The embedded isogeometric Kirchhoff-Love shell: from design to shape optimization of non-conforming stiffened multipatch structures. (English) Zbl 1441.74245
Summary: Isogeometric shape optimization uses a unique model for the geometric description and for the analysis. The benefits are multiple: in particular, it avoids tedious procedures related to mesh updates. However, although the analysis of complex multipatch structures now becomes tractable with advanced numerical tools, isogeometric shape optimization has not yet been proven to be applicable for designing such structures. Based on the initial concept of integrating design and analysis, we develop a new approach that deals with the shape optimization of non-conforming multipatch structures. The model is built by employing the Free-Form Deformation principle. Introducing NURBS composition drastically simplifies the imposition of the shape updates in case of a non-conforming multipatch configuration. In the case of stiffened structures, the use of embedded surfaces enables to tackle the geometric constraint of connecting interfaces between the panel and the stiffeners during shape modifications. For the analysis, we introduce the embedded Kirchhoff-Love shell formulation. The NURBS composition defines the geometry of the shell while the displacement field is approximated using the same spline functions as for the embedded surface. We also formulate a new mortar method to couple non-conforming Kirchhoff-Love shells which intersect with any angle. We apply the developed method on different examples to demonstrate its efficiency and its potential to optimize complex industrial structures in a smooth manner.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65D07 | Numerical computation using splines |
| 74P20 | Geometrical methods for optimization problems in solid mechanics |
Keywords:
shape optimization; shell; mortar coupling; isogeometric analysis; multipatch; stiffened structuresReferences:
| [1] | Hughes, T. J.R.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135-4195 (2005) · Zbl 1151.74419 |
| [2] | Cottrell, J. A.; Hughes, T. J.R.; Bazilevs, Y., Isogeometric Analysis: Toward Integration of CAD and FEA (2009), Wiley Publishing · Zbl 1378.65009 |
| [3] | Wall, W. A.; Frenzel, M. A.; Cyron, C., Isogeometric structural shape optimization, Comput. Methods Appl. Mech. Engrg., 197, 2976-2988 (2008) · Zbl 1194.74263 |
| [4] | Qian, X., Full analytical sensitivities in NURBS based isogeometric shape optimization, Comput. Methods Appl. Mech. Engrg., 199, 2059-2071 (2010) · Zbl 1231.74352 |
| [5] | Nagy, A. P.; Abdalla, M. M.; Gürdal, Z., Isogeometric sizing and shape optimisation of beam structures, Comput. Methods Appl. Mech. Engrg., 199, 1216-1230 (2010) · Zbl 1227.74047 |
| [6] | Nagy, A. P.; Abdalla, M. M.; Gürdal, Z., Isogeometric design of elastic arches for maximum fundamental frequency, Struct. Multidiscip. Optim., 43, 135-149 (2011) · Zbl 1274.74287 |
| [7] | Nagy, A. P.; I. J.sselmuiden, S. T.; Abdalla, M. M., Isogeometric design of anisotropic shells: Optimal form and material distribution, Comput. Methods Appl. Mech. Engrg., 264, 145-162 (2013) · Zbl 1286.74074 |
| [8] | Kiendl, J.; Schmidt, R.; Wüchner, R.; Bletzinger, K.-U., Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting, Comput. Methods Appl. Mech. Engrg., 274, 148-167 (2014) · Zbl 1296.74082 |
| [9] | Taheri, A.; Hassani, B., Simultaneous isogeometrical shape and material design of functionally graded structures for optimal eigenfrequencies, Comput. Methods Appl. Mech. Engrg., 277, 46-80 (2014) · Zbl 1423.74761 |
| [10] | Wang, Z.-P.; Turteltaub, S., Isogeometric shape optimization for quasi-static processes, Internat. J. Numer. Methods Engrg., 104, 347-371 (2015) · Zbl 1352.74257 |
| [11] | Fußeder, D.; Simeon, B.; Vuong, A. V., Fundamental aspects of shape optimization in the context of isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 286, 313-331 (2015) · Zbl 1425.65159 |
| [12] | Kang, P.; Youn, S.-K., Isogeometric shape optimization of trimmed shell structures, Struct. Multidiscip. Optim., 53, 825-845 (2016) |
| [13] | Lian, H.; Kerfriden, P.; Bordas, S., Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines, Comput. Methods Appl. Mech. Engrg., 317, 1-41 (2017) · Zbl 1439.74486 |
| [14] | Wang, Z. P.; Poh, L. H.; Dirrenberger, J.; Zhu, Y.; Forest, S., Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization, Comput. Methods Appl. Mech. Engrg., 323, 250-271 (2017) · Zbl 1439.74318 |
| [15] | Choi, M.-J.; Cho, S., Constrained isogeometric design optimization of lattice structures on curved surfaces: computation of design velocity field, Struct. Multidiscip. Optim., 58, 17-34 (2018) |
| [16] | Lei, Z.; Gillot, F.; Jezequel, L., Shape optimization for natural frequency with isogeometric Kirchhoff-Love shell and sensitivity mapping, Math. Probl. Eng., 2018, 1-11 (2018) · Zbl 1427.74147 |
| [17] | Hirschler, T.; Bouclier, R.; Duval, A.; Elguedj, T.; Morlier, J., Isogeometric sizing and shape optimization of thin structures with a solid-shell approach, Struct. Multidiscip. Optim. (2018) · Zbl 1441.74245 |
| [18] | Ding, C.; Cui, X.; Huang, G.; Li, G.; Tamma, K.; Cai, Y., A gradient-based shape optimization scheme via isogeometric exact reanalysis, Eng. Comput. (2018), EC-08-2017-0292 |
| [19] | Weeger, O.; Narayanan, B.; Dunn, M. L., Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures, Comput. Methods Appl. Mech. Engrg. (2018) |
| [20] | Daxini, S. D.; Prajapati, J. M., Parametric shape optimization techniques based on Meshless methods: A review, Struct. Multidiscip. Optim., 56, 1197-1214 (2017) |
| [21] | Totaro, G.; De Nicola, F., Recent advance on design and manufacturing of composite anisogrid structures for space launchers, Acta Astronaut., 81, 570-577 (2012) |
| [22] | Shroff, S.; Acar, E.; Kassapoglou, C., Design, analysis, fabrication, and testing of composite grid-stiffened panels for aircraft structures, Thin-Walled Struct., 119, 235-246 (2017) |
| [23] | Guinard, S.; Bouclier, R.; Toniolli, M.; Passieux, J.-C., Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling, Adv. Model. Simul. Eng. Sci., 5, 1 (2018) |
| [24] | Al Akhras, H.; Elguedj, T.; Gravouil, A.; Rochette, M., Towards an automatic isogeometric analysis suitable trivariate models generation—Application to geometric parametric analysis, Comput. Methods Appl. Mech. Engrg., 316, 623-645 (2017) · Zbl 1439.65026 |
| [25] | Zhang, W.; Liu, Y.; Du, Z.; Zhu, Y.; Guo, X., A moving morphable component based topology optimization approach for rib-stiffened structures considering buckling constraints, J. Mech. Des., 140, 111404 (2018) |
| [26] | Wang, D.; Abdalla, M. M.; Wang, Z.-P.; Su, Z., Streamline stiffener path optimization (SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (ncgc) structures, Comput. Methods Appl. Mech. Engrg. (2018) · Zbl 1440.74271 |
| [27] | Mulani, S. B.; Slemp, W. C.; Kapania, R. K., EBF3PanelOpt: An Optimization framework for curvilinear blade-stiffened panels, Thin-Walled Struct., 63, 13-26 (2013) |
| [28] | Singh, K.; Zhao, W.; Kapania, R. K., An optimization framework for curvilinearly stiffened composite pressure vessels and pipes, (Volume 3A: Design and Analysis, Vol. 3A-2017 (2017), ASME), V03AT03A066 |
| [29] | Zhao, W.; Kapania, R. K., Blp optimization of composite flying-wings with SpaRibs and multiple control surfaces, (2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2018), American Institute of Aeronautics and Astronautics: American Institute of Aeronautics and Astronautics Reston, Virginia), 1-45 |
| [30] | Sederberg, T. W.; Parry, S. R., Free-form deformation of solid geometric models, SIGGRAPH Comput. Graph., 20, 151-160 (1986) |
| [31] | Marussig, B.; Hughes, T. J.R., A review of trimming in isogeometric analysis: Challenges, data exchange and simulation aspects, Arch. Comput. Methods Eng., 25, 1059-1127 (2018) |
| [32] | Teschemacher, T.; Bauer, A. M.; Oberbichler, T.; Breitenberger, M.; Rossi, R.; Wüchner, R.; Bletzinger, K.-U., Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis, Adv. Model. Simul. Eng. Sci., 5, 19 (2018) |
| [33] | Guo, Y.; Heller, J.; Hughes, T. J.; Ruess, M.; Schillinger, D., Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the STEP exchange format, Comput. Methods Appl. Mech. Engrg., 336, 39-79 (2018) · Zbl 1440.74397 |
| [34] | Apostolatos, A.; Breitenberger, M.; Wüchner, R.; Bletzinger, K.-U., Domain decomposition methods and Kirchhoff-Love shell multipatch coupling in isogeometric analysis, (B. Jüttler, B. Simeon, Isogeometric Analysis and Applications 2014 (2015), Springer International Publishing: Springer International Publishing Cham), 73-101 · Zbl 1382.74115 |
| [35] | Breitenberger, M.; Apostolatos, A.; Philipp, B.; Wüchner, R.; Bletzinger, K.-U., Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures, Comput. Methods Appl. Mech. Engrg., 284, 401-457 (2015) · Zbl 1425.65030 |
| [36] | Herrema, A. J.; Johnson, E. L.; Proserpio, D.; Wu, M. C.; Kiendl, J.; Hsu, M.-C., Penalty coupling of non-matching isogeometric Kirchhoff-Love shell patches with application to composite wind turbine blades, Comput. Methods Appl. Mech. Engrg. (2018) · Zbl 1470.74062 |
| [37] | Brivadis, E.; Buffa, A.; Wohlmuth, B.; Wunderlich, L., Isogeometric mortar methods, Comput. Methods Appl. Mech. Engrg., 284, 292-319 (2015) · Zbl 1425.65150 |
| [38] | Bouclier, R.; Passieux, J.-C.; Salaün, M., Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches, Comput. Methods Appl. Mech. Engrg., 316, 123-150 (2017) · Zbl 1439.74498 |
| [39] | Bouclier, R.; Passieux, J.-C.; Salaün, M., Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture, Comput. Methods Appl. Mech. Engrg., 300, 1-26 (2016) · Zbl 1425.65149 |
| [40] | Dornisch, W.; Stöckler, J.; Müller, R., Dual and approximate dual basis functions for B-splines and NURBS - Comparison and application for an efficient coupling of patches with the isogeometric mortar method, Comput. Methods Appl. Mech. Engrg., 316, 449-496 (2017) · Zbl 1439.65157 |
| [41] | Sommerwerk, K.; Woidt, M.; Haupt, M. C.; Horst, P., Reissner-Mindlin shell implementation and energy conserving isogeometric multi-patch coupling, Internat. J. Numer. Methods Engrg., 109, 982-1012 (2017) · Zbl 07874332 |
| [42] | Zou, Z.; Scott, M.; Borden, M.; Thomas, D.; Dornisch, W.; Brivadis, E., Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry, Comput. Methods Appl. Mech. Engrg., 333, 497-534 (2018) · Zbl 1440.65240 |
| [43] | Wunderlich, L.; Seitz, A.; Alayd, M. D.; Wohlmuth, B.; Popp, A., Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity, Comput. Methods Appl. Mech. Engrg., 346, 197-215 (2019) · Zbl 1440.74451 |
| [44] | Nguyen, V. P.; Kerfriden, P.; Brino, M.; Bordas, S. P.A.; Bonisoli, E., Nitsche’s method for two and three dimensional nurbs patch coupling, Comput. Mech., 53, 1163-1182 (2014) · Zbl 1398.74379 |
| [45] | Schillinger, D.; Harari, I.; Hsu, M.-C.; Kamensky, D.; Stoter, S. K.; Yu, Y.; Zhao, Y., The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements, Comput. Methods Appl. Mech. Engrg., 309, 625-652 (2016) · Zbl 1439.65192 |
| [46] | Guo, Y.; Ruess, M.; Schillinger, D., A parameter-free variational coupling approach for trimmed isogeometric thin shells, Comput. Mech., 59, 693-715 (2017) · Zbl 1398.74333 |
| [47] | Nguyen-Thanh, N.; Zhou, K.; Zhuang, X.; Areias, P.; Nguyen-Xuan, H.; Bazilevs, Y.; Rabczuk, T., Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling, Comput. Methods Appl. Mech. Engrg., 316, 1157-1178 (2017) · Zbl 1439.74455 |
| [48] | Bouclier, R.; Passieux, J.-C., A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis, Comput. Methods Appl. Mech. Engrg., 340, 253-277 (2018) · Zbl 1440.65185 |
| [49] | Duong, T. X.; Roohbakhshan, F.; Sauer, R. A., A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries, Comput. Methods Appl. Mech. Engrg., 316, 43-83 (2017) · Zbl 1439.74409 |
| [50] | Farhat, C.; Lesoinne, M.; LeTallec, P.; Pierson, K.; Rixen, D., FETI-DP: a dual-primal unified FETI method? Part I: A faster alternative to the two-level FETI method, Internat. J. Numer. Methods Engrg., 50, 1523-1544 (2001) · Zbl 1008.74076 |
| [51] | Gosselet, P.; Rey, C., Non-overlapping domain decomposition methods in structural mechanics, Arch. Comput. Methods Eng., 13, 515-572 (2006) · Zbl 1171.74041 |
| [52] | Mobasher Amini, A.; Dureisseix, D.; Cartraud, P.; Buannic, N., A domain decomposition method for problems with structural heterogeneities on the interface: Application to a passenger ship, Comput. Methods Appl. Mech. Engrg., 198, 3452-3463 (2009) · Zbl 1230.74166 |
| [53] | Kleiss, S. K.; Pechstein, C.; Jüttler, B.; Tomar, S., IETI - Isogeometric Tearing and Interconnecting, Comput. Methods Appl. Mech. Engrg., 247-248, 201-215 (2012) · Zbl 1352.65628 |
| [54] | Bauer, A.; Breitenberger, M.; Philipp, B.; Wüchner, R.; Bletzinger, K.-U., Embedded structural entities in NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 325, 198-218 (2017) · Zbl 1439.74388 |
| [55] | Coox, L.; Greco, F.; Atak, O.; Vandepitte, D.; Desmet, W., A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces, Comput. Methods Appl. Mech. Engrg., 316, 235-260 (2017) · Zbl 1439.65154 |
| [56] | Kiendl, J.; Bletzinger, K.-U.; Linhard, J.; Wüchner, R., Isogeometric shell analysis with Kirchhoff-Love elements, Comput. Methods Appl. Mech. Engrg., 198, 3902-3914 (2009) · Zbl 1231.74422 |
| [57] | Echter, R.; Oesterle, B.; Bischoff, M., A hierarchic family of isogeometric shell finite elements, Comput. Methods Appl. Mech. Engrg., 254, 170-180 (2013) · Zbl 1297.74071 |
| [58] | Rank, E.; Ruess, M.; Kollmannsberger, S.; Schillinger, D.; Düster, A., Geometric modeling, isogeometric analysis and the finite cell method, Comput. Methods Appl. Mech. Engrg., 249-252, 104-115 (2012) · Zbl 1348.74340 |
| [59] | Legrain, G., A nurbs enhanced extended finite element approach for unfitted CAD analysis, Comput. Mech., 52, 913-929 (2013) · Zbl 1311.65017 |
| [60] | Schillinger, D.; Ruess, M., The finite cell method: A review in the context of higher-order structural analysis of CAD and image-based geometric models, Arch. Comput. Methods Eng., 22, 391-455 (2015) · Zbl 1348.65056 |
| [61] | Hansbo, P.; Larson, M. G.; Larsson, K., (Cut Finite Element Methods for Linear Elasticity Problems. Cut Finite Element Methods for Linear Elasticity Problems, Lecture Notes in Computational Science and Engineering, vol. 121 (2017)), 25-63 · Zbl 1390.74180 |
| [62] | Burman, E.; Hansbo, P., Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method, Appl. Numer. Math., 62, 328-341 (2012) · Zbl 1316.65099 |
| [63] | Kiendl, J., Isogeometric analysis and shape optimal design of shell structures (2011), Technische Universit at M unchen: Technische Universit at M unchen Lehrstuhl f ur Statik, (Ph.D. thesis) |
| [64] | Cirak, F.; Ortiz, M.; Schröder, P., Subdivision surfaces: a new paradigm for thin-shell finite-element analysis, Internat. J. Numer. Methods Engrg., 47, 2039-2072 (2000) · Zbl 0983.74063 |
| [65] | Kiendl, J.; Hsu, M.-C.; Wu, M. C.; Reali, A., Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials, Comput. Methods Appl. Mech. Engrg., 291, 280-303 (2015) · Zbl 1423.74177 |
| [66] | Bernadou, M.; Fayolle, S.; Léné, F., Numerical analysis of junctions between plates, Comput. Methods Appl. Mech. Engrg., 74, 307-326 (1989) · Zbl 0687.73068 |
| [67] | Bernadou, M.; Cubier, A., Numerical analysis of junctions between thin shells Part 1: Continuous problems, Comput. Methods Appl. Mech. Engrg., 161, 349-363 (1998) · Zbl 0943.74038 |
| [68] | Kraft, D., A software package for sequential quadratic programming, (Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt Köln: Forschungsbericht (1988), Wiss. Berichtswesen d. DFVLR) · Zbl 0646.90065 |
| [69] | Jones, E.; Oliphant, T.; Peterson, P., SciPy: Open Source scientific tools for Python (2001) |
| [70] | Bletzinger, K.-U.; Wüchner, R.; Daoud, F.; Camprubí, N., Computational methods for form finding and optimization of shells and membranes, Comput. Methods Appl. Mech. Engrg., 194, 3438-3452 (2005) · Zbl 1092.74032 |
| [71] | Kegl, M.; Brank, B., Shape optimization of truss-stiffened shell structures with variable thickness, Comput. Methods Appl. Mech. Engrg., 195, 2611-2634 (2006) · Zbl 1142.74035 |
| [72] | Balesdent, M.; Bérend, N.; Dépincé, P.; Chriette, A., A survey of multidisciplinary design optimization methods in launch vehicle design, Struct. Multidiscip. Optim., 45, 619-642 (2012) · Zbl 1274.74002 |
| [73] | Martins, J. R.R. A.; Lambe, A. B., Multidisciplinary design optimization: A survey of architectures, AIAA J., 51, 2049-2075 (2013) |
| [74] | Kenway, G. K.W.; Martins, J. R.R. A., Multipoint high-fidelity aerostructural optimization of a transport aircraft configuration, J. Aircr., 51, 144-160 (2014) |
| [75] | Keye, S.; Klimmek, T.; Abu-Zurayk, M.; Schulze, M.; Ilic, C., Aero-structural optimization of the NASA common research model, (18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (2017), American Institute of Aeronautics and Astronautics: American Institute of Aeronautics and Astronautics Reston, Virginia), 1-9 |
| [76] | Gillebaart, E.; De Breuker, R., Geometrically consistent static aeroelastic simulation using isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 340, 296-319 (2018) · Zbl 1440.74393 |
| [77] | Dubois, A.; Farhat, C.; Abukhwejah, A. H.; Shageer, H. M., Parameterization framework for the MDAO of wing structural layouts, AIAA J., 56, 1627-1638 (2018) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
