• Journal of the Computational Structural Engineering Institute of Korea
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• v.35 no.6
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• pp.367-374
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• 2022

This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

• Economic and Environmental Geology
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• v.30 no.4
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• pp.289-301
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• 1997

The Boguk cobalt mine is located within the Cretaceous Gyeongsang Sedimentary Basin. Major ore minerals including cobalt-bearing minerals (loellingite, cobaltite, and glaucodot) and Co-bearing arsenopyrite occur together with base-metal sulfides (pyrrhotite, chalcopyrite, pyrite, sphalerite, etc.) and minor amounts of oxides (magnetite and hematite) within fracture-filling $quartz{\pm}actinolite{\pm}carbonate$ veins. These veins are developed within an epicrustal micrographic granite stock which intrudes the Konchonri Formation (mainly of shale). Radiometric date of the granite (85.98 Ma) indicates a Late Cretaceous age for granite emplacement and associated cobalt mineralization. The vein mineralogy is relatively complex and changes with time: cobalt-bearing minerals with actinolite, carbonates, and quartz gangues (stages I and II) ${\rightarrow}$ base-metal sulfides, gold, and Fe oxides with quartz gangues (stage III) ${\rightarrow}$ barren carbonates (stages IV and V). The common occurrence of high-temperature minerals (cobalt-bearing minerals, molybdenite and actinolite) with low-temperature minerals (base-metal sulfides, gold and carbonates) in veins indicates a xenothermal condition of the hydrothermal mineralization. High enrichment of Co in the granite (avg. 50.90 ppm) indicates the magmatic hydrothermal derivation of cobalt from this cooling granite stock, whereas higher amounts of Cu and Zn in the Konchonri Formation shale suggest their derivations largely from shale. The decrease in temperature of hydrothermal fluids with a concomitant increase in fugacity of oxygen with time (for cobalt deposition in stages I and II, $T=560^{\circ}C-390^{\circ}C$ and log $fO_2=$ >-32.7 to -30.7 atm at $350^{\circ}C$; for base-metal sulfide deposition in stage III, $T=380^{\circ}-345^{\circ}C$ and log $fO_2={\geq}-30.7$ atm at $350^{\circ}C$) indicates a transition of the hydrothermal system from a magmatic-water domination toward a less-evolved meteoric-water domination. Sulfur isotope data of stage II sulfide minerals evidence that early, Co-bearing hydrothermal fluids derived originally from an igneous source with a ${\delta}^{34}S_{{\Sigma}S}$ value near 3 to 5‰. The remarkable increase in ${\delta}^{34}S_{H2S}$ values of hydrothermal fluids with time from cobalt deposition in stage II (3-5‰) to base-metal sulfide deposition in stage III (up to about 20‰) also indicates the change of the hydrothermal system toward the meteoric water domination, which resulted in the leaching-out and concentration of isotopically heavier sulfur (sedimentary sulfates), base metals (Cu, Zn, etc.) and gold from surrounding sedimentary rocks during the huge, meteoric water circulation. We suggest that without the formation of the later, meteoric water circulation extensively through surrounding sedimentary rocks the Boguk cobalt deposits would be simple veins only with actinolite + quartz + cobalt-bearing minerals. Furthermore, the formation of the meteoric water circulation after the culmination of a magmatic hydrothermal system resulted in the common occurrence of high-temperature minerals with later, lower-temperature minerals, resulting in a xenothermal feature of the mineralization.