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edited by Maïtine Bergounioux ... [et al.]
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Seymour Lipschutz, Ph.D
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X. Huang, Y.M. Xie
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edited by Jan van Mill, George M. Reed
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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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M.P. Bendsøe, O. Sigmund
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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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Stephan C. Carlson
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Stephen Huggett and David Jordan
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論文
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Nakanishi, Yasuhiko
概要:
application/pdf<br />Journal Article<br />Genetic algorithm (GA) is one of the most useful methods to optimize topology of structures. The performance of GA, however, deeply depends upon a rule of coding from a structure to a string (a
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chromosome), which must be decided before the execution of GA. An improper coding can cause a lot of unanalyzable structures to be generated in the process of optimization, which are separated into several pieces with no supporting or loading points. In this paper, a method to give such unanalyzable structures a fitness value based upon their topology using homology theory is proposed to raise the probability of obtaining the optimum structures. As numerical examples, topology of two-dimensional frames and three-dimensional structures consisting of triangular elements supported on a rigid wall and loaded vertically on a point distant from the wall are optimized under a constraint of constant weight. As a result, it was found that the proposed method increased the average fitness value and the number of optimum structures obtained in 100 trials of GA in comparison with other methods that considered unanalyzable structures to be useless.
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