• Structural Engineering and Mechanics
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• v.4 no.2
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• pp.139-148
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• 1996

Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.2201-2210
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• 2002

The accurate analysis of ultrasonic wave propagation and scattering plays an important role in many aspects of nondestructive evaluation. A numerical analysis makes it possible to perform parametric studies, and in this way the probability of detection and reliability of test results can be improved. In this paper, a finite element method was employed for the analysis of ultrasonic wave propagation in anisotropic materials, and the accuracy of results was checked by comparing with analytical predictions. The element size and the integral time step, which are the critical components for the convergence of finite element solutions, were determined using a commercial finite element code. Some differences for wave propagation in anisotropic media were illustrated when plane waves are propagating in a unidirectionally reinforced composite materials. When plane waves are propagating in nonsymmetric directions in a symmetric plane, deviation angles between the wave vector and the energy vector were found from finite element analyses and the results agreed well with analytical calculations.

• Computational Structural Engineering
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• v.4 no.1
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• pp.95-108
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• 1991

An explicit finite element method can be executed more rapidly and effectively on vector computer than on the scalar computer because it has suitable structures for vector processing. In this paper, an efficient vectorization method of the explicit finite element program on the memory-to-memory type vector computer is proposed. First, the general vectorization method which can be applied regardless of the vector architecture is investigated, then the method which is suitable for the memory-to-memory type vector computer is proposed. To illustrate the usefulness of the proposed vectorization method, DYNA3D, the existing explicit finite element program, is migrated on HDS AS/XL V50 which is the memory-to-memory type vector computer. Performance results on actual test show a vector/scalar speedup is above 2.4.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.679-682
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• 1997

This paper presents finite element analysis algorithm combined with vector hysteresis model for accurate analysis of the hysteresis motor. Magnetization-dependent vector model is adapted to calculate the vector magnetization. That is to say, from the magnitude and direction of the magnetic field intensity, the magnetization of each ring element is computed by the vector model. By comparing the simulation results with the experimental ones, it is found that good results are obtained.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.3B no.1
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• pp.16-22
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• 2003

This paper presents an application of an impedance boundary condition to 3D vector finite element analysis of a multi-port cylidrical microwave cavity using Snell's law. Computing memory benefits and computing time reduction are obtained from this method compared with the conventional finite element method(FEM). To verify the method, a high permittivity scatterer in free space is analyzed and compared with the results of conventional (FEM). In addition, this method has been analyzed several types of cavities, including water load, to demonstrate the validity and accuracy of the program.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.50 no.6
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• pp.296-302
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• 2001

In this paper, the vector finite elements are adopted to calculate eigenvalues of RF and microwave components. Simulation results show that spurious are completely avoided because of the divergence free nature of the vector elements. This paper seeks to extend these low-order elements to higher orders to improve the accuracy of numerical solution. Investigation of numerical results for a rectangular waveguide was provided. A vector finite element program was implemented to allow propagation constants and electric field distributions to be directly computed in the rectangular and circular waveguides which are partially filled with the dielectric.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.735-748
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• 1998

We analyze the error in the p version of the of the finite element method when the effect of the quadrature error is taken in the load vector. We briefly study some results on the $H^{1}$ norm error and present some new results for the error in the $L^{2}$ norm. We inves-tigate the quadrature error due to the numerical integration of the right hand side We present theoretical and computational examples showing the sharpness of our results.

• Korean Journal of Computational Design and Engineering
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• v.15 no.6
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• pp.411-417
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• 2010

In this paper, the boom of a floating crane is modeled as a 3-dimensional elastic beam in order to analyze the dynamic response of the crane and its cargo. The boom is divided into more than two elements based on finite element formulation, and deformation of each element is expressed in terms of shape matrix and nodal coordinates. The equations of motion for the elastic boom consist of a mass matrix, a stiffness matrix, and a quadratic velocity vector that contains the gyroscopic and Coriolis forces. The size and complicity of the matrices increase in proportion with the number of elements. Therefore, it is not possible to derive the equations of motion explicitly for different number of elements. To overcome this difficulty, matrices for one 3-dimensional element are expressed with elementary sub-matrices. In particular, the quadratic velocity vector is derived as a product of a shape matrix and a 3-dimensional rotation matrix. By using the derived matrices, the equations of motion for the multi-element boom are automatically constructed. To verify the implementation of the elastic boom based on finite element formulation, we simulated a simple vibration of the elastic boom and compared the average deformation with the analytic solution. Finally, heave motion of the floating crane and surge motion of the cargo are presented as application examples of the elastic boom.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.20 no.9
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• pp.84-89
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• 2006

This paper presents the thickness effect of hysteresis ring of hysteresis motor using finite element method combined with a vector hysteresis model. From the magnitude and direction of the magnetic field intensity, the magnetization of each ring element is calculated by a vector hysteresis model. The developed torque can be obtained with the vector sum of individual torque of each element on the hysteresis ring. From these calculations, it can be found that the motor torque is not in proportion to the thickness of the ring. As a result, there exists a proper point of thickness and that can be determined using the proposed methoㅇ in this paper.

• Journal of Advanced Marine Engineering and Technology
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• v.2 no.1
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• pp.3-14
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• 1978

The authors have developed a calculating method of propeller shaft alignment by the finite element method. The propeller shaft is divided into finite elements which can be treated as uniform section bars. For each element, the nodal point equation is derived from the stiffness matrix, the external force vector and the section force vector. Then the overall nodal point equation is derived from the element nodal point equation. The deflection, offset, bending moment and shearing force of each nodal point are calculated from the overall nodal point equation by the digital computer. Reactions and deflections of supporting points of straight shaft are calculated and also the reaction influence number is derived. With the reaction influence number the optimum alignment condition that satisfies all conditions is calculated by the simplex method of linear programming. All results of calculation are compared with those of Det norske Veritas, which has developed a computor program based on the three-moment theorem of the strength of materials. The authors finite element method has shown good results and will be used effectively to design the propeller shaft alignment.