• Computers and Concrete
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• 제31권3호
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• pp.223-239
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• 2023

Geometric nonlinear performance simulation and analysis of complex modern buildings and industrial products require high-performance shell elements. Balancing multiple aspects of performance in the one geometric nonlinear analysis element remains challenging. We present a new shell element, flat shell DKMGQ-CR (Co-rotational Discrete Kirchhoff-Mindlin Generalized Conforming Quadrilateral), for linear and geometric nonlinear analysis of both thick and thin shells. The DKMGQ-CR shell element was developed by combining the advantages of high-performance membrane and plate elements in a unified coordinate system and introducing the co-rotational formulation to adapt to large deformation analysis. The effectiveness of linear and geometric nonlinear analysis by DKMGQ-CR is verified through the tests of several classical numerical benchmarks. The computational results show that the proposed new element adapts to mesh distortion and effectively alleviates shear and membrane locking problems in linear and geometric nonlinear analysis. Furthermore, the DKMGQ-CR demonstrates high performance in analyzing thick and thin shells. The proposed element DKMGQ-CR is expected to provide an accurate, efficient, and convenient tool for the geometric nonlinear analysis of shells.

• International Journal of Naval Architecture and Ocean Engineering
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• 제4권3호
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• pp.313-321
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• 2012

Vibration analysis of a thin-walled structure can be performed with a consistent mass matrix determined by the shape functions of all degrees of freedom (d.o.f.) used for construction of conventional stiffness matrix, or with a lumped mass matrix. In similar way stability of a structure can be analysed with consistent geometric stiffness matrix or geometric stiffness matrix with lumped buckling load, related only to the rotational d.o.f. Recently, the simplified mass matrix is constructed employing shape functions of in-plane displacements for plate deflection. In this paper the same approach is used for construction of simplified geometric stiffness matrix. Beam element, and triangular and rectangular plate element are considered. Application of the new geometric stiffness is illustrated in the case of simply supported beam and square plate. The same problems are solved with consistent and lumped geometric stiffness matrix, and the obtained results are compared with the analytical solution. Also, a combination of simplified and lumped geometric stiffness matrix is analysed in order to increase accuracy of stability analysis.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1996년도 추계학술대회 논문집
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• pp.157-161
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• 1996

In the geometric accuracy, most of studies have been concentrated on the analysis of the geometric error, or a control path of grinding using the value of measured geometric error. In this paper, by using the value of measured motor current through hall sensor, detection of the geometric error have been accomplished, and in-process control path of grinding for improvement geometric accuracy, too.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.196-220
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• 2021

This study formulates a new geometric parameterization scheme to effectively address numerical analysis subject to the variation of the fiber radius of a square unit cell. In particular, the proposed mesh-morphing approach may lead to a parameterized weak form whose bilinear and linear forms are affine in the geometric parameter of interest, i.e. the fiber radius. As a result, we may certify the reduced basis analysis of a square unit cell model for any parameters in a predetermined parameter domain with a rigorous a posteriori error bound. To demonstrate the utility of the proposed geometric parameterization, we consider a two-dimensional, steady-state heat conduction analysis dependent on two parameters: a fiber radius and a thermal conductivity. For rapid yet rigorous a posteriori error evaluation, we estimate a lower bound of a coercivity constant via the min-θ method as well as the successive constraint method. Compared to the corresponding finite element analysis, the constructed reduced basis analysis may yield nearly the same solution at a computational speed about 29 times faster on average. In conclusion, the proposed geometric parameterization scheme is conducive for accurate yet efficient reduced basis analysis.

• East Asian mathematical journal
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• 제26권4호
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• pp.553-579
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• 2010

Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

• Applied Microscopy
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• 제45권2호
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• pp.101-105
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• 2015

Numerous digital image analysis techniques have been developed with regard to transmission electron microscopy (TEM) with the help of programming. DigitalMicrograph (DM, Gatan Inc., USA), which is installed on most TEMs as operational software, includes a script language to develop customized software for image analysis. Based on the DM script language, this work provides a script source listing for quantitative strain measurements based on a geometric phase analysis.

• 대한전기학회논문지:시스템및제어부문D
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• 제49권5호
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• pp.278-286
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• 2000

A new large-scale network geometric analysis is introduced. For a large-scale circuit, it must be analyzed with a geometric diagram and figure. So many equations are induced from a geometric loop-node diagram. The results are arranged into a simple matrix, of course. In case of constructing a network diagram, it is not easy to handle voltage and current sources together. Geometric loop analysis is related to voltage sources, and node analysis is to current sources. The reciprocal transfer is possible only to have series or parallel impedance. If not having this impedance, in order to obtain equivalent circuit, many equations must be derived. In this paper a loop-reduction method is proposed. With this method current source branch is included into the other branch, and disappears in circuit diagram. So the number of independent circuit equations are reduced as much as that of current sources. The number is not (b-n+1), but (b-n+1-p). Where p is the number of current sources. The reduction procedure is verified with a geometric principle and circuit theory. A resultant matrix can be constructed directly from this diagram structure, not deriving circuit equations. We will obtain the last results with the help of a computer.

• 한국생산제조학회지
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• 제19권2호
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• pp.178-183
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• 2010

Base-mounted type(BMT) driving assembly in CNC machine tools is an indispensable part to improve productivity by reducing tool changeover time and to meet the ever-increasing demand of precision machine tools. This study aimed to perform finite element analysis and geometric parameter optimization to improve the efficiency of BMT driving assembly. First, simulations for three-dimensional structural and vibration analysis were performed using ANSYS/Workbench on the initial geometric models of BMT driving assembly. After analyzing stress and deformation concentration zones, several new geometrical models were designed and evaluated by design of experiments and ANSYS/DesignXplorer. Through a series of analysis-evaluation-modification cycles, it was seen that designed models were effective in determining optimal geometry of BMT driving assembly.

• 대한기계학회논문집
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• 제17권8호
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• pp.2051-2060
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• 1993

A finite element program using degenerated shell element was developed to solve the geometric, material and combined nonlinear behaviors of composite laminated shell. The total Lagrangian method was implemented for geometric nonlinear analysis. The material nonlinear behavior was analyzed by considering the matrix degradation due to the progressive failure in the matrix and matrix-fiber interface after initial failure. The result of the geometric nonlinear analysis showed good agreement with the other exact and numerical solutions. The results of the combined analyses considered both geometric and material nonlinear analyses were compared with the experiments in which internal pressure was applied to the filament wound antisymmetric tubes.

• 대한기계학회논문집A
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• 제31권1호
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• pp.105-112
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• 2007

The linkage framework of geometric modeling based on NURBS(Non-Uniform Rational B-Spline) surface and shell finite analysis is developed in the present study. For this purpose, geometrically exact shell finite element is implemented. NURBS technology is employed to obtain the exact geometric quantities for the analysis. Especially, because NURBS is the most powerful and wide-spread method to represent general surfaces in the field of computer graphics and CAD(Computer Aided Design) industry, the direct computation of surface geometric quantities from the NURBS surface equation without approximation shows great potential for the integration between geometrically exact shell finite element and geometric modeling in the CAD systems. Some numerical examples are given to verify the performance and accuracy of the developed linkage framework. In additions, trimmed surfaces with some cutouts are considered for more practical applications.