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| 1.
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論文
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中西, 康彦
概要:
application/pdf<br />Journal Article<br />In this paper, we propose a topology optimization method for two-dimensional structures. Virtual nodal forces are employed as design variables that are functions of parameters derived from
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boundary cycles in the homology theory. The density of material in each element is determined by the design variables so that the density of strain energy is equal to the prescribed value. The objective function is the volume of a plate, and it is minimized. The virtual nodal forces always satisfy the equilibrium at each node in the process of optimization without constraints on parameters, although all elastic equations are not satisfied until the process is completed. In other words, the finite element analysis and topology optimization progress simultaneously. This method does not require repeating finite element analysis. Although the optimum structures obtained by this method as numerical examples varied depending on values of constants in the optimization method or the size of elements, the conditions of the density of strain energy were almost satisfied. It can be said that the validity of the proposed method was proved.
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| 2.
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論文
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中西, 康彦
概要:
application/pdf<br />Journal Article<br />In the process of topology optimization, topology of a structure is, in general, changed in succession. In this paper, a method of inferring the change of topology is proposed. This
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method makes it possible to impose constraint conditions upon topology of the structure. Topological constraint conditions can be expressed by homology groups. As a numerical example, topology of a plate is optimized using an artificial model (the density approach) under topological constraint conditions that (I) the structure is not divided into pieces during the optimization process, and (II) the number of holes is less than or equal to the prescribed number. As a result, it was found that (1) topological constraints were correctly satisfied by the proposed method, (2) the least useful members tend to be removed by topological constraints, and other ones are reinforced, and (3) the strain energy of structures obtained under certain topological constraints is somewhat higher than that of ones without topological constraints
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| 3.
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論文
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中西, 康彦 ; 松原, 雅昭
概要:
application/pdf<br />Journal Article<br />In this paper, location, angle and size of plural defects in a structural component are identified by an elastodynamic boundary element method. Each defect is noncircular and
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represented by 5 parameters, a radius, an angle, x and y coordinates of the location and the degree of distortion of its shape. External force of harmonic excitation is applied to the component and the displacements at points on its boundary are chosen as additional information. The square sum of the differences in displacements between real values and inference from numerical solutions is minimized to identify the defects using the conjugate gradient method. Though the number of defects is assumed to be one in the beginning of the identification process, the assumed defect is divided into two parts when the value of the parameter representing its distortion satisfies a certain condition. To judge correctly whether it should be divided, it is assumed that defects are filled with imaginary material of which mass density and Young's modulus are considerably low in comparison with those of a structural component.
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| 4.
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論文
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中西, 康彦
概要:
application/pdf<br />Journal Article<br />When an element is removed from a ground structure or an initial shape by genetic algorithm, homogenization method and so forth in the process for optimizing topology of a structure, its topology
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is probably changed. In this paper, we propose a new method of inferring the change in topology of a structure before the elimination of each element. This method can show the relation between elements of a structure and invariant factors in homology groups representing topology of the structure. As a numerical example, the proposed method is utilized for imposing topological constraint conditions on a three-dimensional structure consisting of triangular elements. The number of elements and strain energy of the structure are minimized under the conditions. As a result, it was found that a topological constraint on a zero-dimensional homology group of which rank is equal to the number of connected components of the structure is the most important one to reduce the number of elements and strain energy.
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