• Title/Summary/Keyword: Cauchy

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A Study on the Cutting characteristics of a plastic sheet including Friction (마찰을 고려한 플라스틱 시트의 절단특성에 관한 연구)

  • Han Joohyun;Kim Dohyun;Kim Chungkyun
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 2004.11a
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    • pp.245-248
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    • 2004
  • The press cutter is productive equipment that practically manufactures materials such as fabrics, papers, films, leathers, rubbers etc. into the desired shapes using cutting method. Plate cutting process is one of the primary energy absorbing mechanisms in a grounding or collision event. The cutting mechanism is complicated and involves plastic flow of plate in the vicinity of the tip, friction between wedge and plate, deformation of plate. In this paper, we studied the effect of friction between cutter and plastic sheet for producing precise and superior products. The press cutter is analyzed numerically using MARC finite element program according to the variation of friction coefficients. The FEM results showed that normal stress, equivalent cauchy stress, normal total strain, equivalent total strain are good when friction coefficient is 0.0 and shear stress, shear total strain are good when friction coefficient is 0.8.

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Crystallite Size Measurement of Uranium Oxide Fuel Powders by Neutron Diffraction (중성자 회절에 의한 산화우라늄 핵연료 분말의 결정크기 측정)

  • 류호진;강권호;문제선;송기찬;최용남
    • Journal of Powder Materials
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    • v.10 no.5
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    • pp.318-324
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    • 2003
  • The nano-scale crystallite sizes of uranium oxide powders in simulated spent fuel were measured by the neutron diffraction line broadening method in order to analyze the sintering behavior of the dry process fuel. The mixed $UO_2$ and fission product powders were dry-milled in an attritor for 30, 60, and 120 min. The diffraction patterns of the powders were obtained by using the high resolution powder diffractometer in the HANARO research reactor. Diffraction line broadening due to crystallite size was measured using various techniques such as the Stokes' deconvolution, profile fitting methods using Cauchy function, Gaussian function, and Voigt function, and the Warren-Averbach method. The non-uniform strain, stacking fault and twin probability were measured using the information from the diffraction pattern. The realistic crystallite size could be obtained after separation of the contribution from the non-uniform strain, stacking fault and twin.

Nonlinear analysis of RC structure with massive infill wall exposed to shake table

  • Onat, Onur;Lourenco, Paulo B.;Kocak, Ali
    • Earthquakes and Structures
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    • v.10 no.4
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    • pp.811-828
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    • 2016
  • This study aims to present nonlinear time history analysis results of double leaf cavity wall (DLCW) reinforced concrete structure exposed to shake table tests. Simulation of the model was done by a Finite Element (FE) program. Shake table experiment was performed at the National Civil Engineering Laboratory in Lisbon, Portugal. The results of the experiment were compared with numeric DLCW model and numeric model of reinforced concrete structure with unreinforced masonry wall (URM). Both DLCW and URM models have two bays and two stories. Dimensions of the tested structure and finite element models are 1:1.5 scaled according to Cauchy Froude similitude law. The URM model has no experimental results but the purpose is to compare their performance level with the DLCW model. Results of the analysis were compared with experimental response and were evaluated according to ASCE/SEI 41-06 code.

Dynamic analysis of a magneto-electro-elastic material with a semi-infinite mode-III crack under point impact loads

  • Feng, Wenjie;Liu, Jinxi
    • Structural Engineering and Mechanics
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    • v.27 no.5
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    • pp.609-623
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    • 2007
  • The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.

An analysis of an elastic solid incorporating a crack under the influences of surface effects in plane & anti-plane deformations

  • Kim, Chun Il
    • Interaction and multiscale mechanics
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    • v.4 no.2
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    • pp.123-137
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    • 2011
  • We review a series of crack problems arising in the general deformations of a linearly elastic solid (Mode-I, Mode-II and Mode-III crack) and, perhaps more significantly, when the contribution of surface effects are taken into account. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. We show that the deformations of an elastic solid containing a single crack can be decoupled into in-plane (Mode-I and Mode-II crack) and anti-plane (Mode-III crack) parts, even when the surface mechanics is introduced. In particular, it is shown that, in contrast to classical fracture mechanics (where surface effects are neglected), the incorporation of surface elasticity leads to the more accurate description of a finite stress at the crack tip. In addition, the corresponding stress fields exhibit strong dependency on the size of crack.

Large post-buckling behavior of Timoshenko beams under axial compression loads

  • Akbas, Seref D.
    • Structural Engineering and Mechanics
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    • v.51 no.6
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    • pp.955-971
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    • 2014
  • Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

Mode III SIFs for interface cracks in an FGM coating-substrate system

  • Monfared, Mojtaba Mahmoudi
    • Structural Engineering and Mechanics
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    • v.64 no.1
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    • pp.71-79
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    • 2017
  • In this study, interaction of several interface cracks located between a functionally graded material (FGM) layer and an elastic layer under anti-plane deformation based on the distributed dislocation technique (DDT) is analyzed. The variation of the shear modulus of the functionally graded coating is modeled by an exponential and linear function along the thickness of the layer. The complex Fourier transform is applied to governing equation to derive a system of singular integral equations with Cauchy type kernel. These equations are solved by a numerical method to obtain the stress intensity factors (SIFs) at the crack tips. The effects of non-homogeneity parameters for exponentially and linearly form of shear modulus, the thickness of the layers and the length of crack on the SIFs for several interface cracks are investigated. The results reveal that the magnitude of SIFs decrease with increasing of FG parameter and thickness of FGM layer. The values of SIFs for FGM layer with exponential form is less than the linear form.

APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASS

  • Akgun Ramazan;Israfilov Daniyal M.
    • Journal of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.413-424
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    • 2006
  • Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A KELLER-SEGEL-FLUID MODEL WITH NONLINEAR DIFFUSION

  • Chung, Yun-Sung;Kang, Kyungkeun;Kim, Jaewoo
    • Journal of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.635-654
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    • 2014
  • We consider the Cauchy problem for a Keller-Segel-fluid model with degenerate diffusion for cell density, which is mathematically formulated as a porus medium type of Keller-Segel equations coupled to viscous incompressible fluid equations. We establish the global-in-time existence of weak solutions and bounded weak solutions depending on some conditions of parameters such as chemotactic sensitivity and consumption rate of oxygen for certain range of diffusive exponents of cell density in two and three dimensions.

A FIXED POINT APPROACH TO THE STABILITY OF QUADRATIC FUNCTIONAL EQUATION

  • Jung, Soon-Mo;Kim, Tae-Soo;Lee, Ki-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.531-541
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    • 2006
  • [ $C\u{a}dariu$ ] and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of $C\u{a}dariu$ and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation for a large class of functions from a vector space into a complete ${\gamma}-normed$ space.