• Structural Engineering and Mechanics
• /
• v.72 no.6
• /
• pp.713-722
• /
• 2019

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G₂₃ and G₁₂, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G₁₂, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 1993.05a
• /
• pp.85-87
• /
• 1993

We have investigated three polyene systems, $X-(-HC=CH-)_n-Y$, where X/Y=H/H, $F/CH_3$, and $NH_2/NO_2$. We estimated asymptotic values (for $n=\infty$ of the electronic properties with $logA=a_o+a_1/(n+1)+a_2/(n+1)^2+a_3/(n+1)^3$, so that the cases n=0 can be included in that equation. Here, A can be $\mu$, $\beta$, $\alpha/(n+1)$ or $\gamma/(n+1)$. For these asymptotic values. the SCF results are more reliable due to the higher level of theory, while the PM3 results can give better trend with more data for polyene systems with longer chain length.

• Journal of Korean Society for Quality Management
• /
• v.23 no.4
• /
• pp.157-166
• /
• 1995

Process capability indices are used to determine whether a production process is capable of producing items within a specified tolerance. We could estimate the finite sample distributions of some process capability indices with bootstrap method. In this paper, we derive the asymptotic bootstrap distributions of some process capability indices ${\hat{C}}^*_p$, ${\hat{C}}^*_{pk}$ and ${\hat{C}}^*_{pm}$ under general proper conditions. These asymptotic distributiops would be used in constructing some bootstrap confidence intervals. Also, we examine some small sample properties related to these estimators by some simulations.

• Journal of the Korean Statistical Society
• /
• v.26 no.1
• /
• pp.31-46
• /
• 1997

Let $X_{t}$ = .beta. $X_{{t-1}}$ + .epsilon.$_{t}$ be an autoregressive process where $\mid$.beta.$\mid$ < 1 and {.epsilon.$_{t}$} is independent and identically distriubted with regularly varying tail probabilities. This process is called the asymptotically stationary first-order autoregressive process (AR(1)) with infinite variance. In this paper, we obtain a host of weak convergences of some point processes based on bootstrapping of { $X_{t}$}. These kinds of results can be generalized under the infinite variance assumption to ensure the asymptotic validity of the bootstrap method for various functionals of { $X_{t}$} such as partial sums, sample covariance and sample correlation functions, etc.ions, etc.

• International Journal of Reliability and Applications
• /
• v.9 no.2
• /
• pp.125-140
• /
• 2008

The new better than used failure rate (NBUFR), Abouammoh and Ahmed (1988), and new better than average failure rate (NBAFR) Loh (1984) classes of life distributions, have been considered in the literature as natural weakenings of NBU (NWU) property. The paper considers testing exponentiality against strictly NBUFR (NBAFR) alternatives, or their duals, based on goodness of fit approach that is possible in life testing problems and that it results in simpler procedures that are asymptotically equivalent or better than standard ones. They may also have superior finite sample behavior. The asymptotic normality are proved. Powers, Pitman asymptotic efficiency and critical points are computed. Dealing with censored data case also studied. Practical applications of our tests in the medical sciences are present.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.35-43
• /
• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• Korean Journal of Mathematics
• /
• v.8 no.2
• /
• pp.121-126
• /
• 2000

B.Djafari Rouhani and W.A.Kirk [3] proved the following theorem: Let Xbe a reflexive Banach space and $(x_n)_{n{\geq}0}$ be a nonexpansive (resp., firmly nonexpansive )sequence in X. Then the set of weak ${\omega}$-limit points of the sequence $(\frac{x_n}{n})_{n{\geq}1}$(resp., $(x_{n+1}-x_n)_{n{\geq}0$) always lies on a convex subset of a sphere centered at the origin of radius $d={\lim}_{n{\rightarrow}{\infty}}\frac{{\parallel}x_n{\parallel}}{n}$. In this paper we show that the above theorem for nonexpansive(resp., firmly nonexpansive) sequences holds in a general Banach space(resp., a strictly convex dual $X^*$).

• 한국전산유체공학회:학술대회논문집
• /
• 2004.10a
• /
• pp.7-14
• /
• 2004

It is well known that preconditioning methods are efficient for convergence acceleration at compressible low Mach number flows. In this study, the original Euler equations and three preconditioners nondimensionalized differently are implemented in two dimensional inviscid bump flows using the 3rd order MUSCL and DADI schemes as flux discretization and time integration respectively. The multigrid and local time stepping methods are also used to accelerate the convergence. The test case indicates that a properly modified local preconditioning technique involving concepts of a global preconditioning one produces Mach number independent convergence. Besides, an asymptotic analysis for properties of preconditioning methods is added.

• Journal of Korean Society for Quality Management
• /
• v.22 no.4
• /
• pp.59-78
• /
• 1994

In some observational studies, we have often random censoring model. However, the data available may be partially observable censored data consisting of the observed failure times and only those nonfailure times which are subject to follow up. In this paper, we present an extension of the problem of partially parametric estimation of the survival function to such partially observable censored data. The proposed estimator treats the observed failure times nonparametrically and uses a parametric model only for those nonfailure times which are subject to follow-up. We discuss the motivation and construction of the proposed estimator and investigate the limiting properties of the proposed estimator such as asymptotic normality. Also, when the assumed parametric model is exponential, the asymptotic variance of the estimator is obtained. Furthermore, an example is given to compare the proposed estimator with the modified Kaplan Meier(MKM) estimator. From the results, it is shown that the relative efficiency of the proposed estimator is higher than that of the MKM estimator in the follow-up study with increasing time.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.19 no.7
• /
• pp.35-40
• /
• 2020

This work is concerned with various planar deformations of an isotropic sandwich beam, which generally consists of three layers: two stiff skin layers and one soft core layer. When one layer of the sandwich beam is modeled as a beam, the variational-asymptotic method is rigorously used to construct a zeroth-order beam model, which is similar to a generalized Timoshenko beam model capable of capturing the transverse shear deformations but still carries out the zeroth-order approximation. To analyze the planar sandwich beam, the sum of the energies of the two skin layers and one core layer is then formulated with different material and geometric properties and represented by a universal beam model in terms of the core-layer kinematics through interface displacement and stress continuity conditions. As a preliminary validation, two extreme examples are presented to demonstrate the capability and accuracy of this present approach.