• Journal of Korea Society of Industrial Information Systems
• /
• v.12 no.4
• /
• pp.107-118
• /
• 2007

A single-server queueing model with infinite buffer and batch arrival of customers is considered. In contrast to the standard batch arrival when a whole batch arrives into the system at one epoch, we assume that the customers of an accepted batch arrive one-by one in exponentially distributed times. Service time is exponentially distributed. Flow of batches is the stationary Poisson arrival process. Batch size distribution is geometric. The number of batches, which can be admitted into the system simultaneously, is subject of control. Analysis of the joint distribution of the number batches and customers in the system and sojourn time distribution is implemented by means of the matrix technique and method of catastrophes. Effect of control on the main performance measures of the system is demonstrated numerically.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.34 no.7
• /
• pp.881-889
• /
• 2010

A volume integral equation method (VIEM) is introduced for solving the elastostatic problems related to an unbounded isotropic elastic solid; this solid is subjected to remote uniaxial tension, and it contains multiple interacting isotropic inclusions. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central inclusion is carried out; square and hexagonal packing of the inclusions are considered. The effects of the number of isotropic inclusions and different fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy and efficiency of the method are clarified by comparing the results obtained by analytical and finite element methods. The VIEM is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic fibers.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.36 no.1
• /
• pp.59-71
• /
• 2012

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in unbounded isotropic elastic solids containing multiple interacting isotropic or anisotropic diamond-shaped inclusions subject to remote uniaxial tension. The method is applied to two-dimensional problems involving long parallel diamond-shaped cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of the inclusions. The effects of the number of isotropic or anisotropic diamond-shaped inclusions and of the various fiber volume fractions for the circular inclusions circumscribing its respective diamond-shaped inclusion on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy and efficiency of the method are examined through comparison with results obtained using the finite element method.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.25 no.12
• /
• pp.822-829
• /
• 2015

A transfer matrix method has been developed to determine the more accurate natural frequencies for the bending vibration of Bernoulli-Euler beam with linearly reduced width and a concentrated tip mass. The proposed method can be computed an infinite number of the natural frequencies using a single element. Using the differential equation, shear force, and bending moment in which can be deduced by the diverse variational principles, a transfer matrix is formulated. The roots of the differential equation are computed by the Frobenius method. The effect of the concentrated mass for the natural frequencies of width-tapered beams is examined through a parametric study, and to show the accuracy of the proposed method, the computed results compared with those obtained from commercial finite element analysis program(ANSYS).

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.22 no.8
• /
• pp.800-807
• /
• 2012

In this paper, radiation efficiency of the plate surround by an infinite rigid baffle is studied. The plate is simply supported and one side is in contact with air, while other side with water. The pressure and normal velocity over the plate surface are assumed as modal summations, from which a set of linear equations is obtained for fluid-structure coupled problem. It is shown that neglect of the cross modes results in overestimation of the radiation efficiency specifically for mid-frequency ranges. Based on the fact that the responses are mainly determined from the first few cross modes in addition to the diagonal terms, a new algorithm is proposed, where banded matrix is iteratively solved in computing radiation efficiency. In numerical examples, it is found that radiation efficiency obtained from banded matrix is in excellent agreement with the one from the full matrix, while computing time is significantly reduced. It is also found that as frequency grows larger, radiation efficiency considering only diagonal terms is a good approximation.

• Structural Engineering and Mechanics
• /
• v.72 no.5
• /
• pp.617-629
• /
• 2019

Based on the finite element method of traditional straight Euler-Bernoulli beams and the coupled relations between linear displacement and angular displacement of a pre-twisted Euler-Bernoulli beam, the shape functions and stiffness matrix are deduced. Firstly, the stiffness of pre-twisted Euler-Bernoulli beam is developed based on the traditional straight Euler-Bernoulli beam. Then, a new finite element model is proposed based on the displacement general solution of a pre-twisted Euler-Bernoulli beam. Finally, comparison analyses are made among the proposed Euler-Bernoulli model, the new numerical model based on displacement general solution and the ANSYS solution by Beam188 element based on infinite approach. The results show that developed numerical models are available for the pre-twisted Euler-Bernoulli beam, and which provide more accurate finite element model for the numerical analysis. The effects of pre-twisted angle and flexural stiffness ratio on the mechanical property are investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.26 no.1
• /
• pp.75-81
• /
• 2016

In this study, a transfer matrix method in which can produce an infinite number of accurate natural frequencies using a single element for the bending vibration of rotating Bernoulli-Euler beam with linearly reduced width, is developed. The roots of the differential equation in the proposed method are calculated using the Frobenius method in the power series solution. To demonstrate the accuracy of the method, the calculated natural frequencies are compared with the results given by using the commercial finite element analysis program(ANSYS), and the comparison results between these two methods show the excellent agreement. Based on the comparison results, a parametric study is performed to investigate the effect of the centrifugal forces on the non-dimensional natural frequencies for rotating beam with the variable width.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2001.10a
• /
• pp.87-90
• /
• 2001

In particle or short-fiber reinforced composites, cracking of the reinforcements is a significant damage mode because the broken reinforcements lose load carrying capacity. This paper deals with elastic stress distributions and load carrying capacity of intact and cracked ellipsoidal inhomogeneities. Three dimensional finite element analysis has been carried out on intact and broken ellipsoidal inhomogeneities in an infinite body under pure shear. For the intact inhomogeneity, as well known as Eshelby(1957) solution, the stress distribution is uniform in the inhomogeneity and non-uniform in the surrounding matrix. On the other hand, for the broken inhomogeneity, the stress in the region near crack surface is considerably released and the stress distribution becomes more complex. The average stress in the inhomogeneity represents its load carrying capacity, and the difference of average stresses between the intact and broken inhomogeneities indicates the loss of load carrying capacity due to cracking damage. The load carrying capacity of the broken inhomogeneity is expressed in terms of the average stress of the intact inhomogeneity and some coefficients. It is found that the broken inhomogeneity with higher aspect ratio still maintains higher load carrying capacity.

• Journal of Mechanical Science and Technology
• /
• v.15 no.6
• /
• pp.709-719
• /
• 2001

In particle or short-fiber reinforced composites, cracking of reinforcements is a significant damage mode because the cracked reinforcements lose carrying capacity. This paper deals with elastic stress distributions and load carrying capacity of intact and cracked ellipsoidal inhomogeneities. Three dimensional finite element analysis has been carried out on intact and cracked ellipsoidal inhomogeneities in an infinite body under uniaxial tension and pure shear. For the intact inhomogeneity, as well known as Eshelbys solution, the stress distribution is uniform in the inhomogeneity and nonuniform in the surrounding matrix. On the other hand, for the cracked inhomogeneity, the stress in the region near the crack surface is considerably released and the stress distribution becomes more complex. The average stress in the inhomogeneity represents its load carrying capacity, and the difference between the average stresses of the intact and cracked inhomogeneities indicates the loss of load carrying capacity due to cracking damage. The load carrying capacity of the cracked inhomogeneity is expressed in to cracking damage. The load carrying capacity of the cracked inhomogeneity is expressed in terms of the average stress of the intact inhomogeneity and some coefficients. It is found that a cracked inhomogeneity with high aspect ratio still maintains higher load carrying capacity.

• Kyungpook Mathematical Journal
• /
• v.63 no.2
• /
• pp.235-250
• /
• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.