• Title/Summary/Keyword: Boundary-Value Problems

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A Study on the Stability Boundaries for Single Layer Latticed Domes and Arch under Combined Loads (조합하중를 받는 단층 래티스 돔과 아치의 안정경계에 관한 연구)

  • Han, Sang-Eul;Lee, Sang-Ju;Lee, Kap-Su
    • Journal of Korean Association for Spatial Structures
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    • v.4 no.3 s.13
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    • pp.103-109
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    • 2004
  • The lowest load when the equilibrium condition becomes to be unstable is defined as the buckling load. The primary objective of this paper is to be analyse stability boundaries for star dome under combined loads and is to investigate the iteration diagram under the independent loading parameter. In numerical procedure of the geometrically nonlinear problems, Arc Length Method and Newton-Raphson iteration method is used to find accurate critical point(bifurcation point and limit point). In this paper independent loading vector is combined as proportional value and star dome was used as numerical analysis model to find stability boundary among load parameters and many other models as multi-star dome and arch were studied. Through this study we can find the type of buckling mode and the value of buckling load.

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Microstructural modeling of two-way bent shape change of composite two-layer beam comprising a shape memory alloy and elastoplastic layers

  • Belyaev, Fedor S.;Evard, Margarita E.;Volkov, Aleksandr E.;Volkova, Natalia A.;Vukolov, Egor A.
    • Smart Structures and Systems
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    • v.30 no.3
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    • pp.245-253
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    • 2022
  • A two-layer beam consisting of an elastoplastic layer and a functional layer made of shape memory alloy (SMA) TiNi is considered. Constitutive relations for SMA are set by a microstructural model capable to calculate strain increment produced by arbitrary increments of stress and temperature. This model exploits the approximation of small strains. The equations to calculate the variations of the strain and the internal variables are based on the experimentally registered temperature kinetics of the martensitic transformations with an account of the crystallographic features of the transformation and the laws of equilibrium thermodynamics. Stress and phase distributions over the beam height are calculated by steps, by solving on each step the boundary-value problem for given increments of the bending moment (or curvature) and the tensile force (or relative elongation). Simplifying Bernoulli's hypotheses are applied. The temperature is considered homogeneous. The first stage of the numerical experiment is modeling of preliminary deformation of the beam by bending or stretching at a temperature corresponding to the martensitic state of the SMA layer. The second stage simulates heating and subsequent cooling across the temperature interval of the martensitic transformation. The curvature variation depends both on the total thickness of the beam and on the ratio of the layer's thicknesses.

Reading education in secondary schools (중. 고등학교에 있어서 독서교육)

  • 변우열
    • Journal of Korean Library and Information Science Society
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    • v.14
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    • pp.181-215
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    • 1987
  • Reading education is very important in order to promote the refinement, cultivate the emotion and complete the character to the secondary school students. This thesis deals with the establishment of reading education as a formal course in secondary schools, responsibility of teaching and problems related to recommended reading lists. Reading education must separate from the national language education because of literature centered education in reading education. If reading education was separated from the national language education, students can a n.0, pproach to the other cultural boundary besides other own and exchange their information and ideas. So, reading education must be included to the elective subjects in a independent course or become a compulsory subject in secondary school curriculum. The teacher of reading education must become the teacher librarian who has a firm faith and an intellectual accomplishment. But, teacher-librarian has much disadvantages such as the problems of promotion, the division of qualification between elementary school and secondary school, and a short-term training courses for teacher-librarian. Hence, theses problems music be solved in national administrative level. Recommended reading lists must be provided to the student in order to prevent confusion of the sense of value, to estimate their own reading ability by themselves and to establish life long reading plan. Therefore, both Korean Library Association and the Ministry of Education should re-examine and develop recommended reading lists. Finally, problems of a juvenile delinquency in the post industrial society have to be solved through reading education. To solve the juvenile delinquency problems, adolescents should cultivate their moral character and possesses abundant knowledge through reading education. Then, young adults will grow as sound citizen in the society.

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A Combined Finite Element -Boundary Element Method of Underground Displacements Analysis (유한요소와 경계요소를 결합한 지하공동의 변위해석)

  • 황창규;박성재
    • Geotechnical Engineering
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    • v.6 no.1
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    • pp.25-34
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    • 1990
  • The finite element and boundary element methods of underground analysis are both well established numerical techniques for determination of stress and displacement distributions at underground excavation. The finite element method presents antithetical advantages and limitations. Complex constitutive behaviour may be modelled, at the expense of numerical efficiency and, for infinite domain, inadequate representation of remote bounadry conditions. The inherent advantages of the boundary element method are the ease with which infinite domain problems may be analysed, and the efficiency of analysis typically associated with a boundary value solution procedure. Application of the method is limited by the requirements linear constitutive behaviour for the medium. A combined of the finite element and boundary element methods of underground analysis is shown to preserve the advantages of each procedure, and, eliminates their individual disadvantages. Procedures employed in this papers described combined FEBEM algorithm. Solutions of underground excavation verifying the performance of combined FEBEM code are compared with theoretical solution, boundary element solution and finite element solution.

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A Stress-Based Gradient Elasticity in the Smoothed Finite Element Framework (평활화 유한요소법을 도입한 응력기반 구배 탄성론)

  • Changkye Lee;Sundararajan Natarajan
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.37 no.3
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    • pp.187-195
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    • 2024
  • This paper presents two-dimensional boundary value problems of the stress-based gradient elasticity within the smoothed finite element method (S-FEM) framework. Gradient elasticity is introduced to address the limitations of classical elasticity, particularly its struggle to capture size-dependent mechanical behavior at the micro/nano scale. The Ru-Aifantis theorem is employed to overcome the challenges of high-order differential equations in gradient elasticity. This theorem effectively splits the original equation into two solvable second-order differential equations, enabling its incorporation into the S-FEM framework. The present method utilizes a staggered scheme to solve the boundary value problems. This approach efficiently separates the calculation of the local displacement field (obtained over each smoothing domain) from the non-local stress field (computed element-wise). A series of numerical tests are conducted to investigate the influence of the internal length scale, a key parameter in gradient elasticity. The results demonstrate the effectiveness of the proposed approach in smoothing stress concentrations typically observed at crack tips and dislocation lines.

Design and Implementation of code generator to remove the parameter boundary failure in the unit test (단위테스트 중 매개변수 경계오류제거를 위한 코드 자동생성 시스템 설계와 구현)

  • Park, Youngjo;Bang, Hyeja
    • Journal of Korea Society of Digital Industry and Information Management
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    • v.11 no.2
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    • pp.1-10
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    • 2015
  • As programs get more complicated and they are developed by various hands, the possibility that there are program bugs in the code has been increasing. And developers usually run unit tests to find these problems in the code. Besides, the developers are at the pain of getting stability of the code when they have to modify a code very often for clients requirements. In the methodlogy of TDD(Test Driven Development), developers write a unit test code first, and then write a program code for passing the unit test. The unit test must include the boundary condition test the reason why the possibility of occurring the bugs is very high. When failed to pass the test because of the value of a function is incorrect, not existed, out of the range or not matched etc, the program code will return the error code or occur the exception. In the document, the system is designed and implemented in order to insert the generated code automatically or suggest it to the developer, when the boundary condition test is failed. In conclusion, it is possible that the developer will get the code stability by searching the code and checking the code to be omitted automatically through this system.

Dynamic Stiffness of the Scaled Boundary Finite Element Method for Non-Homogeneous Elastic Space (비동질 탄성 무한공간에 대한 비례경계유한요소법의 동적강도행렬)

  • Lee, Gye-Hee
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.23 no.2
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    • pp.165-173
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    • 2010
  • In this paper, the dynamic stiffness of scaled boundary finite element method(SBFEM) was analytically derived to represent the non-homogeneous space. The non-homogeneous parameters were introduced as an expotential value of power function which denoted the non-homogeneous properties of analysis domain. The dynamic stiffness of analysis domain was asymptotically expanded in frequency domain, and the coefficients of polynomial series were determined to satify the radiational condition. To verify the derived dynamic stiffness of domain, the numerical analysis of the typical problems which have the analytical solution were performed as various non-homogeneous parameters. As results, the derived dynamic stiffness adequatlly represent the features of the non-homogeneous space.

THREE-DIMENSIONAL INFINITE ELEMENTS FOR WAVE FORCE EVALUATION OF OFFSHORE STRUCTURES (해양구조물의 파력산정을 위한 3-차원 무한요소)

  • 박우선;윤정방
    • Computational Structural Engineering
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    • v.4 no.4
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    • pp.135-144
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    • 1991
  • The finite element technique incorporatating infinite elements is applied to analyzing the general three dimensional wave-structure interaction problems within the limits of linear wave theory. The hydrodynamic forces are assumed to be inertially dominated, and viscous effects are neglected. In order to analyze the corresponding boundary value problems efficiently, two types of elements are developed. One is the infinite element for modeling the radiation condition at infinity, and the other is the fictitious bottom boundary element for the case of deep water. To validate those elements, numerical analyses are performed for several floating structures. Comparisons with the results by using other available solution methods show that the present method incorporating the infinite and the fictitious bottom boundary elements gives good results.

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The Nonlinear Motions of Cylinders(I) (주상체의 비선형 운동(I) -강제동요문제, 조파저항문제-)

  • H.Y. Lee;J.H. Hwang
    • Journal of the Society of Naval Architects of Korea
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    • v.29 no.4
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    • pp.114-131
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    • 1992
  • In the present work, a two-dimensional boundary-value problem for a large amplitude motion is treated as an initial-value problem by satisfying the exact body-boundary and nonlinear free-surface boundary conditions. The present nonlinear numerical scheme is similar to that described by Vinje and Brevig(1981) who utilized the Cauchy's theorem and assumed the periodicity in the horizontal coordinate. In the present thesis, however, the periodicity in the horizontal coordinate is not assumed. Thus the present method can treat more realistic problems, which allow radiating waves to infinities. In the present method of solution, the original infinite fluid domain, is divided into two subdomains ; ie the inner and outer subdomains which are a local nonlinear subdomain and the truncated infinite linear subdomain, respectively. By imposing an appropriate matching condition, the computation is carried out only in the inner domain which includes the body. Here we adopt the nonlinear scheme of Vinje & Brevig only in the inner domain and respresent the solution in the truncated infinite subdomains by distributing the time-dependent Green function on the matching boundaries. The matching condition is that the velocity potential and stream function are required to be continuous across the matching boundary. In the computations we used, if necessary, a regriding algorithm on the free surface which could give converged stable solutions successfully even for the breaking waves. In harmonic oscillation problem, each harmonic component and time-mean force are obtained by the Fourier transform of the computed forces in the time domain. The numerical calculations are made for the following problems. $\cdot$ Forced harmonic large-amplitude oscillation(${\omega}{\neq}0,\;U=0$) $\cdot$ Translation with a uniform speed(${\omega}=0,\;U{\neq}0$) The computed results are compared with available experimental data and other analytical results.

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Hamilton제s Principle for the Free Surface Waves of Finite Depth (유한수심 자유표면파 문제에 적용된 해밀톤원리)

  • 김도영
    • Journal of Ocean Engineering and Technology
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    • v.10 no.3
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    • pp.96-104
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    • 1996
  • Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

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