• Proceedings of the KSR Conference
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• 2004.10a
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• pp.906-915
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• 2004

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using clement force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.385-392
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• 2002

Derivation procedures of exact elastic element stiffness matrix of thin-walled curved beams are rigorously presented for the static analysis. An exact elastic element stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The displacement and normal stress of the section are evaluated and compared with thin-walled straight and curved beam element or results of the analysis using shell elements for the thin-walled curved beam structure in order to demonstrate the validity of this study.

• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.383-392
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• 2009

The static and dynamic analyses of simply supported beams are studied by using the U-transformation method and the finite difference method. When the beam is divided into the mesh of equal elements, the mesh may be treated as a periodic structure. After an equivalent cyclic periodic system is established, the difference governing equation for such an equivalent system can be uncoupled by applying the U-transformation. Therefore, a set of single-degree-of-freedom equations is formed. These equations can be used to obtain exact analytical solutions of the deflections, bending moments, buckling loads, natural frequencies and dynamic responses of the beam subjected to particular loads or excitations. When the number of elements approaches to infinity, the exact error expression and the exact convergence rates of the difference solutions are obtained. These exact results cannot be easily derived if other methods are used instead.

• Journal of the Korean institute of surface engineering
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• v.23 no.4
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• pp.225-229
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• 1990

Solubility Products of metal oxides, such as Al2O3 and UO2 in KCl-LiCl eutectic composition was calculated by using an exact an exact thermodynamic. The values for Al2O3 ThO2 and UO2 were found to be 2.51$\times$10-27, 4.97$\times$10-15and 2.17$\times$10-12in mole per liter basis at 743 K, respectively. The correlation of theoretical values with those of experiment were in good agreement. It is worth to note that the exact cycle method was proved to be satisfactory in making predictions of solubillities and also solubility products of sparingly soluble metal oxides in an ionic salt system.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.643-657
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• 2022

Let R be a ring and S a multiplicative subset of R. An R-module T is called u-S-torsion (u-always abbreviates uniformly) provided that sT = 0 for some s ∈ S. The notion of u-S-exact sequences is also introduced from the viewpoint of uniformity. An R-module F is called u-S-flat provided that the induced sequence 0 → A ⊗_R F → B ⊗_R F → C ⊗_R F → 0 is u-S-exact for any u-S-exact sequence 0 → A → B → C → 0. A ring R is called u-S-von Neumann regular provided there exists an element s ∈ S satisfying that for any a ∈ R there exists r ∈ R such that sα = rα². We obtain that a ring R is a u-S-von Neumann regular ring if and only if any R-module is u-S-flat. Several properties of u-S-flat modules and u-S-von Neumann regular rings are obtained.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.899-913
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• 2024

In this article, the Series Solution Method (SSM) is employed to solve the linear or non-linear Volterra integro-differential equations. Numerous examples have been presented to explain the numerical results, which is the comparison between the exact solution and the numerical solution, and it is found through the tables. The amount of error between the exact solution and the numerical solution is very small and almost nonexistent, and it is also illustrated through the graph how the exact solution completely applies to the numerical solution. This proves the accuracy of the method, which is the Series Solution Method (SSM) for solving the linear or non-linear Volterra integro-differential equations using Mathematica. Furthermore, this approach yields numerical results with remarkable accuracy, speed, and ease of use.

• Honam Mathematical Journal
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• v.18 no.1
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• pp.91-97
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• 1996

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.1
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• pp.143-150
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• 2019

We focus on the weapon target assignment and fire scheduling problem (WTAFSP) with the objective of minimizing the makespan, i.e., the latest completion time of a given set of firing operations. In this study, we assume that there are m available weapons to fire at n targets (> m). The artillery attack operation consists of two steps of sequential procedure : assignment of weapons to the targets; and scheduling firing operations against the targets that are assigned to each weapon. This problem is a combination of weapon target assignment problem (WTAP) and fire scheduling problem (FSP). To solve this problem, we define the problem with a mixed integer programming model. Then, we develop exact algorithms based on a dynamic programming technique. Also, we suggest how to find lower bounds and upper bounds to a given problem. To evaluate the performance of developed exact algorithms, computational experiments are performed on randomly generated problems. From the results, we can see suggested exact algorithm solves problems of a medium size within a reasonable amount of computation time. Also, the results show that the computation time required for suggested exact algorithm can be seen to increase rapidly as the problem size grows. We report the result with analysis and give directions for future research for this study. This study is meaningful in that it suggests an exact algorithm for a more realistic problem than existing researches. Also, this study can provide a basis for developing algorithms that can solve larger size problems.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.195-203
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• 2005

We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.