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Generation of a Quadrilateral Mesh based on NURBS for Gyroids of Variable Thickness and Porosity | ||
| Journal of Applied and Computational Mechanics | ||
| دوره 8، شماره 2، تیر 2022، صفحه 684-698 اصل مقاله (1.35 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22055/jacm.2021.38645.3260 | ||
| نویسندگان | ||
| Mariana S. Flores-Jimenez1؛ Arturo Delgado-Gutiérrez2؛ Rita Q. Fuentes-Aguilar* 1؛ Diego Cardenas1 | ||
| 1School of Engineering and Sciences, Tecnológico de Monterrey. Av. General Ramón Corona 2514, Col. Nuevo México, Zapopan, Jalisco, México, CP 45138 | ||
| 2School of Engineering and Sciences, Tecnológico de Monterrey. Calle del Puente 222, Col. Ejidos de Huipulco, Tlalpan, Ciudad de México, México, CP 14380 | ||
| چکیده | ||
| The Gyroid is a periodic minimal surface explored in different applications, such as architecture and nanotechnology. The general topology is suitable for the construction of porous structures. This paper presents a non-iterative, novel methodology for the generation of a NURBS-based Gyroid volume. The Gyroid fundamental patch is defined with the Weierstrass parameterization. Furthermore, the geometry is manipulated to generate a structured mesh, allowing better element quality for FEM and IGA simulations. The re-parametrization is carried out by a Least-Squares approximation with a parametric NURBS surface, enabling a better definition of the mid-surface normals for the generation of the complete Gyroid volume. Different cases of variational thickness and porosity are presented to validate the versatility of our method. | ||
| کلیدواژهها | ||
| Gyroid؛ NURBS؛ Parametric mesh؛ TPMS | ||
| مراجع | ||
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[1] Karcher, H., Polthier, K., Construction of Triply Periodic Minimal Surfaces, Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 354(1715), 1996, 2077-2104.
[2] Han, L., Che, S., An Overview of Materials with Triply Periodic Minimal Surfaces and Related Geometry: From Biological Structures to Self-Assembled Systems, Advanced Materials, 30(17), 2018, 1705708.
[3] Emmer, M., Minimal Surfaces and Architecture: New Forms, Nexus Network Journal, 15(2), 2013, 227-239.
[4] Sychov, M.M., Lebedev, L.A., Dyachenko, S.V., Nefedova, L.A., Mechanical properties of energy-absorbing structures with triply periodic minimal surface topology, Acta Astronautica, 150, 2018, 81-84.
[5] Thomas, N., Sreedhar, N., Al-Ketan, O., Rowshan, R., Al-Rub, R.K., Arafat, H., 3D printed triply periodic minimal surfaces as spacers for enhanced heat and mass transfer in membrane distillation, Desalination, 443, 2018, 256-271.
[6] Park, J.H., Lee, J.C., Unusually high ratio of shear modulus to Young’s modulus in a nano-structured gyroid metamaterial, Scientific Reports, 7(10533), 2017.
[7] Wei, D., Scherer, M.R., Bower, C., Andrew, P., Ryhanen, T., Steiner, U., A nanostructured electrochromic supercapacitor, Nano Letters, 12(4), 2012, 1857-62.
[8] Qin, Z., Jung, G.S., Kang, M.J., Buehler, M.J., The mechanics and design of a lightweight three-dimensional graphene assembly, Science Advances, 3(1), 2017, 1601536.
[9] Yang, Y., Wang, G., Liang, H., Gao, C., Peng, S., Shen, L., Shuai, C., Additive manufacturing of bone scaffolds, International Journal of Bioprinting, 5(1), 2019, 148.
[10] Bobber, F.S.L, Zadpoor, A.A., Effects of bone substitute architecture and surface properties on cell response, angiogenesis, and structure of new bone, Journal of Materials Chemistry B, 5(31), 2017, 6175-6192.
[11] Melchels, F.P.W., Bertoldi, K., Gabbrielli, R., Velders, A.H., Feijen, J., Grijpma, D.W., Mathematically defined tissue engineering scaffold architectures prepared by stereolithography, Biomaterials, 31(27), 2010, 6909-6916.
[12] Callens, S.J.P, Uyttendaele, R.J.C, Fratila-Apachitei, L.E., Zadpoor, A.A., Substrate curvature as a cue to guide spatiotemporal cell and tissue organization, Biomaterials, 23, 2020, 119739.
[13] Fantini, M., Curto, M., Crescenzio, F., TPMS for interactive modelling of trabecular scaffolds for Bone Tissue Engineering, Advances on Mechanics, Design Engineering and Manufacturing, Springer, 2016.
[14] Walker, J.M., Bodamer, E., Kleinfehn, A., Luo, Y., Becker, M., Dean, D., Design and mechanical characterization of solid and highly porous 3D printed poly(propylene fumarate) scaffolds, Progress in Additive Manufacturing, 2, 2017, 99-108.
[15] Al-Ketan, O., Al-Rub, R.K.A., MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces, Material Design & Processing Communications, 2020, e205.
[16] Shi, J., Yang, J., Zhu, L., Li, L., Li, Z., Wang, X., A Porous Scaffold Design Method for Bone Tissue Engineering Using Triply Periodic Minimal Surfaces, IEEE Access, 6, 2018, 1015-1022.
[17] Feng, J., Fu, J., Shang, C., Lin, Z., Li, B., Porous scaffold design by solid T-splines and triply periodic minimal surfaces, Computer Methods in Applied Mechanics and Engineering, 336, 2018, 333-352.
[18] Brakke, K., The Surface Evolver and the Stability of Liquid Surfaces, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 354(1715), 1996, 2143-2157.
[19] Otoguro, Y., Mochizuki, H., Takizawa, K., Tezduyar, T.E., Space–Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine, Computational Mechanics, 66(6), 2020, 1443-1460.
[20] Costa, G., Montemurro, M., Pailhès, J., Minimum length scale control in a NURBS-based SIMP method, Computer Methods in Applied Mechanics and Engineering, 354, 2019, 963-989.
[21] Costa, G., Montemurro, M., Pailhès, J., Perry, N., Maximum length scale requirement in a topology optimization method based on NURBS hyper-surfaces. CIRP Annals Manufacturing Technology, 68, 2019, 153-156.
[22] Roiné, T., Montemurro, M., Pailhès, J., Stress-based topology optimization through non-uniform rational basis spline hyper-surfaces, Mechanics of Advanced Materials and Structures, 2021, 1-29.
[23] Montemurro, M., Bertolino, G., Roiné, T., A general multi-scale topology optimisation method for lightweight lattice structures obtained through additive manufacturing technology, Composite Structures, 258, 2021, 113360.
[24] Montemurro, M., Costa, G., Eigen-frequencies and harmonic responses in topology optimization: A CAD-compatible algorithm, Engineering Structures, 214, 2020, 110602.
[25] Montemurro, M., Refai, K., A Topology Optimization Method Based on Non-Uniform Rational Basis Spline Hyper-Surfaces for Heat Conduction Problems, Symmetry, 13(5), 2021, 888.
[26] Leyendecker, S., Penner, J., Biomechanical simulations with dynamic muscle paths on NURBS surfaces, PAAM, 19(1), 2019, 201900230.
[27] Audoux, Y., Montemurro, M., Pailhès, J., Non-Uniform Rational Basis Spline hyper-surfaces for metamodelling, Computer Methods in Applied Mechanics and Engineering, 364(4), 2020, 112918.
[28] Audoux, Y., Montemurro, M., Pailhès, J., A Metamodel Based on Non-Uniform Rational Basis Spline Hyper-Surfaces for Optimisation of Composite Structures, Composite Structures, 247, 2020, 112439.
[29] Moutsanidis, G., Li, W., Bazilevs, Y., Reduced quadrature for FEM, IGA and meshfree methods, Computer Methods in Applied Mechanics and Engineering, 373, 2021, 113521.
[30] Voruganti, H.K., Gondeagaon, S., Comparative study of isogeometric analysis with finite element analysis, Energy Procedia, 2016, 8.
[31] Fiordilino, G.A., Izzi, M.I., Montemurro, M., A general isogeometric polar approach for the optimisation of variable stiffness composites: Application to eigenvalue buckling problems, Mechanics of Materials, 153, 2021, 103574.
[32] Gandy, P., Klinowski, J., Exact computation of the triply periodic G (‘Gyroid’) minimal surface, Chemical Physics Letters, 321(5-6), 2000, 363-371.
[33] Cottrell, J., Hughes, T., Bazilevs, Y., Isogeometric Analysis. Toward Integration of CAD and FEA, John Wiley & Sons Inc, United States, 2009.
[34] Floater, M., Parametrization and smooth approximation of surface triangulations, Computer Aided Geometric Design, 14(3), 1997, 231-250.
[35] Costa, G., Montemurro, M., Pailhès, J., A General Optimization Strategy for Curve Fitting in the Non-Uniform Rational Basis Spline Framework, Journal of Optimization Theory and Applications, 176, 2018, 225-251.
[36] Bertolino, G., Montemurro, M., Perry, N., Pourroy, F., An Efficient Hybrid Optimization Strategy for Surface Reconstruction, Computer Graphics Forum, 40(6), 2021, 215-241.
[37] Chen, X.D., Ma, W., Paul, J.C., Cubic B-spline curve approximation by curve unclamping, Computer-Aided Design, 42(6), 2010, 523-534.
[38] Vartziotis, D., Wipper, J., Papadrakakis, M., Improving mesh quality and finite element solution accuracy by GETMe smoothing in solving the Poisson equation, Finite Elements in Analysis and Design, 66, 2013, 36-52.
[39] Gandy, P., Cvijovic, D., Mackay, A., Klinowski, J., Exact computation of the triply periodic D (‘diamond’) minimal surface, Chemical Physics Letters, 314(5-6), 1999, 543-551.
[40] Gandy, P., Klinowski, J., Exact computation of the triply periodic Schwarz P minimal surface, Chemical Physics Letters, 322(6), 2000, 579-586.
[41] Cvijovic, D., Klinowski, J. The T and CLP families of triply periodic minimal surfaces. Part 1. Derivation of parametric equations, Journal de Physique I., 1992, 137-147. | ||
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