• Title/Summary/Keyword: Number Theory

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Thermal buckling of functionally graded plates using a n-order four variable refined theory

  • Abdelhak, Z.;Hadji, L.;Daouadji, T.H.;Bedia, E.A.
    • Advances in materials Research
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    • v.4 no.1
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    • pp.31-44
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    • 2015
  • This paper presents a simple n-order four variable refined theory for buckling analysis of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and eliminates the shear stresses at the top and bottom surfaces. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present n-order refined theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

Decoupling of Background and Resonance Scatterings in Multichannel Quantum Defect Theory and Extraction of Dynamic Parameters from Lu-Fano Plot

  • Lee, Chun-Woo
    • Bulletin of the Korean Chemical Society
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    • v.30 no.4
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    • pp.891-896
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    • 2009
  • Giusti-Suzor and Fano introduced translations of the scales of Lu-Fano plots by phase renormalization in order to decouple the intra- and inter-channel couplings in multichannel quantum defect theory (MQDT). Their theory was further developed by others to deal with systems involving a larger number of channels. In different directions, MQDT was reformulated into forms with a one-to-one correspondence to those in Fano's configuration mixing theory of resonance for photofragmentation processes involving one closed and many open channels. In this study, the theory was further developed to fully reveal the coupling nature, decoupling of the background and resonance scattering in physical scattering matrices as well as to further extract the dynamic parameters undiscovered by Fano and his colleagues. This theory was applied to the photoabsorption spectrum of $H_2$ observed by Herzberg's group.

양력선 이론을 이용한 EDISON CFD 해석자의 검증

  • Kim, Tae-Hui
    • Proceeding of EDISON Challenge
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    • 2016.11a
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    • pp.101-105
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    • 2016
  • Prandtl's Lifting-line theory is the classical theory of calculating aerodynamic properties. Though it is classical method, it predicts the aerodynamic properties well. By lifting-line theory, high aspect ratio is critical factor to decrease induced drag. And 'elliptic-similar' wing also makes the minimum induced drag. But due to the problem of manufacturing, tapered wing is preferred and have been utilized. In this Paper, by using Edison CFD, verifying the classical lifting-line theory. To consider induced drag only, using Euler equation as governing equation instead of full Navier-Stokes equation. Refer to the theory, optimum taper ratio which makes the minimum induced drag is 0.3. Utilizing the CFD results, plotting oswald factor over various taper ratio and investigating whether the consequences are valid or not. As a result, solving Euler equation by EDISON CFD cannot guarantee the theoretical values because it is hard to set the proper grid to solve. Results are divided into two cases. One is the values are decreased gradually and another seems to following tendency, but values are all negative number.

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A Study on Cutural Capital Influencing Organization Performance

  • Yookyung Kim;Myoenggil Choi
    • Journal of Information Technology Applications and Management
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    • v.29 no.6
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    • pp.95-122
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    • 2022
  • The rapid development of technology, the spread of information, and the implementation of the government's start-up support policy exponentially increase the number of start-up companies. The purpose of this study is to investigate each company's cultural capital's effect on organization performance by promoting knowledge management activities and forming organization habitus based on Cultural Reproduction Theory and Cultural Mobility Theory. As a result of the study, it confirmed that the relationship between cultural capital, knowledge management activities, habitus, and organization performance was significant. The results of this study have academic implications as follows: First, the field of research has expanded by studying the effects of cultural capital on business administration, which is less active than existing education and sociology. Second, it accepts and supports Cultural Reproduction Theory and Cultural Mobility Theory from different perspectives.

Mechanism and Application Methodology of Mental Practice (정신 연습의 기전과 적용 방법)

  • Kim Jong-soon;Lee Keun-heui;Bae Sung-soo
    • The Journal of Korean Physical Therapy
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    • v.15 no.2
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    • pp.75-84
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    • 2003
  • The purpose of this study was to review of mechanism and application methodology about mental practice. The mental practice is symbolic rehearsal of physical activity in the absence of any gross muscular movements. Human have the ability to generate mental correlates of perceptual and motor events without any triggering external stimulus, a function known as imagery, Practice produces both internal and external sensory consequences which are thought to be essential for learning to occur, It is for this reason that mental practice, rehearsal of skill in imagination rather than by overt physical activity, has intrigued theorists, especially those interested in cognitive process. Several studies in sport psychology have shown that mental practice can be effective in optimizing the execution of movements in athletes and help novice learner in the incremental acquisition of new skilled behaviors. There are many theories of mental practice for explaining the positive effect In skill learning and performance. Most tenable theories are symbolic learning theory, psyconeuromuscular theory, Paivio's theory, regional cerebral blood flow theory, motivation theory, modeling theory, mental and muscle movement nodes theory, insight theory, selective attention theory, and attention-arousal set theory etc.. The factors for influencing to effects of mental practice are application form, application period, time for length of the mental practice, number of repetition, existence of physical practice.

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A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates

  • Houari, Mohammed Sid Ahmed;Tounsi, Abdelouahed;Bessaim, Aicha;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.22 no.2
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    • pp.257-276
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    • 2016
  • In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Flexural and free vibration responses of thick isotropic bridge deck using a novel two variable refined plate theory

  • Djidar, Fatima Zohra;Hebali, Habib;Amara, Khaled;Tounsi, Abdelouahed;Bendaho, Boudjema;Ghazwani, M.H.;Hussain, Muzamal
    • Structural Engineering and Mechanics
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    • v.82 no.6
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    • pp.725-734
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    • 2022
  • This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

A NOTE ON THE VALUATION

  • Park, Joong-Soo
    • The Pure and Applied Mathematics
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    • v.1 no.1
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    • pp.7-11
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    • 1994
  • Classically, valuation theory is closely related to the theory of divisors and conversely. If D is a Dedekined ring and K is its quotient field, then we can clearly construct the theory of divisors on D (or K), and then we can induce all the valuations on K ([3]). In particular, if K is a number field and A is the ring of algebraic integers, then since Z is Dedekind, A is a Dedekind rign and K is the field of fractions of A.(omitted)

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A high-order gradient model for wave propagation analysis of porous FG nanoplates

  • Shahsavari, Davood;Karami, Behrouz;Li, Li
    • Steel and Composite Structures
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    • v.29 no.1
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    • pp.53-66
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    • 2018
  • A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

Isogeometric Collocation Method to solve the strong form equation of UI-RM Plate Theory

  • Katili, Irwan;Aristio, Ricky;Setyanto, Samuel Budhi
    • Structural Engineering and Mechanics
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    • v.76 no.4
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    • pp.435-449
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    • 2020
  • This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.