• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1721-1730
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• 2000

An eccentric degenerated shell element with geometric non-linearity for the precise and efficient analysis of stiffened shell structures is developed. To deal with the eccentricity, we define the e ccentric shell and the master shell that constitute one combined shell. It is assumed that the sections remain plane after deformation. The internal force vector and the tangent stiffness matrix based on the virtual work principle in the natural coordinate system are derived. To enhance the robustness of the element, assumed strain method for transverse shear and membrane strains is used. Through numerical experiments the effectiveness of the proposed element is demonstrated.

• Korean Management Science Review
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• v.26 no.3
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• pp.145-156
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• 2009

The probability distribution of the repair process should be determined to choose the optimal spare level of a weapon system with a queueing model. Though most weapon systems have a multi-step repair process, previous studies use the exponential distribution for the multi-step repair process. But the PH distribution is more appropriate for this case. We utilize the PH distribution on a queueing model and solve it with MGM(Matrix Geometric Method). We derive the optimal spare level using the PH distribution and show the difference of results between the PH and exponential distribution.

• International Journal of Railway
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• v.3 no.2
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• pp.46-53
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• 2010

Electric railroad systems consist of rolling stock, track, signal and catenary system. In the catenary system, one of the most important factors is the impedance according to the design and characteristic. Before the catenary system is designed, the impedance should be precedently researched. The railroad catenary system is complex system which is composed by five conductors. The five conductors classify up and down feeders, up and down contact wire group, rail group. Therefore, we should compose the catenary system of the equivalent five-conductors model. In this paper, we suggest a geometrical model and a equivalent conductor model by using geometric mean radius of five conductors in the catenary system. Also, we calculate demanded parameter values in the model. By using those, line constants of five conductors are analyzed by applying the equivalent method called as the condensed joint matrix.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.10
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• pp.4034-4053
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• 2015

In order to meet various requirements for transmission quality of both primary users (PUs) and secondary users (SUs) in cognitive radio networks, we introduce a channel bonding mechanism for PUs and a channel reservation mechanism for SUs, then we propose a novel spectrum allocation strategy. Taking into account the mistake detection and false alarm due to imperfect channel sensing, we establish a three-dimensional Markov chain to model the stochastic process of the proposed strategy. Using the method of matrix geometric solution, we derive the performance measures in terms of interference rate of PU packets, average delay and throughput of SU packets. Moreover, we investigate the influence of the number of the reserved (resp. licensed) channels on the system performance with numerical experiments. Finally, to optimize the proposed strategy socially, we provide a charging policy for SU packets.

• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.651-659
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• 2021

In this study, a new constitutive model has been developed to predict the elastic behavior of plain weave textile composites, using the finite element (FE) method. The geometric conditions and basic assumptions of this model are based on the basics of a continuum theory developed for the plane curved composites. In this model, the mechanical properties of the weave region and pure matrix region is calculated separately and then imported for the FE analysis. This new constitutive model is used to implement the mechanical properties of weave region in the representative volume element (RVE). The constitutive relations are implemented as user-material subroutine code (UMAT) in ABAQUS® FE software. The results of FE analysis have been compared with experimental results and other data available in the literature. These comparisons confirmed the capability of the presented model for the prediction of effective elastic properties of plain weave fabric composites.

• Steel and Composite Structures
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• v.46 no.3
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• pp.335-344
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• 2023

This investigation presents nonlinear free vibration of a carbon nanotube reinforced composite beam based on the Von Kármán nonlinearity and the Euler-Bernoulli beam theory The material properties of the structure is considered as made of a polymeric matrix by reinforced carbon nanotubes according to different material distributions. The governing equations of the nonlinear vibration problem is delivered by using Hamilton's principle and the Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained with the effect of different patterns of reinforcement.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.749-758
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• 2017

In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, $P=K{\Delta}$, where P is the load vector, K is the stiffness matrix and ${\Delta}$ is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of non-linear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.1
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• pp.17-26
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• 1990

A solution strategy for geometric non-linear analysis for the plane frame structures subjected to conservative and non-conservative forces is presented. By making efficient combination of the load incremental method and the displacement incremental method, this strategy can find postbuckling configuration such as snap-through and turning-back phenomena which cannot be easily found by the conventional load and displacement incrementation scheme. In the case of the analysis of the framed structure subjected to circulatory non-conservative forces, the total tangent stiffness matrix becomes unsymmetric and when calculating the incremental load and unbalanced load vector components, the direction change of the non-conservative forces is considered. Several example problems to demonstrate the feasibility of the present strategy, over ranges of deformation that are well beyond those likly to occur in practical framed structures, are given and discussed.

• Advances in nano research
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• v.14 no.4
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• pp.363-373
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• 2023

A novel type of steel fiber with a rounded-end shape is presented to improve the bonding behavior of fibers with Carbon Nanotubes (CNT)-reinforced Ultra-High Performance Concrete (UHPC) matrix. For this purpose, by performing a parametric study and using the nonlinear finite element method, the impact of geometric characteristics of the fiber end on its bonding behavior with UHPC has been studied. The cohesive zone model investigates the interface between the fibers and the cement matrix. The mechanical properties of the cohesive zone model are determined by calibrating the finite element results and the experimental fiber pull-out test. Also, the results are evaluated with the straight steel fibers outcomes. Using the novel presented fibers, the bond strength has significantly improved compared to the straight steel fibers. The new proposed fibers increase bond strength by 1.1 times for the same diameter of fibers. By creating fillet at the contact area between the rounded end and the fiber, bond strength is significantly improved, the maximum fiber capacity is reachable, and the pull-out occurs in the form of fracture and tearing of the fibers, which is the most desirable bonding mode for fibers. This also improves the energy absorbed by the fibers and is 4.4 times more than the corresponding straight fibers.