• Title/Summary/Keyword: linear elastic analysis

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Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation

  • Mohamed, Nazira;Eltaher, Mohamed A.;Mohamed, Salwa A.;Seddek, Laila F.
    • Structural Engineering and Mechanics
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    • v.70 no.6
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    • pp.737-750
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    • 2019
  • This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young's modulus and Poisson's ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integropartial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton's method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

Dynamic response of a linear two d.o.f system visco-elastically coupled with a rigid block

  • Di Egidio, Angelo;Pagliaro, Stefano;Fabrizio, Cristiano;de Leo, Andrea M.
    • Coupled systems mechanics
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    • v.8 no.4
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    • pp.351-375
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    • 2019
  • The present work investigates the use of a rigid rocking block as a tool to reduce vibrations in a frame structure. The study is based on a simplified model composed by a 2-DOF linear system, meant to represent a general M-DOF frame structure, coupled with a rocking rigid block through a linear visco-elastic device, which connects only the lower part of the 2-DOF system. The possibility to restrain the block directly to the ground, by means of a second visco-elastic device, is investigated as well. The dynamic response of the model under an harmonic base excitation is then analysed in order to evaluate the effectiveness of the coupling in reducing the displacements and the drift of the 2-DOF system. The nonlinear equations of motion of the coupled assemblage 2-DOF-block are obtained by a Lagrangian approach and then numerically integrated considering some reference mechanical and geometrical quantities as variable parameters. It follows an extensive parametric analysis, whose results are summarized through behaviour maps, which portray the ratio between the maximum displacements and drifts of the system, with and without the coupling with the rigid block, for several combinations of system's parameters. When the ratio of the displacements is less than unity, the coupling is considered effective. Results show that the presence of the rocking rigid block improves the dynamics of the system in large ranges of the characterizing parameters.

Evaluation of limit load analysis for pressure vessels - Part I: Linear and nonlinear methods

  • Chen, Xiaohui;Gao, Bingjun;Wang, Xingang
    • Steel and Composite Structures
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    • v.22 no.6
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    • pp.1391-1415
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    • 2016
  • Limit load of pressure bearing structures was reviewed in this article. By means of the finite element analysis, limit load of pressurized cylinder with nozzle was taken as an example. Stress classification method and Elastic-plastic finite element analysis combining with limit load determination methods were used to determine limit load of cylinder with nozzle. Comparison of limit load determined by different methods, the results indicated that limit load determined by linearization method was the smallest. Limit load determined by twice elastic slope criterion was the nearest than experimental results. Elastic-plastic finite element analysis had comparably computational precision, but required time consuming. And then the requirements of computer processing and storage capacity by power system became higher and higher. Most of criteria for limit load estimation included any human factors based on a certain substantive characteristics of experimental results. The reasonable criterion should be objective and operational.

Computer Simulation of Deformation Behavior of the Rubber Diaphragm (고무 다이아프램의 변형거동 전산해석)

  • Cho, Seong-Do-Seong;Kim, Wan-Doo
    • Elastomers and Composites
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    • v.35 no.1
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    • pp.4-11
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    • 2000
  • A rubber diaphragm is a critical element of accumulators. The material of a diaphragm is nitrile rubber so as to recover and adjust the large deformation under external pressure fluctuation. The performance of accumulators is influenced by the deformation behaviors of the diaphragm. A large deformation behavior of the diaphragm has been investigated using the commercial finite element program MARC K7.1. The several elastic moduli have been used in linear analysis and Ogden's coefficients have been used in non-linear analysis. As a result, it has been shown that the deformation behavior with a elastic modulus of $0.3 kg/mm^2$ is similar to the behavior of non-linear analysis. And, the modified diaphragm shape to reduce the stress concentration has been proposed.

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Analysis of Single-Walled Carbon Nanotube under Compression using Elastic Beam Model (탄성 보 모델을 이용한 탄소나노튜브의 압축거동해석)

  • Park, No-Jung;Chun, Yun-Hee;Park, Jae-Gyun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.23 no.5
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    • pp.567-575
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    • 2010
  • The mechanical properties of Carbon nanotube is superior such that it can be used in many areas of engineering field in the future, though the analysis of the mechanical behavior of nanotube is expensive due to its small size and uniqueness when the molecular dynamics or a generalized function theory is applied. To overcome these disadvantages, the force field between Carbon atoms can be substituted by structural members. In this study, main forces between atoms in Carbon nanotube are described by 0.1 nanometer length circular beams and linear behaviors under compression are investigated. The linear behavior is in good agreement with results by other methods. This method can be used in nonlinear analysis of nanotube when the beam elements are properly configured.

FEM Analysis on the Characteristics of Piezoelectric Ceramics Using $L_{1}-B_{4}$ Vibration mode ($L_{1}-B_{4}$ 진동모드를 이용하는 압전 세라믹스의 유한요소 해석)

  • 김범진;정동석;김태열;박태곤;김명호
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.07a
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    • pp.393-397
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    • 2001
  • A linear ultrasonic motor was designed by a combination of the first longitudinal and fourth bending mode, the motor consisted of a straight aluminum alloys bar bonded with a piezoelectric ceramics element as a driving element. That is, L$_1$-B$_4$ linear ultrasonic motor can be constructed using a multi-mode vibrator of longitudinal and bending modes. The simulation with variation of material characteristics of piezoceramic were performed as use of finite element analysis ANSYS 5.5, such as elastic compliance, piezoelectric constant, electro-mechanical coupling coefficient, poisson's ratio and density. The results of simulation, elastic compliance constant s$_{11}$ and piezoelectric constant d$_{31}$ had the most of influence on the elliptic-motion. This results consist with using transverse effect of material. The used motor were piezoceramics of 4 layers, and the dimensions were 65$\times$5$\times$3.5mm(LxWxt).).

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Crack Length Estimation for Large Deformable Non-Linear Elastic Materials (대변형 비선형 탄성재료의 균열길이 예측)

  • Yang, Gyeong-Jin;Gang, Gi-Ju;Park, Sang-Seo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.1 s.173
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    • pp.103-109
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    • 2000
  • A method to measure the crack length in rubbery materials is described. Through dimensional analysis and experiments, an equation is derived to give the crack length as a function of the change of strain energy density in a region remote from the crack. The function is provided in a form of separated terms of loading and material, the validity of which is experimentally proved using separation parameters.

Thermoelastic Finite Element Analysis of Double horizontal Subsurface Cracks Due to Sliding Surface Traction (마찰열을 고려한 미끄럼 접촉시 내부 복수 수평균열 전파해석)

  • 이진영;김석삼;채영훈
    • Tribology and Lubricants
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    • v.18 no.3
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    • pp.219-227
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    • 2002
  • A linear elastic fracture mechanics analysis of double subsurface cracks propagation in a half-space subjected to moving thermomechanical surface traction was performed using the finite element method. The effect of frictional heat at the sliding surface on the crack growth behavior is analyzed in terms of the thermal load and peclet number. The crack propagation direction is predicted in light of the magnitudes of the maximum shear and tensile stress intensity factor ranges. When moving thermomechanical surface traction exists, subsurface horizontal cracks are propagation in-plane crack growth rate at the beginning but they are propagation out-of-plane crack growth rate by the frictional heat which is occurrence by the repeated sliding contact.

Strength of FRP RC sections after long-term loading

  • Pisani, M.A.
    • Structural Engineering and Mechanics
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    • v.15 no.3
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    • pp.345-365
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    • 2003
  • The adoption of fibre reinforced polymer (FRP) rebars (whose behaviour is elastic-brittle) in reinforced concrete (RC) cross sections requires the assessment of the influence of time-dependent behaviour of concrete on the load-carrying capacity of these sections. This paper presents a method of computing the load-carrying capacity of sections that are at first submitted to a constant long-term service load and then overloaded up to ultimate load. The method solves first a non-linear visco-elastic problem, and then a non-linear instantaneous analysis up to ultimate load that takes into account the self-equilibrated stress distribution previously computed. This method is then adopted to perform a parametric analysis that shows that creep and shrinkage of concrete increase the load-carrying capacity of the cross section reinforced with FRP and allows for the suggestion of simple design rules.

Numerical simulation of the crack propagation behavior in 3D elastic body

  • Taniguchi, Takeo;Miyaji, Akihiko;Suetsugu, Takeshi;Matsunaga, Shohgo
    • Structural Engineering and Mechanics
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    • v.2 no.3
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    • pp.227-244
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    • 1994
  • The purpose of this investigation is to propose a numerical simulation method of the crack propagation behavior in 3-dimensionl elastic body. The simulation method is based on the displacement-type finite element method, and the linear fracture theory is introduced. The results from the proposed method are compared with those from the structural experiments, and the good coincidences between them are shown in this paper. At the same time, 2-dimensional analysis is also done, and the results are compared with those obtained from 3-dimensional analysis and the structural experiments.