경계면 손상을 고려하기 위해 서로 다른 4개의 경계면 상태를 정의한 미소구조 모델을 도입하였다. 각각의 상태에 대한 부피분율은 피로 하중의 사이클 수가 증가함에 따라 온전한 상태의 계면에서 완전 박리 상태의 계면으로의 전환이 일어난다. 손상된 경계면의 에쉘비 텐서(Eshelby's tensor)를 계산하기 위해 선형 스프링 모델이 사용되었으며 균질화 방법을 통해 복합재료의 유효 물성을 얻었다. 또한 복합재료의 피로거동을 묘사하기 위해 교번 응력에 대한 섬유, 기지, 그리고 섬유-기지 간의 계면 각각에 대한 손상 변수들이 정의되었고 이를 chaotic firefly 알고리즘을 통해 손상 변수를 특성화 하였다. 제안된 모델은 유한요소해석프로그램 ABAQUS의 UMAT subroutine으로 구현되어 AS4/3501-6 복합재료의 단일방향 라미네이트(unidirectional laminate) 시편들([0]₈, [90]₈,[30]₁₆)을 통해 성공적으로 검증되었다.

• 비파괴검사학회지
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• 제17권2호
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• pp.89-99
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• 1997

단섬유강화금속복합재료는 최근 항공기, 자동차산업에 있어서 관심의 대상이 되고 있는 재료중의 하나이나 재료의 제조 및 성형중에 재료내의 기지재 및 강화재의 열팽창계수의 차이로 인해 재료 내부에 발생되는 열적잔류응력으로 인한 재료 특성의 변화로 실제적인 재료 적용상에 많은 문제점들이 보고되고 있다. 이와 같은 금속복합재료의 잔류응력의 평가에는 몇가지 비파괴적 방법이 적용되고 있으나 그 측정에 많은 어려움이 보고되고 있다. 따라서 금속복합재료의 보다 실제적인 응용을 위하여는 이와 같은 열적잔류응력을 평가하기 위한 이론적모델의 확립이 요구된다. 본 연구에 있어서는 비방향성을 가진 강화재가 2차원 평면 상태로 기지재내에 존재하는 단섬유강화금속복합재료에 있어서 재료에 균일한 온도 변화가 주어질 때 기지재와 강화재의 열팽창계수의 차로 인해 재료 내부에 발생하는 열적잔류응력을 평가, 예측하기 위한 이론적 탄성 모델을 확립하고자 한다. 본 연구에서 해석하고자 하는 이론 모델은 Eshelby의 등가 개재물 방법을 토대로 하고 있으며 과거 제안되고 있는 이론모델을 포함하는 보다 일반성을 가지는 해석 모델로서, 이 해석 모델을 이용하여 열적잔류응력에 미치는 강화재의 체적률, 종횡비, 분포 상태, 분포 cut-off 각도들에 대한 각 인자의 영향을 검토하였다. 그 결과 강화재의 체적률, 종횡비, cut-off 각도들이 강화재의 분포 상태보다도 금속복합재료의 열적잔류응력에 미치는 영향이 현저함을 알 수 있었다.

• Advances in aircraft and spacecraft science
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• 제5권1호
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• pp.21-49
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• 2018

In this paper, geometric nonlinear bending characteristics of single wall carbon nanotube reinforced composite (SWCNTRC) doubly curved shell panels subjected to uniform transversely loadings are investigated. The nonlinear mathematical model is developed for doubly curved SWCNTRC shell panel on the basis of higher-order shear deformation theory and Green- Lagrange nonlinearity. All nonlinear higher order terms are included in the mathematical model. The effective material properties of SWCNTRC are estimated by using Eshelby-Mori-Tanaka micromechanical approach. The governing equation of the shell panel is obtained using the total potential energy principle and a Newton-Raphson iterative method is employed to compute the nonlinear displacement and stresses. The present results are compared with published literature. The effect of SWCNT volume fraction, width-to-thickness ratio, radius-to-width ratio (R/a), boundary condition, linear and nonlinear deflection, stresses and different types of shell geometry on nonlinear bending response is investigated.

• Interaction and multiscale mechanics
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• 제2권3호
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• pp.321-332
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• 2009

Recent development in composites containing phase-transforming particles, such as vanadium dioxide or barium titanate, reveals the overall stiffness and viscoelastic damping of the composites may be unbounded (Lakes et al. 2001, Jaglinski et al. 2007). Negative stiffness is induced from phase transformation predicted by the Landau phase transformation theory. Although this unbounded phenomenon is theoretically supported with the composite homogenization theory, detailed stress analyses of the composites are still lacking. In this work, we analyze the stress distribution of the Hashin-Shtrikman (HS) composite and its two-dimensional variant, namely a circular inclusion in a square plate, under the assumption that the Young's modulus of the inclusion is negative. Assumption of negative stiffness is a priori in the present analysis. For stress analysis, a closed form solution for the HS model and finite element solutions for the 2D composite are presented. A static loading condition is adopted to estimate the effective modulus of the composites by the ratio of stress to average strain on the loading edges. It is found that the interfacial stresses between the circular inclusion and matrix increase dramatically when the negative stiffness is so tuned that overall stiffness is unbounded. Furthermore, it is found that stress distributions in the inclusion are not uniform, contrary to Eshelby's theorem, which states, for two-phase, infinite composites, the inclusion's stress distribution is uniform when the shape of the inclusion has higher symmetry than an ellipse. The stability of the composites is discussed from the viewpoint of deterioration of perfect interface conditions due to excessive interfacial stresses.

• 대한기계학회논문집A
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• 제26권3호
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• pp.553-559
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• 2002

Carbon-fiber which has very small radial dimension makes us difficult to measure it's properties. So in this paper, we suggest a simple method to measure the thermal conductivity of a carbon-fiber's and carbon-fiber-reinforced-plastics(CFRP) laminates. The thermal conductivity of CFRP laminates was measured experimentally at the same time analytically. The experimental model is based on the one-dimensional analysis of fin sample because CFRP laminates has a thin geometric configuration. The analytical model to measure the thermal conductivity of carbon-fiber is expressed by use of mean-field model which is based on Eshelby's elliptical inclusion problem. Therefore the thermal conductivity of angle-ply laminates can be computed by use of effective longitudinal and transverse thermal conductivities of unidirectional composite of the constituents.

• 대한기계학회논문집
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• 제5권2호
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• pp.101-109
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• 1981

균일 인장하중하에 있는 고체 내부에 고립된 제 1형 탄소성 크랙의 반취성 파괴를 경사슬립밴드모델(inclined slip band model)로서 연속크랙전위(conticuum crack dislocation) 및 연속격자 전위(continum lattice dislocation)을 이용하여 이론적으로 연구하였다. 크랙전위 및 격자전위에 관한 힘평형을 나타애는 연립특이적분방정식의 해는크랙전위 및 격자전위에 관한 적정밀도함수를 가지고 특이함을 해소하는 조건을 부가하여 얻는다. 이특이항 해소조건의 타당성은 처음으로 소성영역의 크기를 그 판단기준으로 검토되었으며, 그결과 합당한 것으로 확인되었다. 또한 상기방법으로부터 산출된 COD는 소규모 성역을 넘어서도 선형적으로 .KAPPA.$^{2}$.EPSILON..sigma.$_{Y}$ 에 따라 변화함을 알게 된다. 상기모델에서 위축적분경로(Shrunk path) 상의 J 적분치를 J=.delta..sigma.$_{Y/}$sin2.theta.의 형태로 유도하였는데, 이것은 J 적분에 관한 Eshelby의 힘개념을 구체적으로 표현한다: J는 크랙전파방향으로 탄소성크랙정점에 작용하는 가상적인 힘이며, 1/2 J의 한 슬립편면상에서의 분력은 그 슬립정면사으이 보든 격자전위에 작용하는 전단력의 총화와 같다. 같다.