• Journal of the Korean Society for Advanced Composite Structures
• /
• v.4 no.1
• /
• pp.1-8
• /
• 2013

The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.

• Journal of Korean Society of Steel Construction
• /
• v.13 no.6
• /
• pp.703-713
• /
• 2001

Derivation procedures of exact dynamic stiffness matrices of thin-walled straight beams subjected to eccentrically axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform 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 element force-displacement relationships. The natural frequencies of nonsymmetric thin-walled straight beams are evaluated and compared with analytical solutions or results by thin-walled beam element using the cubic Hermitian polynomials and ABAQU's shell elements in order to demonstrate the validity of this study.

• Journal of Korean Society of Steel Construction
• /
• v.14 no.4
• /
• pp.509-518
• /
• 2002

In order to perform the spatial buckling and static analysis of the nonsymmetric thin-walled beam-column element, improved exact static stiffness matrices were evaluated using equilibrium equation and force-deformation relationships. This numerical technique was obtained using a generalized linear eigenvalue problem, by introducing 14 displacement parameters and system of linear algebraic equations with complex matrices. Unlike the evaluation of dynamic stiffness matrices, some zero eigenvalues were included. Thus, displacement parameters related to these zero eigenvalues were assumed as polynomials, with their exact distributions determined using the identity condition. The exact displacement functions corresponding to three loadingcases for initial stress-resultants were then derived, by consistently combining zero and nonzero eigenvalues and corresponding eigenvectors. Finally, exact static stiffness matrices were determined by applying member force-displacement relationships to these displacement functions. The buckling loads and displacement of thin-walled beam were evaluated and compared with analytic solutions and results using ABAQUS' shell element or straight beam element.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.8 no.5
• /
• pp.442-451
• /
• 1997

We described a miniaturization of microstrip filters by the exact synthesis. With the exact synthesis, we can design completely new circuits physically realizable. The complex procedure for the network synthesis could be reduced by using computer software. It is a new design procedure ensuring the creation of optimum networks which have minimum number of elements. The exact synthesis gives more possibilities to make wideband filters which require bandwidth of 50~100 %. S-plane Bandpass prototypes are made with non-redundant filter synthesis technique that has transmission zero locations at required frequencies. Because this method uses the transmission lines which lengths are ${\lambda}$/4 at the stopband center frequency, we can reduce the size of the filter dramatically.

• Structural Engineering and Mechanics
• /
• v.4 no.5
• /
• pp.553-568
• /
• 1996

Finite element stiffness matrix methods are presented for finding natural frequencies (or buckling loads) and modes of repetitive structures. The usual approximate finite element formulations are included, but more relevantly they also permit the use of 'exact finite elements', which account for distributed mass exactly by solving appropriate differential equations. A transcendental eigenvalue problem results, for which all the natural frequencies are found with certainty. The calculations are performed for a single repeating portion of a rotationally or linearly (in one, two or three directions) repetitive structure. The emphasis is on rotational periodicity, for which principal advantages include: any repeating portions can be connected together, not just adjacent ones; nodes can lie on, and members along, the axis of rotational periodicity; complex arithmetic is used for brevity of presentation and speed of computation; two types of rotationally periodic substructures can be used in a multi-level manner; multi-level non-periodic substructuring is permitted within the repeating portions of parent rotationally periodic structures or substructures and; all the substructuring is exact, i.e., the same answers are obtained whether or not substructuring is used. Numerical results are given for a rotationally periodic structure by using exact finite elements and two levels of rotationally periodic substructures. The solution time is about 500 times faster than if none of the rotational periodicity had been used. The solution time would have been about ten times faster still if the software used had included all the substructuring features presented.

• Polymer(Korea)
• /
• v.38 no.3
• /
• pp.286-292
• /
• 2014

The rheology of highly concentrated polymer bonded explosive (PBX) simulant was studied. An energy material, polyethylene plastomer (Exact$^{TM}$) having similar properties to poly(BAMO-AMMO) was selected as a binder. Dechlorane with similar properties to RDX (Research Department eXplosive) was chosen as a filler. Mixing behavior in a batch melt mixer was investigated. During mixing a large amount of heat of viscous dissipation was generated and a continuous decrease in torque was observed when the filler content was above 70 v%. It was believed due to wall slip phenomena. From the SEM images, the fillers were well dispersed and the effect of mixing condition affected slightly on the dispersion. Owing to distinct shear thinning behavior of the suspensions, measuring viscosity of highly filled suspensions was possible in a high shear rate capillary rheometer though it was impossible even in a low shear rate plateplate rheometer.

• Advances in nano research
• /
• v.8 no.2
• /
• pp.135-148
• /
• 2020

The incorporation of carbon nanotubes in a polymer matrix makes it possible to obtain nanocomposite materials with exceptional properties. It's in this scientific background that this work was based. There are several theories that deal with the behavior of plates, in this research based on the Mindlin-Reissner theory that takes into account the transversal shear effect, for analysis of the critical buckling load of a reinforced polymer plate with parabolic distribution of carbon nanotubes. The equations of the model are derived and the critical loads of linear and parabolic distribution of carbon nanotubes are obtained. With different disposition of nanotubes of carbon in the polymer matrix, the effects of different parameters such as the volume fractions, the plate geometric ratios and the number of modes on the critical load buckling are analysed and discussed. The results show that the critical buckling load of parabolic distribution is larger than the linear distribution. This variation is attributed to the concentration of reinforcement (CNTs) at the top and bottom faces for the X-CNT type which make the plate more rigid against buckling.

• Journal of Communications and Networks
• /
• v.18 no.2
• /
• pp.182-189
• /
• 2016

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

• Journal of the Korean Data and Information Science Society
• /
• v.22 no.6
• /
• pp.1175-1182
• /
• 2011

In this paper, properties of exact confidence interval and some approximate confidence intervals of hyper-geometric parameter, that is the probability of success p in the population is discussed. Usually, binomial distribution is a well known discrete distribution with abundant usage. Hypergeometric distribution frequently replaces a binomial distribution when it is desirable to make allowance for the finiteness of the population size. For example, an application of the hypergeometric distribution arises in describing a probability model for the number of children attacked by an infectious disease, when a fixed number of them are exposed to it. Exact confidence interval estimation of hypergeometric parameter is reviewed. We consider the approximation of hypergeometirc distribution to the binomial and normal distribution respectively. Approximate confidence intervals based on these approximation are also adequately discussed. The performance of exact confidence interval estimates and approximate confidence intervals of hypergeometric parameter is compared in terms of actual coverage probability by small sample Monte Carlo simulation.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.23 no.2
• /
• pp.185-191
• /
• 2023

To the exact cover problem that remains NP-complete to which no polynomial time algorithm is made available, this paper proposes a linear time algorithm that yields an optimal solution. The proposed algorithm makes use of the set cover problem's major feature which states that "no identical element shall be included in more than one covering set". To satisfy this criterion, the proposed algorithm initially selects a subset with the minimum cardinality and deletes those that contain the cardinality identical to that of the selected subset. This process is repeatedly performed on remaining subsets until the final solution is obtained. Provided that the solution is unattainable, it selects subsets with the maximum cardinality and repeats the same process. The proposed algorithm has not only obtained the optimal solution with ease but also proved its wide applicability on N-queens problems, hence disproving the NP-completeness of the exact cover problem.