• Journal of the Korean Society for Precision Engineering
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• v.28 no.7
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• pp.834-850
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• 2011

In this paper, a novel tissue engineering scaffold design method based on triply periodic minimal surface (TPMS) is proposed. After generating the hexahedral elements for a 3D anatomical shape using the distance field algorithm, the unit cell libraries composed of triply periodic minimal surfaces are mapped into the subdivided hexahedral elements using the shape function widely used in the finite element method. In addition, a heterogeneous implicit solid representation method is introduced to design a 3D (Three-dimensional) bio-mimetic scaffold for tissue engineering from a sequence of computed tomography (CT) medical image data. CT image of a human spine bone is used as the case study for designing a 3D bio-mimetic scaffold model from CT image data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.8
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• pp.737-744
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• 2017

A new ultralow density material (ULDM) named Shellular was recently introduced. Shellular has a periodic cellular structure with smooth-curved shells. The template for the first Shellular was fabricated using lithography and its shape was similar to the P-surface, a type of triply periodic minimal surface (TPMS). In this paper, a new fabrication method of Shellular with D-surface, named W-Shellular, is described. W-Shellular is fabricated based on weaving of polymer wires. The compressive properties are evaluated by experiments and analysis in comparison with the previous ULDMs.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.761-778
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• 2024

A separable minimal surface is represented by the form of f(x) + g(y) + h(z) = 0, where f, g and h are real-valued functions of x, y and z, respectively. We provide exact equations for separable minimal surfaces with elliptic functions that are singly, doubly and triply periodic minimal surfaces and completely classify all them. In particular, parameters in the separable minimal surfaces change the shape of the surfaces, such as fundamental periods and its limit behavior, within the form f(x) + g(y) + h(z) = 0.