• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.3
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• pp.39-55
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• 1992

In this research, a Three Level Decomposition technique has been developed for configuration design optimization of truss structures. In the first level, as design variables, behavior variables are used and the strain energy has been treated as the cost function to be maximized so that the truss structure can absorb maximum energy. For design constraint of the optimal design problem, allowable stress, buckling stress, and displacement under multi-loading conditions are considered. In the second level, design problem is formulated using the cross-sectional area as the design variable and the weight of the truss structure as the cost function. As for the design constraint, the equilibrium equation with the optimal displacement obtained in the first level is used. In the third level, the nodal point coordinates of the truss structure are used as coordinating variable and the weight has been taken as the cost function. An advantage of the Three Level Decomposition technique is that the first and second level design problems are simple because they are linear programming problems. Moreover, the method is efficient because it is not necessary to carry out time consuming structural analysis and techniques for sensitivity analysis during the design optimization process. By treating the nodal point coordinates as design variables, the third level becomes unconstrained optimal design problems which is easier to solve. Moreover, by using different convergence criteria at each level of design problem, improved convergence can be obtained. The proposed technique has been tested using four different truss structures to yield almost identical optimum designs in the literature with efficient convergence rate regardless of constraint types and configuration of truss structures.

• Journal of the Korean Magnetics Society
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• v.18 no.6
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• pp.211-216
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• 2008

The effects of Si impurity on electronic structures and magnetism of bcc Fe are investigated by using a first-principles method by considering spin-orbit coupling. In order to describe the Si impurity, a 27 atomic bcc Fe supercell has been considered. The Kohn-Sham equation was solved in terms of the all-electron full-potential linearized augmented plane wave (FLAPW) method within the generalized gradient approximation (GGA). The effects of spin-orbit coupling were calculated self-consistently by considering spin-diagonal terms based on second variation method. For the ferromagnetic (FM) state without considering SOC, the spin magnetic moment of the Si impurity was calculated to be $-0.143{\mu}B$, while the magnetic moments of Fe atoms were calculated to be $2.214{\mu}B$, $2.327{\mu}B$, and $2.354{\mu}B$ in away from the Si atom, respectively. However, the FM state with considering SOC, the spin magnetic moment of the Si impurity was calculated to be $-0.144{\mu}B$, which is not affected significantly by SOC, but the spin magnetic moments of Fe atoms were calculated $2.189{\mu}B$, $2.310{\mu}B$, and $2.325{\mu}B$, respectively, which are much reduced value compared to those of the FM state without SOC. Comparing the total charge density and spin density, those features are thought to be originated by the screening distortions of the Fe $t_{2g}$ orbital, which can be obtained by considering SOC.