• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.585-596
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• 1998

Some new problems of the theory of the finite automata are considered. Applying the finite automata in various tasks of the formal languages theory is observed. Special proof of Kleene's theorem is obtained. This proof is used for the defining the star-height of the finite automaton. The proper-ties of the last object are considered. The star-height of the finite automaton is used for reformulating the star-height problem of regular expression for finite automata. The method of the reduction of the star-height problem to the task of making special finite automaton is obtained. This reformulating can help to solve the star-height problem by new way.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.1565-1568
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• 2003

The backward extrusion process is one of the commonly used metal forming processes. In this paper. a battery case which has the rectangular section, is analyzed using a 3D metal forming package(MSC.Superforge). This pacakge uses the finite volume analysis method. It is shown that the MSC.Superforge package using finite volume method provides result very close to those obtained from a finite element analysis package(MSC.Superform). However, the simulation time using the finite volume method was almost 10 % of the simulation time consumed by the other package using finite element method. Moreover, the finite volume method used in MSC.Superforge can eliminate the remeshing problems that make the simulating a metal forming process with severe deformation, such as the extrusion process, so difficult.

• Structural Engineering and Mechanics
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• 제83권2호
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• pp.273-282
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• 2022

In this paper, we propose a new concept for error estimation in finite element solutions, which we call mode-based error estimation. The proposed error estimation predicts a posteriori error calculated by the difference between the direct finite element (FE) approximation and the recovered FE approximation. The mode-based FE formulation for the recently developed self-updated finite element is employed to calculate the recovered solution. The formulation is constructed by searching for optimal bending directions for each element, and deep learning is adopted to help find the optimal bending directions. Through various numerical examples using four-node quadrilateral finite elements, we demonstrate the improved predictive capability of the proposed error estimator compared with other competitive methods.

• 대한수학회논문집
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• 제39권2호
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• pp.313-329
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• 2024

An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of atoms (counting repetitions) in the corresponding sum is called the length of the factorization. Following Geroldinger and Zhong, we say that an atomic monoid M is a length-finite factorization monoid if each b ∈ M has only finitely many factorizations of any prescribed length. An additive submonoid of ℝ_≥0 is called a positive monoid. Factorizations in positive monoids have been actively studied in recent years. The main purpose of this paper is to give a better understanding of the non-unique factorization phenomenon in positive monoids through the lens of the length-finite factorization property. To do so, we identify a large class of positive monoids which satisfy the length-finite factorization property. Then we compare the length-finite factorization property to the bounded and the finite factorization properties, which are two properties that have been systematically investigated for more than thirty years.

• 대한수학회보
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• 제34권3호
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• pp.351-358
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• 1997

A conjugacy theorem which holds for finite groups is proven to hold for Cernikov groups and locally finite CC-groups.

• 한국전산구조공학회논문집
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• 제22권4호
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• pp.335-341
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• 2009

본 논문에서는 MLS기반 유한요소에 대한 현재 개발상황에 대한 개관과 향후 예상할 수 있는 응용분야에 대한 제안을 하였다. 이동최소제곱근사를 이용하여 형상함수를 생성하는 MLS기반 유한요소는, 요소의 경계에서 기존 유한요소의 성질-크로네커 델타 조건-을 가지면서도 기존 요소가 갖지 못했던 임의의 절점 추가가 자유롭다는 장점이 있어 다양한 변절점 요소로의 개발이 이루어져 왔다. 선형 또는 이차형상함수를 갖는 2차원 변절점요소 뿐 아니라, 균열선단과 균열면을 포함하고 있는 2차원 균열요소와 3차원에서의 제한적인 변절점요소 등이 개발되어 다양한 불연속성 문제에 적용 가능함이 입증되었다. 이러한 MLS기반 유한요소는 향후 2차원 변절점 3각요소, 2차원 삼각균열요소, 변절점 쉘요소, 균열 쉘요소, 마칭큐브알고리즘에 적합한 3차원 다면체요소로의 개발이 가능할 것으로 예상되며, 본 논문에서는 그 일례로 3차원 다면체요소를 이용한 대퇴골의 요소망 생성을 보였다.

• Journal of Mechanical Science and Technology
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• 제17권5호
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• pp.679-690
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• 2003

As the rate of increase in areal density of the HDD has accelerated, dynamic characteristics of the HDD actuator need to be improved with respect to the performance of the tracking servo and shock transmission. Therefore, it is important to analyze the vibration characteristic of the HDD actuator that consists of the VCM part, E-block and pivot bearing. In this paper, vibration modes of the HDD actuator are investigated the using finite element and experimental modal analyses methods. To develop a detailed finite element model, finite element models of each components of the actuator assembly are constructed and tuned to the results of the EMA. The VCM coil is modeled as an equivalent finite element model that has an orthotropic material property using auto-model updating program. Auto-model updating program with improved sensitivity based iterative method is applied to build a detailed finite element model using the result of the EMA. A detailed finite element model of the HDD actuator is then constructed and analyzed.

• Biomaterials and Biomechanics in Bioengineering
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• 제3권2호
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• pp.71-84
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• 2016

The finite element method is wide used in simulation in the biomechanical structures, but a lack of studies concerning finite element mesh quality in biomechanics is a reality. The present study intends to analyze the importance of the mesh quality in the finite element model results from humeral structure. A sensitivity analysis of finite element models (FEM) is presented for the humeral bone and cartilage structures. The geometry of bone and cartilage was acquired from CT scan and geometry reconstructed. The study includes 54 models from same bone geometry, with different mesh densities, constructed with tetrahedral linear elements. A finite element simulation representing the glenohumeral-joint reaction force applied on the humerus during $90^{\circ}$ abduction, with external load as the critical condition. Results from the finite element models suggest a mesh with 1.5 mm, 0.8 mm and 0.6 mm as suitable mesh sizes for cortical bone, trabecular bone and humeral cartilage, respectively. Relatively to the higher minimum principal strains are located at the proximal humerus diaphysis, and its highest value is found at the trabecular bone neck. The present study indicates the minimum mesh size in the finite element analyses in humeral structure. The cortical and trabecular bone, as well as cartilage, may not be correctly represented by meshes of the same size. The strain results presented the critical regions during the $90^{\circ}$ abduction.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2005년도 춘계종합학술대회
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• pp.925-927
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• 2005

The study is about a finite field multiplying unit, which performs a calculation t-times as fast as the Mastrovito's multiplier architecture, suggesting and using the 2-times faster multiplier architecture. Former studies on finite field multiplication architecture includes the serial multiplication architecture, the array multiplication architecture, and the hybrid finite field multiplication architecture. Mastrovito's serial multiplication architecture has been regarded as the basic architecture for the finite field multiplication, and in order to exploit parallelism, as much resources were expensed to get as much speed in the finite field array multipliers. The array multiplication architecture has weakness in terms of area/performance ratio. In 1999, Parr has proposed the hybrid multipcliation architecture adopting benefits from both architectures. In the hybrid multiplication architecture, the main hardware frame is based on the Mastrovito's serial multiplication architecture with smaller 2-dimensional array multipliers as processing elements, so that its calculation speed is fairly fast costing intermediate resources. However, as the order of the finite field, complex integers instead of prime integers should be used, which means it cannot be used in the high-security applications. In this paper, we propose a different approach to devise a finite field multiplication architecture using Mastrovito's concepts.

• Structural Engineering and Mechanics
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• 제27권3호
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• pp.311-331
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• 2007

The purpose of this paper is to study shear locking-free analysis of thick plates using Mindlin's theory and to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to uniformly distributed loads. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 8- and 17-noded quadrilateral finite elements are used. Graphs and tables are presented that should help engineers in the design of thick plates. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates. It is also concluded, in general, that the maximum displacement and bending moment increase with increasing aspect ratio, and that the results obtained in this study are better than the results given in the literature.