참고문헌
- Atluri, S.N. and Zhu, T. (1998), "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics", Computat. Mech., 22(2), 117-127. https://doi.org/10.1007/s004660050346
- Bartezzaghi, A., Dede, L. and Quarteroni, A. (2015), "Isogeometric analysis of high order partial differential equations on surfaces", Comput. Methods Appl. Mech. Eng., 295, 446-469. https://doi.org/10.1016/j.cma.2015.07.018
- Bazilevs, Y., Calo, V.M., Cottrell, J.A., Evans, J.A., Hughes, T., Lipton, S., Scott, M.A. and Sederberg, T.W. (2010), "Isogeometric analysis using T-splines", Comput. Methods Appl. Mech. Eng., 199(5), 229-263. https://doi.org/10.1016/j.cma.2009.02.036
- Beirao da Veiga, L., Buffa, A., Sangalli, G. and Vazquez, R. (2013), "Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties", Math. Models Methods Appl. Sci., 23(11), 1979-2003. https://doi.org/10.1142/S0218202513500231
- Belytschko, T., Stolarski, H., Liu, W.K., Carpenter, N. and Ong, J.S. (1985), "Stress projection for membrane and shear locking in shell finite elements", Comput. Methods Appl. Mech. Eng., 51, 221-258. https://doi.org/10.1016/0045-7825(85)90035-0
- Belytschko, T., Lu, Y.Y. and Gu, L. (1994), "Element-free Galerkin methods", Int. J. Numer. Methods Eng., 37(2), 229-256. https://doi.org/10.1002/nme.1620370205
- Bornemann, P. and Cirak, F. (2013), "A subdivision-based implementation of the hierarchical b-spline finite element method", Comput. Methods Appl. Mech. Eng., 253, 584-598. https://doi.org/10.1016/j.cma.2012.06.023
- Bressan, A. (2013), "Some properties of LR-splines", Comput. Aid. Geomet. Des., 30. 778-794. https://doi.org/10.1016/j.cagd.2013.06.004
- Bressan, A. and Juttler, B. (2015), "A hierarchical construction of LR meshes in 2D", Comput. Aid. Geomet. Des., 37, 9-24. https://doi.org/10.1016/j.cagd.2015.06.002
- Buffa, A., Cho, D. and Sangalli, G. (2010), "Linear independence of the T-spline blending functions associated with some particular T-meshes", Comput. Methods Appl. Mech. Eng., 199(23), 1437-1445. https://doi.org/10.1016/j.cma.2009.12.004
- Bui, T.Q., Nguyen, M.N. and Zhang, C. (2011), "An efficient meshfree method for vibration analysis of laminated composite plates", Computat. Mech., 48(2), 175-193. https://doi.org/10.1007/s00466-011-0591-8
- Burkhart, D., Hamann, B. and Umlauf, G. (2010), "Iso-geometric Finite Element Analysis Based on Catmull-Clark: ubdivision Solids", In: Computer Graphics Forum, Wiley Online Library, pp. 1575-1584.
- Casquero, H., Liu, L., Zhang, Y., Reali, A., Kiendl, J. and Gomez, H. (2017), "Arbitrary-degree T-splines for isogeometric analysis of fully nonlinear Kirchhoff-Love shells", Comput.-Aid. Des., 82, 140-153. https://doi.org/10.1016/j.cad.2016.08.009
- Catmull, E. and Clark, J. (1978), "Recursively generated B-spline surfaces on arbitrary topological meshes", Comput.-Aid. Des., 10, 350-355. https://doi.org/10.1016/0010-4485(78)90110-0
- Chen, Y., Lee, J. and Eskandarian, A. (2006), Meshless Methods in Solid Mechanics, Springer Science & Business Media.
- Cirak, F., Ortiz, M. and Schroder, P. (2000), "Subdivision surfaces: a new paradigm for thin-shell finite-element analysis", Int. J. Numer. Methods Eng., 47, 2039-2072. https://doi.org/10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1
- Cirak, F., Scott, M.J., Antonsson, E.K., Ortiz, M. and Schroder, P. (2002), "Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision", Comput.-Aid. Des., 34, 137-148. https://doi.org/10.1016/S0010-4485(01)00061-6
- da Veiga, L.B., Buffa, A., Cho, D. and Sangalli, G. (2012), "Analysis-suitable T-splines are dual-compatible", Comput. Methods Appl. Mech. Eng., 249, 42-51.
- Dede, L. and Quarteroni, A. (2015), "Isogeometric Analysis for second order partial differential equations on surfaces", Comput. Methods Appl. Mech. Eng., 284, 807-834. https://doi.org/10.1016/j.cma.2014.11.008
- Deng, J., Chen, F., Li, X., Hu, C., Tong, W., Yang, Z. and Feng, Y. (2008), "Polynomial splines over hierarchical T-meshes", Graph. Models, 70, 76-86. https://doi.org/10.1016/j.gmod.2008.03.001
- Dokken, T., Lyche, T. and Pettersen, K.F. (2013), "Polynomial splines over locally refined box-partitions", Comput. Aid. Geomet. Des., 30(3), 331-356. https://doi.org/10.1016/j.cagd.2012.12.005
- Dorfel, M.R., Juttler, B. and Simeon, B. (2010), "Adaptive isogeometric analysis by local h-refinement with T-splines", Comput. Methods Appl. Mech. Eng., 199(5), 264-275. https://doi.org/10.1016/j.cma.2008.07.012
- Evans, E., Scott, M., Li, X. and Thomas, D. (2015), "Hierarchical T-splines: Analysis-suitability, Bezier extraction, and application as an adaptive basis for isogeometric analysis", Comput. Methods Appl. Mech. Eng., 284, 1-20. https://doi.org/10.1016/j.cma.2014.05.019
- Flugge, S. and Truesdell, C. (1972), Handbuch der Physik: Encyclopedia of physics. vol. VIa/2, Mechanics of solids II. Festkorpermechanik II. Bd. VIa/2: Springer-Verlag.
- Forsey, D.R. and Bartels, R.H. (1988), "Hierarchical B-spline refinement", ACM Siggraph Computer Graphics, 22(4), 205-212. https://doi.org/10.1145/378456.378512
- Giannelli, C., JuTtler, B. and Speleers, H. (2012), "THB-splines: The truncated basis for hierarchical splines", Comput. Aid. Geomet. Des., 29, 485-498. https://doi.org/10.1016/j.cagd.2012.03.025
- Giannelli, C., Juttler, B., Kleiss, S.K., Mantzaflaris, A., Simeon, B. and Speh, J. (2016), "THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis", Comput. Methods Appl. Mech. Eng., 299, 337-365. https://doi.org/10.1016/j.cma.2015.11.002
- Gonzalez, D., Cueto, E. and Doblare, M. (2008), "Higher-order natural element methods: Towards an isogeometric meshless method", Int. J. Numer. Method. Eng., 74(13), 1928-1954. https://doi.org/10.1002/nme.2237
- Hughes, T.J., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Methods Appl. Mech. Eng., 194(39), 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
- Ivannikov, V., Tiago, C. and Pimenta, P. (2014), "On the boundary conditions of the geometrically nonlinear Kirchhoff-Love shell theory", Int. J. Solids Struct., 51(18), 3101-3112. https://doi.org/10.1016/j.ijsolstr.2014.05.004
- Johannessen, K.A., Kvamsdal, T. and Dokken, T. (2014), "Isogeometric analysis using LR B-splines", Comput. Methods Appl. Mech. Eng., 269, 471-514. https://doi.org/10.1016/j.cma.2013.09.014
- Johannessen, K.A., Remonato, F. and Kvamsdal, T. (2015), "On the similarities and differences between Classical Hierarchical, Truncated Hierarchical and LR B-splines", Comput. Methods Appl. Mech. Eng., 291, 64-101. https://doi.org/10.1016/j.cma.2015.02.031
- Kang, P. and Youn, S.-K. (2016), "Isogeometric topology optimization of shell structures using trimmed NURBS surfaces", Finite Elements in Analysis and Design, 120, 18-40. https://doi.org/10.1016/j.finel.2016.06.003
- Khakalo, S. and Niiranen, J. (2017), "Isogeometric analysis of higher-order gradient elasticity by user elements of a commercial finite element software", Comput.-Aid. Des., 82, 154-169. https://doi.org/10.1016/j.cad.2016.08.005
- Kiss, G., Giannelli, C., Zore, U., Juttler, B., Grossmann, D. and Barner, J. (2014), "Adaptive CAD model (re-) construction with THB-splines", Graph. Models, 76, 273-288. https://doi.org/10.1016/j.gmod.2014.03.017
- Kraft, R. (1997), Adaptive and linearly independent multilevel Bsplines: SFB 404, Geschaftsstelle.
- Lee, S.-W., Yoon, M. and Cho, S. (2017), "Isogeometric topological shape optimization using dual evolution with boundary integral equation and level sets", Comput.-Aid. Des., 82, 88-99. https://doi.org/10.1016/j.cad.2016.08.004
- Li, X., Deng, J. and Chen, F. (2007), "Surface modeling with polynomial splines over hierarchical T-meshes", The Visual Computer, 23(12), 1027-1033. https://doi.org/10.1007/s00371-007-0170-3
- Li, X., Zheng, J., Sederberg, T.W., Hughes, T.J. and Scott, M.A. (2012), "On linear independence of T-spline blending functions", Comput. Aid. Geomet. Des., 29(1), 63-76. https://doi.org/10.1016/j.cagd.2011.08.005
- Liu, G.-R. and Gu, Y. (2001), "A point interpolation method for two-dimensional solids", Int. J. Numer. Methods Eng., 50(4), 937-951. https://doi.org/10.1002/1097-0207(20010210)50:4<937::AID-NME62>3.0.CO;2-X
- Liu, W.K., Jun, S. and Zhang, Y.F. (1995), "Reproducing kernel particle methods", Int. J. Numer. Methods Fluids, 20(8-9), 1081-1106. https://doi.org/10.1002/fld.1650200824
- Liu, H., Zhu, X. and Yang, D. (2016), "Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams", Struct. Eng. Mech., Int. J., 59(3), 503-526. https://doi.org/10.12989/sem.2016.59.3.503
- Morgenstern, P. and Peterseim, D. (2015), "Analysis-suitable adaptive T-mesh refinement with linear complexity", Comput. Aid. Geomet. Des., 34, 50-66. https://doi.org/10.1016/j.cagd.2015.02.003
- Nguyen-Thanh, N., Kiendl, J., Nguyen-Xuan, H., Wuchner, R., Bletzinger, K., Bazilevs, Y. and Rabczuk, T. (2011a), "Rotation free isogeometric thin shell analysis using PHT-splines", Comput. Methods Appl. Mech. Eng., 200, 3410-3424. https://doi.org/10.1016/j.cma.2011.08.014
- Nguyen-Thanh, N., Nguyen-Xuan, H., Bordas, S.P.A. and Rabczuk, T. (2011b), "Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids", Comput. Methods Appl. Mech. Eng., 200, 1892-1908. https://doi.org/10.1016/j.cma.2011.01.018
- Riffnaller-Schiefer, A., Augsdorfer, U. and Fellner, D. (2016), "Isogeometric shell analysis with NURBS compatible subdivision surfaces", Appl. Math. Computat., 272, 139-147. https://doi.org/10.1016/j.amc.2015.06.113
- Rosolen, A. and Arroyo, M. (2013), "Blending isogeometric analysis and local maximum entropy meshfree approximants", Comput. Methods Appl. Mech. Eng., 264, 95-107. https://doi.org/10.1016/j.cma.2013.05.015
- Scott, M., Li, X., Sederberg, T. and Hughes, T. (2012), "Local refinement of analysis-suitable T-splines", Comput. Methods Appl. Mech. Eng., 213, 206-222.
- Sambridge, M., Braun, J. and McQueen, H. (1995), "Geophysical parametrization and interpolation of irregular data using natural neighbours", Geophys. J. Int., 122(3), 837-857. https://doi.org/10.1111/j.1365-246X.1995.tb06841.x
- Schillinger, D., Dede, L., Scott, M.A., Evans, J.A., Borden, M.J., Rank, E. and Hughes, T.J. (2012), "An isogeometric designthrough-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and Tspline CAD surfaces", Comput. Methods Appl. Mech. Eng., 249, 116-150.
- Sederberg, T.W., Zheng, J., Bakenov, A. and Nasri, A. (2003), "Tsplines and T-NURCCs", In: ACM Transactions on Graphics (TOG), ACM, pp. 477-484.
- Sederberg, T.W., Cardon, D.L., Finnigan, G.T., North, N.S., Zheng, J. and Lyche, T. (2004), "T-spline simplification and local refinement", In: Acm Transactions on Graphics (tog), ACM, pp. 276-283.
- Seo, Y.-D., Kim, H.-J. and Youn, S.-K. (2010), "Shape optimization and its extension to topological design based on isogeometric analysis", Int. J. Solids Struct., 47(11), 1618-1640. https://doi.org/10.1016/j.ijsolstr.2010.03.004
- Shojaee, S., Ghelichi, M. and Izadpanah, E. (2013), "Combination of isogeometric analysis and extended finite element in linear crack analysis", Struct. Eng. Mech., Int. J., 48(1), 125-150. https://doi.org/10.12989/sem.2013.48.1.125
- Somireddy, M. and Rajagopal, A. (2014), "Meshless natural neighbor Galerkin method for the bending and vibration analysis of composite plates", Compos. Struct., 111, 138-146. https://doi.org/10.1016/j.compstruct.2013.12.023
- Tagliabue, A., Dede, L. and Quarteroni, A. (2014), "Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics", Comput. Fluids, 102, 277-303. https://doi.org/10.1016/j.compfluid.2014.07.002
- Taheri, A.H., Hassani, B. and Moghaddam, N. (2014), "Thermoelastic optimization of material distribution of functionally graded structures by an isogeometrical approach", Int. J. Solids Struct., 51(2), 416-429. https://doi.org/10.1016/j.ijsolstr.2013.10.014
- Uhm, T.K. and Youn, S.K. (2009), "T-spline finite element method for the analysis of shell structures", Int. J. Numer. Method. Eng., 80(4), 507-536. https://doi.org/10.1002/nme.2648
- unther Greiner, G. and Hormann, K. (1996), "Interpolating and approximating scattered 3D-data with hierarchical tensor product B-splines", In: Proceedings of Chamonix, pp. 1.
- Valizadeh, N., Bazilevs, Y., Chen, J. and Rabczuk, T. (2015), "A coupled IGA-Meshfree discretization of arbitrary order of accuracy and without global geometry parameterization", Comput. Methods Appl. Mech. Eng., 293, 20-37. https://doi.org/10.1016/j.cma.2015.04.002
- Vuong, A.-V., Giannelli, C., Juttler, B. and Simeon, B. (2011), "A hierarchical approach to adaptive local refinement in isogeometric analysis", Comput. Methods Appl. Mech. Eng., 200, 3554-3567. https://doi.org/10.1016/j.cma.2011.09.004
- Wang, P., Xu, J., Deng, J. and Chen, F. (2011), "Adaptive isogeometric analysis using rational PHT-splines", Comput.-Aid. Des., 43, 1438-1448. https://doi.org/10.1016/j.cad.2011.08.026
- Wawrzinek, A., Hildebrandt, K. and Polthier, K. (2011), "Koiter's Thin Shells on Catmull-Clark Limit Surfaces", In: VMV, pp . 113-120.
- Wei, X., Zhang, Y., Hughes, T.J. and Scott, M.A. (2015), "Truncated hierarchical Catmull-Clark subdivision with local refinement", Comput. Methods Appl. Mech. Eng., 291, 1-20. https://doi.org/10.1016/j.cma.2015.03.019
- Willberg, C. (2016), "Analysis of the dynamical behavior of piezoceramic actuators using piezoelectric isogeometric finite elements", Adv. Computat. Des., Int. J., 1(1), 37-60.
- Zore, U. and Juttler, B. (2014), "Adaptively refined multilevel spline spaces from generating systems", Comput. Aid. Geomet. Des., 31, 545-566. https://doi.org/10.1016/j.cagd.2014.04.003