• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1469-1476
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• 2003

This paper provides plastic limit load solutions of cylinders with circumferential part-through surface cracks under combined axial tension, internal pressure and global bending. Such solutions are developed based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic-perfectly-plastic material behaviour, together with analytical solutions based on equilibrium stress fields. For the crack location, both external and internal cracks are considered. Furthermore, in terms of the crack shape, both semi-elliptical and constant-depth surface cracks are considered. The resulting limit load solutions are given in a closed form, and thus can be easily used in practical situations. Being based on detailed 3-D FE limit analysis, the present solutions are believed to most reliable, and thus to be valuable information for integrity assessment of piping.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.2
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• pp.100-105
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• 1989

This paper presents an adaptive finite element method for magnetostatic force computation using Maxwell's stress tensor. Mesh refinements are performed automatically by interelement magnetic field intensity discontinuity errors and element force errors. In initial mesh, the computed forces for different integration paths give great differences, but converge to a certain value as mesh division is performed by the adaptive scheme, We obtained good agreement between analytic solutions and numerical values in typical examples.

• Structural Engineering and Mechanics
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• v.12 no.2
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• pp.135-156
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• 2001

Analytical solutions and finite element results of laminated composite plates with smart material layers embedded in them are presented in this study. The third-order plate theory of Reddy is used to study vibration suppression characteristics. The analytical solution for simply supported boundary conditions is based on the Navier solution procedure. The velocity feedback control is used. Parametric effects of the position of the smart material layers, material properties, and control parameters on the suppression time are investigated. It has been found that (a) the minimum vibration suppression time is achieved by placing the smart material layers farthest from the neutral axis, (b) using thinner smart material layers have better vibration attenuation characteristics, and, (c) the vibration suppression time is larger for a lower value of the feedback control coefficient.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.422-429
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• 2001

A two dimensional hierarchical elements are investigated for a use on the incompressible flow computation. The construction of hierarchical elements are explained through the tensor product of 1-D hierarchical functions, and a systematic treatment of essential boundary values has been developed for the degrees of freedom corresponding to higher order terms. The numerical study for the poisson problem showed that the present scheme can increase the convergence and accuracy of finite element solutions, and can be more efficient than the standard first order with many elements. Also, for Stokes and cavity flow cases, solutions from hierarchical elements showed better resolutions and future promises for higher order solutions.

• Steel and Composite Structures
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• v.9 no.5
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• pp.473-497
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• 2009

For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.711-725
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• 1998

Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babu$\check{s}$ka-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges proposed by Hughes and Franca is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. Also, a solid mechanics problem is presented by which the stability of mixed elements can be studied. It is shown that the pressure solutions, although stable, are shown to exhibit sensitivity to the stabilization parameters.

• East Asian mathematical journal
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• v.33 no.1
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• pp.53-65
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• 2017

Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.7 s.238
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• pp.1013-1021
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• 2005

In this paper, we developed an automatic design optimization system for parametric shape optimization of cooling passages inside axial turbine blades. A parallel three-dimensional thermoelasticity finite element analysis code from an open source system was used to perform automatic thermal and stress analysis of different blade configuration. The developed code was connected to an evolutionary optimizer and built in a design optimization system. Using the optimization system, 279 feasible and optimal solutions were searched. It is provided not only one best solution of the searched solutions, but also information of variation structure and correlation of the 279 solutions in function, variable, and real design spaces. To explore design information, it is proposed a new interpretation approach based on evolutionary clustering and principal component analysis. The interpretation approach might be applicable to the increasing demands in the general area of design optimization.

• Structural Engineering and Mechanics
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• v.38 no.5
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• pp.549-571
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• 2011

This paper presents analytical solutions for skewed thick plates under transverse loading that have previously been unreported in the literature. The thick plate solution is obtained in a framework of an oblique coordinate system. The governing equation is first derived in the oblique coordinate system, and the solution is obtained using deflection and rotation as partial derivatives of a potential function developed in this research. The solution technique is applied to three illustrative application examples, and the results are compared with numerical solutions in the literature and those derived from the commercial finite element analysis package ANSYS 11. These results are in excellent agreement. The present solution may also be used to model skewed structures such as skewed bridges, to facilitate efficient routine design or evaluation analyses, and to form special elements for finite element analysis. At the same time, the analytical solution developed in this research could be used to develop methods to address post-buckling and dynamic problems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.11
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• pp.2773-2781
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• 1993

Laplace's equation is, perhaps, the most important equation, which governs various kinds of physical phenomena. Due to its importance, there have been several numerical techniques such as the finite element method, the finite difference method, and the boundary element method. However, these techniques do not appear very effective as they require a substantial amount of numerical calculation. In this paper, we develop a new most efficient technique based on analytic solutions for Laplace's equation in some convex polygons. Although a similar approach was used for the same problem, the present technique is unique as it solves directly Laplace's equation with the utilization of analytical solutions.