• 대한수학회보
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• 제59권3호
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• pp.745-756
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• 2022

We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term |u_t|^p-1·u_t (p > 1).

• Journal of Mechanical Science and Technology
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• 제18권9호
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• pp.1549-1558
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• 2004

This study is concerned with the general solution of the field intensity factors and energy release rate for a Griffith crack in a piezoelectric ceramic of finite radius under combined anti-plane mechanical and in-plane electrical loading. Both electrically continuous and impermeable crack surface conditions are considered. Employing Mellin transforms and Fourier series, the problem is reduced to dual integral forms. The solution to the resulting expressions is expressed in terms of Fredholm integral equation of the second kind. The solutions are provided to study the influence of the crack length, the crack surface boundary conditions on the intensity factors and the energy release rate.

• 전기의세계
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• 제30권4호
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• pp.219-226
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• 1981

The magnetic field distribution in saturable iron part of electromagnetic energy conversion divices is defined by the nonlinear quasi-Poisson enquation that is described the electromagnetic field characteristics and satisfied the natural boundary condition. The solution of this equation is obtained by minimizing an energy functional by means of trial function that defined in triangular subregion of two-dimensional field region. As a result, the accuracy of the machine design is increased by use of its solution. In this respect, this study is developed the basic theory to analyze the magnetic flux distribution in saturable iron part and air gap of induction motor that its secondary part is short circuit by the variational principle, the minimized theory of energy functional, the application of F.E.M., and treatment of computer. As theoritical data compared with the practics, the validity of the theory in this study is supported by experimental findings.

• Structural Engineering and Mechanics
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• 제49권5호
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• pp.569-595
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• 2014

In this paper, a novel semi-energy finite strip method (FSM) is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for thin and relatively thick functionally graded (FG) plates under uniform end-shortening. In order to study the effects of through-the-thickness shear stresses on the post-buckling behavior of FG plates, two previously developed finite strip methods, i.e., semi-energy FSM based on the concept of classical laminated plate theory (CLPT) and a CLPT full-energy FSM, are also implemented. Moreover, the effects of aspect ratio on initial post-buckling stiffness of FG rectangular plates are studied. It has been shown that the variation of the ratio of initial post-buckling stiffness to pre-buckling stiffness ($S^*/S$) with respect to aspects ratios is quite independent of volume fractions of constituents in thin FG plates. It has also been seen that the universal curve representing the variation of ($S^*/S$) with aspect ratio of a FG plate demonstrate a saw shape curve. Moreover, it is revealed that for the thin FG plates in contrast to relatively thick plates, the variations of non-dimensional load versus end-shortening is independent of ceramic-metal volume fraction index. This means that the post-buckling behavior of thin FG plates and the thin pure isotropic plates is similar. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results may have a great influence in design of FG plates encountering post-buckling behavior.

• Structural Engineering and Mechanics
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• 제12권5호
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• pp.541-558
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• 2001

The design specifications of guard fences in Japan were reexamined and the revised specifications were implemented from April 1999. Because of the huge consumption in time and cost to test the performances of full-scale guard fences in the field, some assumptions are adopted while modifying the design specifications, and numerical analyses are necessary to confirm the impact performance and safety level of new types of steel highway guard fences. In this study, the finite element models are developed for the heavy trucks and steel highway guard fences to reenact their behaviors, and the solution approach is carried out using nonlinear dynamic analysis software of structures in three dimensions (LS-DYNA). The numerical simulation results are compared with the full-scale on-site testing results to verify the proposed analysis procedure. The collision process is simulated and it is also made possible to visualize the movement of the truck and the performances of guard fences. In addition, the energy shift of the truck kinetic energy to the truck and guard fence Internal energy, and the energy absorption of each guard fence component are studied for the development of a new design methodology of steel highway guard fences based on the energy absorption capacity.

• 대한기계학회논문집
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• 제14권5호
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• pp.1069-1078
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• 1990

본 연구에서는 평면응력 및 평면변형률 문제의 유한요소법해석에 있어서 기존 의 면적좌표를 이용한 삼각형요소나 4절점 isoparametric 사변형요소보다도 정확도가 높은 에너지 직교함수(energy orthogonal function)에 의한 사변형요소를 개발하고 이 유한요소 프로그램을 이용하여 사각형 부재내의 집중하중과 분포하중에 의한 응력집중 현상과 소멸현상을 고찰하는데 있다.

• Steel and Composite Structures
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• 제43권5호
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• pp.533-552
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• 2022

The current article deals with the dynamic stability, and structural improvement of vibrating electrically curved screen on the viscoelastic substrate. By considering optimum value for radius curvature of the electrically curved screen, the structure improvement of the system occurs. For modeling the electrically system, the Maxwell's' equation is developed. Hertz contact model in employed to obtain contact forces between impactor and structure. Moreover, variational methods and nonlinear von Kármán model are used to derive boundary conditions (BCs) and nonlinear governing equations of the vibrating electrically curved screen. Galerkin and Multiple scales solution approach are coupled to solve the nonlinear set of governing equations of the vibrating electrically curved screen. Along with the analytical solution, 3D finite element simulation via ABAQUS package is provided with the aid of a FE package for simulating the current system's response. The results are categorized in 3 different sections. First, effects of geometrical and material parameters on the vibrational performance and stability of the curves panel. Second, physical properties of the impactor are taken in to account and their effect on the absorbed energy and velocity profile of the impactor are presented. Finally, effect of the radius and initial velocity on the mode shapes of the current structure is demonstrated.

• Journal of Theoretical and Applied Mechanics
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• 제3권1호
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• pp.1-15
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• 2002

Reduction methods for large structural systems have been reviewed. Mai emphasis is put on the dynamic reduction. Recently, the computing resources and technologies have been expanded so fast that the huge matrices Invoked In the analysis of structural system can be processed without serious difficulties. For most users, however, the computer facilities are limited and the system reductions in some forms are required. The reduction procedure in static problems is simple and straightforward. The major task is the book-keeping in computations. In dynamic problems and structural optimization. however. the problem is much more complicated. The problem is, in general, nonlinear and hence the exact solution is not available. Therefore, approximate solutions are sought in an iterative manner. A proper convergence criterion needs to be employed in order to get an accurate solution efficiently. Several research works have been reported fer the structural optimization combined with system reductions.

• Computers and Concrete
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• 제4권2호
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• pp.101-117
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• 2007

A new model predicting the nonlinear basic creep behaviour of concrete structures subjected to high multi-axial stresses is proposed. It combines a model based on the thermodynamic framework of the elasto-plastic continuum damage theory for time-independent material behaviour and a rheological model describing phenomenologically the long-term delayed deformation. Strength increase due to ageing is regarded. The general 3D solution for the creep theory is derived from a rate-type form of the uniaxial formulation by the assumption of associated creep flow and a theorem of energy equivalence. The model is able to reproduce linear primary creep as well as secondary and tertiary creep stages under high compressive stresses. For concrete in tension a simple viscoelastic formulation is applied. The material law is then incorporated into a finite element solution procedure for analysis of reinforced concrete structures. Numerical examples of uniaxial creep tests and concrete members show excellent agreement with experimental results.

• 한국자동차공학회논문집
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• 제4권5호
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• pp.16-25
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• 1996

In the present work a rigid-plastic finite element formulation using dynamic explicit time integration scheme is proposed for numerical analysis of auto-body panel stamping processes. The rigid-plastic finite element method based on membrane elements has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM(abbreviated from Bending Energy Augmented Membrane) elements are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and the direct trial-and-error method. Computations are carried out for analysis of complicated auto-body panel stamping processes such as forming of an oilpan, a fuel tank and a front fender. The numerical results of explicit analysis are compared with the implicit results with good agreements and it is shown that the explicit scheme requires much shorter computational time, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigid-plastic finite element method enables an effective computation for complicated autobody panel stamping processes.