• Title/Summary/Keyword: differential forms

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Computational Structural Engineering -Recent Developments and Applications (전산 구조 공학의 연구동향)

  • 최창근;유원진
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1998.04a
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    • pp.3-14
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    • 1998
  • Computational structural engineering is the base on which most of the achievements of engineering and physics are built. Since most of the theory underlying physical phenomena is involved differential equations for which closed forms of solution are seldom possible, the numerical approximation is necessary for a quantitative solution. Some areas where progress and research on computational mechanics are currently active are discussed. In the first part of this paper the development of the improved non-conforming elements for the analysis of plates and shells is described. Recent developments in the adaptive analysis for the structural and the wind problem and meshless method are also discussed in the second part.

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Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation

  • Limkatanyu, Suchart;Kuntiyawichai, Kittisak;Spacone, Enrico;Kwon, Minho
    • Structural Engineering and Mechanics
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    • v.42 no.1
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    • pp.39-53
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    • 2012
  • This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called "natural" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

Construction of the shape functions of beam vibrations for analysis of the rectangular plates by Kantorovich-Vlasov's method

  • Olodo, Emmanuel E.T.;Degan, Gerard
    • Structural Engineering and Mechanics
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    • v.52 no.3
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    • pp.595-601
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    • 2014
  • For analysis of the plates and membranes by numerical or analytical methods, the question of choice of the system of functions satisfying the different boundary conditions remains a major challenge to address. It is to this issue that is dedicated this work based on an approach of choice of combinations of trigonometric functions, which are shape functions of a bended beam with the boundary conditions corresponding to the plate support mode. To do this, the shape functions of beam vibrations for strength analysis of the rectangular plates by Kantorovich-Vlasov's method is considered. Using the properties of quasi-orthogonality of those functions allowed assessing to differential equation for every member of the series. Therefore it's proposed some new forms of integration of the beam functions, in order to simplify the problem.

The Performance Comparison Evaluation of Control Valve Shape (제어밸브 트림부 형태에 따른 성능 비교 평가)

  • Yoon, I.S.;Kim, Y.B.;Jang, H.;Hwang, J.H.;Kang, Y.M.
    • Proceedings of the KSME Conference
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    • 2008.11b
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    • pp.2771-2776
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    • 2008
  • AOV is fluid capacity and fluid pressure control in nuclear power plant with heating power plant. The control valve in order channel to control a high differential pressure developed in the form which is complicated and precise control form. Form the research which sees in order description below analyzed the performance comparison which follows in trim forms of the control valve with CFD. The Result, multi-stage trim are a fluid kinetic energy small will prevent damages of AOV.

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Analysis of Viscous Free Surface Flow around a Ship by a Level-set Method

  • Park, Il-Ryong;Chun, Ho-Hwan
    • Journal of Ship and Ocean Technology
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    • v.6 no.2
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    • pp.37-50
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    • 2002
  • In the present numerical simulation of viscous free surface flow around a ship, two-fluids in-compressible Reynolds-averaged Navier-Stokes equations with the standard $\textsc{k}-\varepsilon$turbulence model are discretized on a regular grid by using a finite volume method. A local level-set method is introduced for capturing the free surface movement and the influence of the viscous layer and dynamic boundary condition of the free surface are implicitly considered. Partial differential equations in the level-set method are discretized with second order ENO scheme and explicit Euler scheme in the space and time integration, respectively. The computational results for the Series-60 model with $C_B=0.6$ show a good agreement with the experimental data, but more validation studies for commercial complicated hull forms are necessary.

A study on the spectrum assignment problem for a functional linear system (함수선형계의 스펙트럼지정문제에 관한 연구)

  • 이장우
    • 전기의세계
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    • v.31 no.3
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    • pp.209-217
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    • 1982
  • This paper considers a finite spectrum assignment Problem for a functional retarded linear differential system with delays in control only. In this problem, by generalizing from an abstract linear system characterized by Semigroups on a Hilbert space to a finite dimensional linear system, we unify the relationship between a control-delayed system and its non-delayed system, and then by using the spectrum of the generator-decomposition of Semigroup, we try to get a feedback law which yields a finite spectrum of the closed-loop system, located at an arbitrarily preassigned sets of n points in the complex plane. The comparative examinations between the standard spectrum assignment method and the method of spectral projection for the feedback law which consists of proportional and finite interval terms over present and past values of control variables are also considered. The analysis is carry down to the elementary spectral projection level because, in spite of all the research efforts, so far there has been no significant attempt to obtain the feedback implementation directly from the abstract representation forms in the case of multivariables.

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Dimesogenic Compounds Consisting of Two Identical Terminal N-(4-Oxybenzylidene)-4-n-butylaniline Units and a Central Polymethylene Spacer

  • Jung-Il Jin;Bong Young Chung;Joo-Hoon Park
    • Bulletin of the Korean Chemical Society
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    • v.12 no.5
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    • pp.583-588
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    • 1991
  • A series of dimesogenic compounds having two identical, terminal Schiff base type mesogens and a central polymethylene spacer were prepared and their properties were compared with those of the corresponding monomesogenic compounds. The mesomorphic properties of the compounds were studied by differential scanning calorimetry and on a hot-stage of a polarizing microscope. All of the dimesogenic compounds formed mesophases enantiotropically with the exception of pentamethylene-1,5-bis(4-oxybenzylidene 4-n-butylaniline). This compound was monotropic and formed only a nematic phase on heating the solid, whereas it formed nematic as well as smectic A phases on cooling the isotropic liquid. Those compounds containing longer (octamethylene and decamethylene) spacers favored the formation of nematic phase whereas those having shorter (dimethylene and tetramethylene) spacers formed smectic phases. In general, the variety of mesophase forms exhibited by the dimesogenic compounds was significantly less than that shown by the corresponding monomesogenic compounds.

TUBULAR SURFACES WITH MODIFIED ORTHOGONAL FRAME IN EUCLIDEAN 3-SPACE

  • Akyigit, Mahmut;Eren, Kemal;Kosal, Hidayet Huda
    • Honam Mathematical Journal
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    • v.43 no.3
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    • pp.453-463
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    • 2021
  • In this study, tubular surfaces that play an important role in technological designs in various branches are examined for the case of the base curve is not satisfying the fundamental theorem of the differential geometry. In order to give an alternative perspective to the researches on tubular surfaces, the modified orthogonal frame is used in this study. Firstly, the relationships between the Serret-Frenet frame and the modified orthogonal frame are summarized. Then the definitions of the tubular surfaces, some theorems, and results are given. Moreover, the fundamental forms, the mean curvature, and the Gaussian curvature of the tubular surface are calculated according to the modified orthogonal frame. Finally, the properties of parameter curves of the tubular surface with modified orthogonal frame are expressed and the tubular surface is drawn according to the Frenet frame and the modified orthogonal frame.

A GN model of thermoelastic interaction in a 2D orthotropic material due to pulse heat flux

  • Hobiny, Aatef;Abbas, Ibrahim A.
    • Structural Engineering and Mechanics
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    • v.80 no.6
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    • pp.669-675
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    • 2021
  • A GN model with and without energy dissipations is used to discuss the waves propagation in a two-dimension orthotropic half space by the eigenvalues approach. Using the Laplace-Fourier integral transforms to get the solutions of the problem analytically, the basic formulations of the two-dimension problem are given by matrices-vectors differential forms, which are then solved by the eigenvalues scheme. Numerical techniques are used for the inversion processes of the Laplace-Fourier transform. The results for physical quantities are represented graphically. The numerical outcomes show that the characteristic time of pulse heat flux have great impacts on the studied fields values.

Green's function coupled with perturbation approach to dynamic analysis of inhomogeneous beams with eigenfrequency and rotational effect's investigations

  • Hamza Hameed;Sadia Munir;F.D. Zaman
    • Structural Monitoring and Maintenance
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    • v.11 no.1
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    • pp.19-40
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    • 2024
  • The elastic theory of beams is fundamental in engineering of design and structure. In this study, we construct Green's function for inhomogeneous fourth-order differential operators subjected to associated constraints that arises in dealing with dynamic problems in the Rayleigh beam. We obtain solutions for homogeneous and completely inhomogeneous beam problems using Green's function. This enables us to consider rotational influences in determining the eigenfrequency of beam vibrations. Additionally, we investigate the dynamic vibration model of inhomogeneous beams incorporating rotational effects. The eigenvalues of Rayleigh beams, including first-order correction terms, are also computed and displayed in tabular forms.