Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry

dc.contributor.affiliationEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
dc.contributor.affiliationDepartamento de Ingeniería Mecánica y de Materiales
dc.contributor.affiliationInstituto Universitario de Investigación Concertado de Ingeniería Mecánica y Biomecánica
dc.contributor.authorMarco Alacid, Onofrees_ES
dc.contributor.authorSevilla, R.es_ES
dc.contributor.authorZhang, Yongjiees_ES
dc.contributor.authorRódenas, Juan José
dc.contributor.authorTur Valiente, Manuel
dc.contributor.funderEuropean Commission
dc.contributor.funderMinisterio de Economía y Competitividad
dc.contributor.funderGeneralitat Valenciana
dc.date.accessioned2017-04-11T12:19:13Z
dc.date.available2017-04-11T12:19:13Z
dc.date.issued2015-08
dc.description.abstract[EN] This paper proposes a novel Immersed Boundary Method where the embedded domain is exactly described by using its Computer-Aided Design (CAD) boundary representation with Non-Uniform Rational B-Splines (NURBS) or T-splines. The common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation. In contrast, the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain. A novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests. The applicability, performance, and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions. It is also shown that the accuracy of the proposed methodology is independent on the CAD technology used to describe the geometry of the embedded domain.en_EN
dc.description.accrualMethodSes_ES
dc.description.bibliographicCitationMarco Alacid, O.; Sevilla, R.; Zhang, Y.; Ródenas, J.; Tur Valiente, M. (2015). Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. International Journal for Numerical Methods in Engineering. 103(6):445-468. https://doi.org/10.1002/nme.4914es_ES
dc.description.issue6es_ES
dc.description.referencesHughes, T. J. R., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194(39-41), 4135-4195. doi:10.1016/j.cma.2004.10.008es_ES
dc.description.referencesSederberg, T. W., Zheng, J., Bakenov, A., & Nasri, A. (2003). T-splines and T-NURCCs. ACM Transactions on Graphics, 22(3), 477. doi:10.1145/882262.882295es_ES
dc.description.referencesEscobar, J. M., Cascón, J. M., Rodríguez, E., & Montenegro, R. (2011). A new approach to solid modeling with trivariate T-splines based on mesh optimization. Computer Methods in Applied Mechanics and Engineering, 200(45-46), 3210-3222. doi:10.1016/j.cma.2011.07.004es_ES
dc.description.referencesWang, W., Zhang, Y., Scott, M. A., & Hughes, T. J. R. (2011). Converting an unstructured quadrilateral mesh to a standard T-spline surface. Computational Mechanics, 48(4), 477-498. doi:10.1007/s00466-011-0598-1es_ES
dc.description.referencesZhang, Y., Wang, W., & Hughes, T. J. R. (2012). Solid T-spline construction from boundary representations for genus-zero geometry. Computer Methods in Applied Mechanics and Engineering, 249-252, 185-197. doi:10.1016/j.cma.2012.01.014es_ES
dc.description.referencesZhang, Y., Wang, W., & Hughes, T. J. R. (2012). Conformal solid T-spline construction from boundary T-spline representations. Computational Mechanics, 51(6), 1051-1059. doi:10.1007/s00466-012-0787-6es_ES
dc.description.referencesLiu, L., Zhang, Y., Hughes, T. J. R., Scott, M. A., & Sederberg, T. W. (2013). Volumetric T-spline construction using Boolean operations. Engineering with Computers, 30(4), 425-439. doi:10.1007/s00366-013-0346-6es_ES
dc.description.referencesLiu, L., Zhang, Y., Liu, Y., & Wang, W. (2015). Feature-preserving T-mesh construction using skeleton-based polycubes. Computer-Aided Design, 58, 162-172. doi:10.1016/j.cad.2014.08.020es_ES
dc.description.referencesDolbow, J., Moës, N., & Belytschko, T. (2000). Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 36(3-4), 235-260. doi:10.1016/s0168-874x(00)00035-4es_ES
dc.description.referencesStrouboulis, T., Babuška, I., & Copps, K. (2000). The design and analysis of the Generalized Finite Element Method. Computer Methods in Applied Mechanics and Engineering, 181(1-3), 43-69. doi:10.1016/s0045-7825(99)00072-9es_ES
dc.description.referencesMelenk, J. M., & Babuška, I. (1996). The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139(1-4), 289-314. doi:10.1016/s0045-7825(96)01087-0es_ES
dc.description.referencesBordas, S. P. A., Rabczuk, T., Rodenas, J.-J., Kerfriden, P., Moumnassi, M., & Belouettar, S. (2010). Recent Advances Towards Reducing the Meshing and Re-Meshing Burden in Computational Sciences. Computational Technology Reviews, 2, 51-82. doi:10.4203/ctr.2.3es_ES
dc.description.referencesPeskin, C. S. (1977). Numerical analysis of blood flow in the heart. Journal of Computational Physics, 25(3), 220-252. doi:10.1016/0021-9991(77)90100-0es_ES
dc.description.referencesZhang, L., Gerstenberger, A., Wang, X., & Liu, W. K. (2004). Immersed finite element method. Computer Methods in Applied Mechanics and Engineering, 193(21-22), 2051-2067. doi:10.1016/j.cma.2003.12.044es_ES
dc.description.referencesMittal, R., & Iaccarino, G. (2005). IMMERSED BOUNDARY METHODS. Annual Review of Fluid Mechanics, 37(1), 239-261. doi:10.1146/annurev.fluid.37.061903.175743es_ES
dc.description.referencesLiu, W. K., Liu, Y., Farrell, D., Zhang, L., Wang, X. S., Fukui, Y., … Hsu, H. (2006). Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering, 195(13-16), 1722-1749. doi:10.1016/j.cma.2005.05.049es_ES
dc.description.referencesLiu, W. K., Kim, D. W., & Tang, S. (2005). Mathematical foundations of the immersed finite element method. Computational Mechanics, 39(3), 211-222. doi:10.1007/s00466-005-0018-5es_ES
dc.description.referencesGil, A. J., Arranz Carreño, A., Bonet, J., & Hassan, O. (2010). The Immersed Structural Potential Method for haemodynamic applications. Journal of Computational Physics, 229(22), 8613-8641. doi:10.1016/j.jcp.2010.08.005es_ES
dc.description.referencesCirak, F., Ortiz, M., & Schr�der, P. (2000). Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. International Journal for Numerical Methods in Engineering, 47(12), 2039-2072. doi:10.1002/(sici)1097-0207(20000430)47:12<2039::aid-nme872>3.0.co;2-1es_ES
dc.description.referencesInoue, K., Kikuchi, Y., & Masuyama, T. (2005). A nurbs finite element method for product shape design. Journal of Engineering Design, 16(2), 157-171. doi:10.1080/01405110500033127es_ES
dc.description.referencesCottrell, J. A., Hughes, T. J. R., & Bazilevs, Y. (2009). Isogeometric Analysis. doi:10.1002/9780470749081es_ES
dc.description.referencesSevilla, R., Fernández-Méndez, S., & Huerta, A. (2011). NURBS-Enhanced Finite Element Method (NEFEM). Archives of Computational Methods in Engineering, 18(4), 441-484. doi:10.1007/s11831-011-9066-5es_ES
dc.description.referencesSevilla, R., Fernández-Méndez, S., & Huerta, A. (2011). 3D NURBS-enhanced finite element method (NEFEM). International Journal for Numerical Methods in Engineering, 88(2), 103-125. doi:10.1002/nme.3164es_ES
dc.description.referencesLegrain, G. (2013). A NURBS enhanced extended finite element approach for unfitted CAD analysis. Computational Mechanics, 52(4), 913-929. doi:10.1007/s00466-013-0854-7es_ES
dc.description.referencesRüberg, T., & Cirak, F. (2012). Subdivision-stabilised immersed b-spline finite elements for moving boundary flows. Computer Methods in Applied Mechanics and Engineering, 209-212, 266-283. doi:10.1016/j.cma.2011.10.007es_ES
dc.description.referencesKim, H.-J., Seo, Y.-D., & Youn, S.-K. (2010). Isogeometric analysis with trimming technique for problems of arbitrary complex topology. Computer Methods in Applied Mechanics and Engineering, 199(45-48), 2796-2812. doi:10.1016/j.cma.2010.04.015es_ES
dc.description.referencesParvizian, J., Düster, A., & Rank, E. (2007). Finite cell method. Computational Mechanics, 41(1), 121-133. doi:10.1007/s00466-007-0173-yes_ES
dc.description.referencesNadal, E., Ródenas, J. J., Albelda, J., Tur, M., Tarancón, J. E., & Fuenmayor, F. J. (2013). Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization. Abstract and Applied Analysis, 2013, 1-19. doi:10.1155/2013/953786es_ES
dc.description.referencesNadal E Cartesian grid FEM (cgFEM): high performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization Ph.D Thesis Valencia 2014es_ES
dc.description.referencesZienkiewicz, O. C., & Zhu, J. Z. (1987). A simple error estimator and adaptive procedure for practical engineerng analysis. International Journal for Numerical Methods in Engineering, 24(2), 337-357. doi:10.1002/nme.1620240206es_ES
dc.description.referencesTur, M., Albelda, J., Nadal, E., & Ródenas, J. J. (2014). Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers. International Journal for Numerical Methods in Engineering, 98(6), 399-417. doi:10.1002/nme.4629es_ES
dc.description.referencesDe Boor, C. (1978). A Practical Guide to Splines. Applied Mathematical Sciences. doi:10.1007/978-1-4612-6333-3es_ES
dc.description.referencesPiegl, L., & Tiller, W. (1995). The NURBS Book. Monographs in Visual Communications. doi:10.1007/978-3-642-97385-7es_ES
dc.description.referencesSederberg, T. W., Cardon, D. L., Finnigan, G. T., North, N. S., Zheng, J., & Lyche, T. (2004). T-spline simplification and local refinement. ACM Transactions on Graphics, 23(3), 276. doi:10.1145/1015706.1015715es_ES
dc.description.referencesBorden, M. J., Scott, M. A., Evans, J. A., & Hughes, T. J. R. (2010). Isogeometric finite element data structures based on Bézier extraction of NURBS. International Journal for Numerical Methods in Engineering, 87(1-5), 15-47. doi:10.1002/nme.2968es_ES
dc.description.referencesWang, W., Zhang, Y., Xu, G., & Hughes, T. J. R. (2011). Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline. Computational Mechanics, 50(1), 65-84. doi:10.1007/s00466-011-0674-6es_ES
dc.description.referencesJohnson, A. A., & Tezduyar, T. E. (1999). Advanced mesh generation and update methods for 3D flow simulations. Computational Mechanics, 23(2), 130-143. doi:10.1007/s004660050393es_ES
dc.description.referencesSevilla, R., Hassan, O., & Morgan, K. (2014). The use of hybrid meshes to improve the efficiency of a discontinuous Galerkin method for the solution of Maxwell’s equations. Computers & Structures, 137, 2-13. doi:10.1016/j.compstruc.2013.01.014es_ES
dc.description.referencesMartin, W., Cohen, E., Fish, R., & Shirley, P. (2000). Practical Ray Tracing of Trimmed NURBS Surfaces. Journal of Graphics Tools, 5(1), 27-52. doi:10.1080/10867651.2000.10487519es_ES
dc.description.referencesLorensen, W. E., & Cline, H. E. (1987). Marching cubes: A high resolution 3D surface construction algorithm. ACM SIGGRAPH Computer Graphics, 21(4), 163-169. doi:10.1145/37402.37422es_ES
dc.description.referencesSevilla, R., Fernández-Méndez, S., & Huerta, A. (2011). Comparison of high-order curved finite elements. International Journal for Numerical Methods in Engineering, 87(8), 719-734. doi:10.1002/nme.3129es_ES
dc.description.referencesGordon, W. J., & Hall, C. A. (1973). Transfinite element methods: Blending-function interpolation over arbitrary curved element domains. Numerische Mathematik, 21(2), 109-129. doi:10.1007/bf01436298es_ES
dc.description.referencesWandzurat, S., & Xiao, H. (2003). Symmetric quadrature rules on a triangle. Computers & Mathematics with Applications, 45(12), 1829-1840. doi:10.1016/s0898-1221(03)90004-6es_ES
dc.description.referencesSevilla, R., & Fernández-Méndez, S. (2011). Numerical integration over 2D NURBS-shaped domains with applications to NURBS-enhanced FEM. Finite Elements in Analysis and Design, 47(10), 1209-1220. doi:10.1016/j.finel.2011.05.011es_ES
dc.description.sponsorshipWith the support of the European Union Framework Program (FP7) under grant No. 289361 INSIST, Ministerio de Economia y Competitividad of Spain (DPI2010-20542)(DPI2013-46317-R), FPI program (BES-2011-044080), and Generalitat Valenciana (PROMETEO/2012/023). R. Sevilla gratefully acknowledges the financial support provided by the Ser Cymru National Research Network in Advanced Engineering and Materials. Y. Zhang was supported in part by the PECASE Award N00014-14-1-0234 and NSF CAREER Award OCI-1149591.en_EN
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dc.description.volume103es_ES
dc.identifier.doi10.1002/nme.4914
dc.identifier.eissn1097-0207
dc.identifier.issn0029-5981
dc.identifier.urihttps://riunet.upv.es/handle/10251/79660
dc.languageIngléses_ES
dc.publisherWileyes_ES
dc.relationMINECO/DPI2010-20542es_ES
dc.relation.ispartofInternational Journal for Numerical Methods in Engineeringes_ES
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dc.relation.references10.1016/j.cma.2004.10.008es_ES
dc.relation.references10.1145/882262.882295es_ES
dc.relation.references10.1016/j.cma.2011.07.004es_ES
dc.relation.references10.1007/s00466-011-0598-1es_ES
dc.relation.references10.1016/j.cma.2012.01.014es_ES
dc.relation.references10.1007/s00466-012-0787-6es_ES
dc.relation.references10.1007/s00366-013-0346-6es_ES
dc.relation.references10.1016/j.cad.2014.08.020es_ES
dc.relation.references10.1016/S0168-874X(00)00035-4es_ES
dc.relation.references10.1016/S0045-7825(99)00072-9es_ES
dc.relation.references10.1016/S0045-7825(96)01087-0es_ES
dc.relation.references10.4203/ctr.2.3es_ES
dc.relation.references10.1016/0021-9991(77)90100-0es_ES
dc.relation.references10.1016/j.cma.2003.12.044es_ES
dc.relation.references10.1146/annurev.fluid.37.061903.175743es_ES
dc.relation.references10.1016/j.cma.2005.05.049es_ES
dc.relation.references10.1007/s00466-005-0018-5es_ES
dc.relation.references10.1016/j.jcp.2010.08.005es_ES
dc.relation.references10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1es_ES
dc.relation.references10.1080/01405110500033127es_ES
dc.relation.references10.1002/9780470749081es_ES
dc.relation.references10.1007/s11831-011-9066-5es_ES
dc.relation.references10.1002/nme.3164es_ES
dc.relation.references10.1007/s00466-013-0854-7es_ES
dc.relation.references10.1016/j.cma.2011.10.007es_ES
dc.relation.references10.1016/j.cma.2010.04.015es_ES
dc.relation.references10.1007/s00466-007-0173-yes_ES
dc.relation.references10.1155/2013/953786es_ES
dc.relation.references10.1002/nme.1620240206es_ES
dc.relation.references10.1002/nme.4629es_ES
dc.relation.references10.1007/978-1-4612-6333-3es_ES
dc.relation.references10.1007/978-3-642-97385-7es_ES
dc.relation.references10.1145/1015706.1015715es_ES
dc.relation.references10.1002/nme.2968es_ES
dc.relation.references10.1007/s00466-011-0674-6es_ES
dc.relation.references10.1007/s004660050393es_ES
dc.relation.references10.1016/j.compstruc.2013.01.014es_ES
dc.relation.references10.1080/10867651.2000.10487519es_ES
dc.relation.references10.1145/37402.37422es_ES
dc.relation.references10.1002/nme.3129es_ES
dc.relation.references10.1007/BF01436298es_ES
dc.relation.references10.1016/S0898-1221(03)90004-6es_ES
dc.relation.references10.1016/j.finel.2011.05.011es_ES
dc.relation.senia302569es_ES
dc.rightsReserva de todos los derechoses_ES
dc.rights.accessRightsAbiertoes_ES
dc.subjectImmersed Boundary Methodses_ES
dc.subjectCartesian gridses_ES
dc.subjectNURBSes_ES
dc.subjectT-splinees_ES
dc.subjectBézier extractiones_ES
dc.subjectNEFEMes_ES
dc.subject.classificationINGENIERIA MECANICAes_ES
dc.titleExact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometryes_ES
dc.typeArtículoes_ES
dc.type.versioninfo:eu-repo/semantics/publishedVersiones_ES
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