• The Mathematical Education
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• v.45 no.1 s.112
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• pp.61-74
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• 2006

The ability of understanding the number and number systems, grasping the properties of number systems, and manipulating number systems is the foundation to understand algebra. It is useful to deepen students' mathematical understanding of number systems and operations. The authentic understanding of numbers and operations can make it possible for the students to manipulate algebraic symbols, to represent relationship among sets of numbers, and to use variables to investigate the properties of sets of numbers. The high school students need to understand the number systems from more abstract perspective. The purpose of this study is to study on understanding and application ability of eleventh graders of basic properties of operations with real numbers.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.12
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• pp.1094-1101
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• 2013

This paper proposes an improved branch predictor that reduces the number execution cycles of applications by selectively accessing a specific element in 4-way associative cache. When a branch instruction is fetched, the proposed branch predictor acquires a branch target address from the selected element in the cache by referring to MRU buffer. Branch prediction rate and application execution speed are considerably improved by increasing the number of BTAC entries in restricted power condition, when compared with that of previous branch predictor which accesses all elements. The effectiveness of the proposed dynamic branch predictor is verified by executing benchmark applications on the core simulator. Experimental results show that number of execution cycles decreases by an average of 10.1%, while power consumption increases an average of 7.4%, when compared to that of a core without a dynamic branch predictor. Execution cycles are reduced by 4.1% in comparison with a core which employs previous dynamic branch predictor.

• Journal of the Korean Society of Industry Convergence
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• v.7 no.4
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• pp.355-361
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• 2004

The finite element method were used to determine the stress intensity factor of cracked plate. The stress method, displacement method and J Integral are most popular finte element method. ANSYS proposed another a kind of displacement method. In this paper, it was examined that the accuracy and utility of the ANSYS method could believable to determine the stress intensity factors of centered inclined crack. Generally, inclined crack has two portion of stress intensity factors, tensile mode F1 and shear mode F2. For the purpose of increasing the accuracy of stress intensity factors, examined the effect of the numbers of nodes and elements, crack tip element size and number of partition of the crack tip vicinity. It was found that the method proposed by ANSYS is useful and has high accuracy. Accuracy of calculated stress intensity factors was increased by increase of the number of nodes and elements, and at the small size of crack tip elements can get more highly accuracy.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.25-32
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• 2004

In this proposed work new finite element model for multi-delaminated plates is proposed. In the current analysis procedures of multi-delaminated plates, plate element based on Mindlin plate theory is used in order to obtain accurate results of out-of-plane displacement of thick plate. And for delaminated region, plate element based on Kirchhoff plate theory is considered. To satisfy the displacement continuity conditions, displacement vector based on Kirchhoff theory is transformed to displacement of transition element. The numerical results show that the effect of delaminations on the modal parameters of delaminated composites plates is dependent not only on the size, the location and the number of the delaminations but also on the mode number and boundary conditions. Kirchhoff based model have higher natural frequency than Mindlin based model and natural frequency of the presented model is closed to Mindlin based model.

• Structural Engineering and Mechanics
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• v.25 no.1
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• pp.91-106
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• 2007

A new class of finite elements is described for dealing with mesh gradation. The approach employs the moving least square (MLS) scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain. This approach generally leads to elements with rational shape functions, which significantly extends the function space of the conventional finite element method. With a special choice of the nodal points and the base functions, the method results in useful elements with polynomial shape functions for which the $C^1$ continuity breaks down across the boundaries between the subdomains comprising one element. Among those, (4 + n)-noded MLS based finite elements possess the generality to be connected with an arbitrary number of linear elements at a side of a given element. It enables us to connect one finite element with a few finite elements without complex remeshing. The effectiveness of the new elements is demonstrated via appropriate numerical examples.

• Journal of ILASS-Korea
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• v.20 no.1
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• pp.1-6
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• 2015

Visualization of the mixing pattern in a non-element mixer was carried out using laser induced fluorescence(LIF) to evaluate characteristics of mixer consisting of the main flow pipe and branch flow pipes. The branch flows were injected periodically with the period $T_{in}$ normal to the main flow, and rhodamine B was mixed into the most upstream branch flow to visualize mixing pattern in the main flow pipe by LIF. The length of boundary line L of the LIF image was measured. In this study, a numerical analysis was performed to identify the mixing process of the non-element mixer, and the results were compared with experimental results. Each result was almost the same. When the number of branch flows is increased, the mixing pattern became complicated and was supposed to become chaotic. The length of boundary line L increased exponentially with an increase in the number of branch flows.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.291-300
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• 1998

This paper demonstrates how ambient vibration measurements at a limited number of locations can be effectively utilized to estimate parameters of a finite element model of a large-scale structural system involving a large number of elements. System identification using ambient vibration measurements presents a challenge requiring the use of special identification techniques, which ran deal with very small magnitudes of ambient vibration contaminated by noise without the knowledge of input farces. In the present study, the modal parameters such as natural frequencies, damping ratios, and mode shapes of the structural system were estimated by means of appropriate system identification techniques including the random decrement method. Moreover, estimation of parameters such as the stiffness matrix of the finite element model from the system response measured by a limited number of sensors is another challenge. In this study, the system stiffness matrix was estimated by using the quadratic optimization involving the computed and measured modal strain energy of the system, with the aid of a sensitivity relationship between each element stiffness and the modal parameters established by the second order inverse modal perturbation theory. The finite element models thus identified represent the actual structural system very well, as their calculated dynamic characteristics satisfactorily matched the observed ones from the ambient vibration test performed on a large-scale structural system subjected primarily to ambient wind excitations. The dynamic models identified by this study will be used for design of an active mass damper system to be installed on this structure fer suppressing its wind vibration.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.10
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• pp.1702-1711
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• 1997

A numerical study for the number of terms of a power series stress function and the effect of hybrid element size on stress analysis around a hole in loaded orthotropic composites is presented. The hybrid method coupling experimental and/or theoretical inputs and complex variable formulations involving conformal mappings and analytical continuity is used to calculate tangential stress on the boundary of the hole in uniaxially loaded, finite width glass epoxy tensile plate. The tests are done by rarying the number of terms, element size and nodal locations on the external boundary of the hybrid region. The numerical results indicate that the hybrid method is accurate and powerful in both experimental and numerical stress analysis.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.310-317
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• 2006

Currently most practical vibration and structural problems in automotive suspensions require the use of the finite element method to obtain their structural responses. When the finite element model has a very large number of degrees of freedom the harmonic and dynamic analyses are computationally too expensive to repeat within a feasible design process time. To alleviate the computational difficulty, this paper presents a moment-matching based model order reduction (MOR) which reduces the number of degrees of freedom of the original finite element model and speeds up the necessary simulations with the reduced-size models. The moment-matching model reduction via the Arnoldi process is performed directly to ANSYS finite element models by software mor4ansys. Among automotive suspension components, a knuckle is taken as an example to demonstrate the advantages of this approach for vibration simulation. The frequency and transient dynamic responses by the MOR are compared with those by the mode superposition method.

• Geomechanics and Engineering
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• v.1 no.2
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.