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Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection

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Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection

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Marco, O.; Ródenas, J.; Albelda Vitoria, J.; Nadal, E.; Tur Valiente, M. (2017). Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection. Structural and Multidisciplinary Optimization. 1-21. doi:10.1007/s00158-017-1875-1

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/103270

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Title: Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection
Author: Marco, Onofre Ródenas, J.J. Albelda Vitoria, José Nadal, Enrique Tur Valiente, Manuel
UPV Unit: Universitat Politècnica de València. Departamento de Ingeniería Mecánica y de Materiales - Departament d'Enginyeria Mecànica i de Materials
Issued date:
Embargo end date: 2018-12-06
Abstract:
[EN] We present a novel approach to 3D structural shape optimization that leans on an Immersed Boundary Method. A boundary tracking strategy based on evaluating the intersections between a fixed Cartesian grid and the ...[+]
Subjects: Cartesian grids , H-refinement , Shape optimization , NEFEM
Copyrigths: Reserva de todos los derechos
Source:
Structural and Multidisciplinary Optimization. (issn: 1615-147X )
DOI: 10.1007/s00158-017-1875-1
Publisher:
Springer-Verlag
Publisher version: https://doi.org/10.1007/s00158-017-1875-1
Project ID:
MINISTERIO DE ECONOMIA INDUSTRIA Y COMPETITIVIDAD /BES-2011-044080
info:eu-repo/grantAgreement/MINECO//DPI2013-46317-R/ES/PERSONALIZACION DE IMPLANTES MEDIANTE MODELOS DE ELEMENTOS FINITOS A PARTIR DE IMAGENES MEDICAS 3D/
GENERALITAT VALENCIANA/PROMETEO/2016/007
Thanks:
The authors wish to thank the Spanish Ministerio de Economia y Competitividad for the financial support received through the project DPI2013-46317-R and the FPI program (BES-2011-044080), and the Generalitat Valenciana ...[+]
Type: Artículo

References

MATLAB version 8.3.0.532 (R2014a) (2014) Documentation. The Mathworks, Inc., Natick, Massachusetts

Abel JF, Shephard MS (1979) An algorithm for multipoint constraints in finite element analysis. Int J Numer Methods Eng 14(3):464–467

Amestoy P, Davis T, Duff I (1996) An approximate minimum degree ordering algorithm. SIAM J Matrix Anal Appl 17(4):886–905 [+]
MATLAB version 8.3.0.532 (R2014a) (2014) Documentation. The Mathworks, Inc., Natick, Massachusetts

Abel JF, Shephard MS (1979) An algorithm for multipoint constraints in finite element analysis. Int J Numer Methods Eng 14(3):464–467

Amestoy P, Davis T, Duff I (1996) An approximate minimum degree ordering algorithm. SIAM J Matrix Anal Appl 17(4):886–905

Barth W, Stürzlinger W (1993) Efficient ray tracing for Bezier and B-spline surfaces. Comput Graph 17 (4):423–430

Bennett J A, Botkin M E (1985) Structural shape optimization with geometric problem description and adaptive mesh refinement. AIAA J 23(3):459–464

Braibant V, Fleury C (1984) Shape optimal design using b-splines. Comput Methods Appl Mech Eng 44 (3):247–267

Bugeda G, Oliver J (1993) A general methodology for structural shape optimization problems using automatic adaptive remeshing. Int J Numer Methods Eng 36(18):3161–3185

Bugeda G, Ródenas J J, Oñate E (2008) An integration of a low cost adaptive remeshing strategy in the solution of structural shape optimization problems using evolutionary methods. Comput Struct 86(13–14):1563–1578

Chang K, Choi K K (1992) A geometry-based parameterization method for shape design of elastic solids. Mech Struct Mach 20(2):215–252

Cho S, Ha S H (2009) Isogeometric shape design optimization: exact geometry and enhanced sensitivity. Struct Multidiscip Optim 38(1):53–70

Belegundu D, Zhang YMS, Salagame R (1991) The natural approach for shape optimization with mesh distortion control. Tech. rep., Penn State University

Davis T A, Gilbert J R, Larimore S, Ng E (2004) An approximate column minimum degree ordering algorithm. ACM Trans Math Softw 30(3):353–376

Doctor L J, Torborg J G (1981) Display techniques for octree-encoded objects. IEEE Comput Graph Appl 1(3):29–38

Dunning P D, Kim H A, Mullineux G (2011) Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization. Finite Elem Anal Des 47(8):933–941

Düster A, Parvizian J, Yang Z, Rank E (2008) The finite cell method for three-dimensional problems of solid mechanics. Comput Methods Appl Mech Eng 197(45-48):3768–3782

Escobar J M, Montenegro R, Rodríguez E, Cascón J M (2014) The meccano method for isogeometric solid modeling and applications. Eng Comput 30(3):331–343

Farhat C, Lacour C, Rixen D (1998) Incorporation of linear multipoint constraints in substructure based iterative solvers. Part 1: a numerically scalable algorithm. Int J Numer Methods Eng 43(6):997–1016

Fries T P, Omerović S (2016) Higher-order accurate integration of implicit geometries. Int J Numer Methods Eng 106(5):323–371

Fuenmayor F J, Oliver J L (1996) Criteria to achieve nearly optimal meshes in the h-adaptive finite element mehod. Int J Numer Methods Eng 39(23):4039–4061

Fuenmayor F J, Oliver J L, Ródenas J J (1997) Extension of the Zienkiewicz-Zhu error estimator to shape sensitivity analysis. Int J Numer Methods Eng 40(8):1413–1433

García-Ruíz M J, Steven G P (1999) Fixed grid finite elements in elasticity problems. Eng Comput 16 (2):145–164

Gill P, Murray W, Saunders M, Wright M (1984) Procedures for optimization problems with a mixture of bounds and general linear constraints. ACM Trans Math Software 10:282–298

González-Estrada O A, Nadal E, Ródenas J J, Kerfriden P, Bordas S P A, Fuenmayor F J (2014) Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery. Comput Mech 53(5):957–976

Ha S H, Choi K K, Cho S (2010) Numerical method for shape optimization using T-spline based isogeometric method. Struct Multidiscip Optim 42(3):417–428

Haftka R T, Grandhi R V (1986) Structural shape optimization: A survey. Comput Methods Appl Mech Eng 57(1):91–106

Haslinger J, Jedelsky D (1996) Genetic algorithms and fictitious domain based approaches in shape optimization. Struc Optim 12:257–264

Hughes T J R, Cottrell J A, Bazilevs Y (2005) Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry, and Mesh Refinement. Comput Methods Appl Mech Eng 194:4135–4195

Jackins C L, Tanimoto S L (1980) Oct-tree and their use in representing three-dimensional objects. Comput Graphics Image Process 14(3):249–270

Kajiya J T (1982) Ray Tracing Parametric Patches. SIGGRAPH Comput Graph 16(3):245–254

van Keulen F, Haftka R T, Kim N (2005) Review of options for structural design sensitivity analysis. Part I: linear systems. Comput Methods Appl Mech Eng 194(30-33):3213–3243

Kibsgaard S (1992) Sensitivity analysis-the basis for optimization. Int J Numer Methods Eng 34(3):901–932

Kikuchi N, Chung K Y, Torigaki T, Taylor J E (1986) Adaptive finite element methods for shape optimization of linearly elastic structures. Comput Methods Appl Mech Eng 57(1):67–89

Kim N H, Chang Y (2005) Eulerian shape design sensitivity analysis and optimization with a fixed grid. Comput Methods Appl Mech Eng 194(30–33):3291–3314

Kudela L, Zander N, Kollmannsberger S, Rank E (2016) Smart octrees: Accurately integrating discontinuous functions in 3d. Comput Methods Appl Mech Eng 306(1):406–426

Kunisch K, Peichl G (1996) Numerical gradients for shape optimization based on embedding domain techniques. Comput Optim 18:95–114

Li K, Qian X (2011) Isogeometric analysis and shape optimization via boundary integral. Computer-Aided Design 43(11):1427–1437

Lian H, Kerfriden P, Bordas S P A (2016) Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity. Int J Numer Methods Eng 106 (12):972–1017

Liu L, Zhang Y, Hughes T J R, Scott M A, Sederberg T W (2014) Volumetric T-spline Construction using Boolean Operations. Eng Comput 30(4):425–439

Marco O, Sevilla R, Zhang Y, Ródenas J J, Tur M (2015) Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. Int J Numer Methods Eng 103:445–468

Marco O, Ródenas J J, Fuenmayor FJ, Tur M (2017a) An extension of shape sensitivity analysis to an immersed boundary method based on cartesian grids. Computational Mechanics Submitted

Marco O, Ródenas J J, Navarro-Jiménez JM, Tur M (2017b) Robust h-adaptive meshing strategy for arbitrary cad geometries in a cartesian grid framework. Computers & Structures Submitted

Meagher D (1980) Octree Encoding: A New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer. Tech. Rep. IPL-TR-80-11 I, Rensselaer Polytechnic Institute

Moita J S, Infante J, Mota C M, Mota C A (2000) Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells. Comput Struct 76(1–3):407–420

Nadal E (2014) Cartesian Grid FEM (cgFEM): High Performance h-adaptive FE Analysis with Efficient Error Control. Application to Structural Shape Optimization. PhD Thesis. Universitat Politècnica de València

Nadal 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. Abstr Appl Anal 2013:1–19

Najafi A R, Safdari M, Tortorelli D A, Geubelle P H (2015) A gradient-based shape optimization scheme using an interface-enriched generalized FEM. Comput Methods Appl Mech Eng 296:1–17

Nguyen V P, Anitescu C, Bordas S P A, Rabczuk T (2015) Isogeometric analysis: An overview and computer implementation aspects. Math Comput Simul 117:89–116

Nishita T, Sederberg TW, Kakimoto M (1990) Ray Tracing Trimmed Rational Surface Patches. SIGGRAPH Comput Graph 24(4):337–345

Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer-Verlag, New York

Pandey P C, Bakshi P (1999) Analytical response sensitivity computation using hybrid finite elements. Comput Struct 71(5):525–534

Parvizian J, Düster A, Rank E (2007) Finite Cell Method: h- and p- Extension for Embedded Domain Methods in Solid Mechanics. Comput Mech 41(1):121–133

Peskin C S (1977) Numerical Analysis of Blood Flow in the Heart. J Comput Phys 25:220–252

Poldneff M J, Rai I S, Arora J S (1993) Implementation of design sensitivity analysis for nonlinear structures. AIAA J 31(11):2137–2142

Powell M (1983) Variable metric methods for constrained optimization. In: Bachem A, Grotschel M, Korte B (eds) Mathematical Programming: The State of the Art, Springer, Berlin, Heidelberg, pp 288–311

Qian X (2010) Full analytical sensitivities in NURBS based isogeometric shape optimization. Comput Methods Appl Mech Eng 199(29–32):2059–2071

Riehl S, Steinmann P (2014) An integrated approach to shape optimization and mesh adaptivity based on material residual forces. Comput Methods Appl Mech Eng 278:640–663

Riehl S, Steinmann P (2016) On structural shape optimization using an embedding domain discretization technique. Int J Numer Methods Eng 109(9):1315–1343

Ródenas J J, Tarancón J E, Albelda J, Roda A, Fuenmayor F J (2005) Hierarchical Properties in Elements Obtained by Subdivision: a Hierarquical h-adaptivity Program. In: Díez P, Wiberg N E (eds) Adaptive Modeling and Simulation, p 2005

Ródenas J J, Corral C, Albelda J, Mas J, Adam C (2007a) Nested domain decomposition direct and iterative solvers based on a hierarchical h-adaptive finite element code. In: Runesson K, Díez P (eds) Adaptive Modeling and Simulation 2007, Internacional Center for Numerical Methods in Engineering (CIMNE), pp 206–209

Ródenas J J, Tur M, Fuenmayor F J, Vercher A (2007b) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70(6):705–727

Ródenas J J, Bugeda G, Albelda J, Oñate E (2011) On the need for the use of error-controlled finite element analyses in structural shape optimization processes. Int J Numer Methods Eng 87(11):1105–1126

Schillinger D, Ruess M (2015) The finite cell method: A review in the context of higher-order structural analysis of cad and image-based geometric models. Arch Comput Meth Eng 22(3):391– 455

Sevilla R, Fernández-Méndez S, Huerta A (2011a) 3D-NURBS-enhanced Finite Element Method (NEFEM). Int J Numer Methods Eng 88(2):103–125

Sevilla R, Fernández-Méndez S, Huerta A (2011b) Comparison of High-order Curved Finite Elements. Int J Numer Methods Eng 87(8):719–734

Sevilla R, Fernández-Méndez S, Huerta A (2011c) NURBS-enhanced Finite Element Method (NEFEM): A Seamless Bridge Between CAD and FEM. Arch Comput Meth Eng 18(4):441–484

Sweeney M, Bartels R (1986) Ray tracing free-form b-spline surfaces. IEEE Comput Graph Appl 6(2):41–49

Toth D L (1985) On Ray Tracing Parametric Surfaces. SIGGRAPH Comput Graph 19(3):171–179

Tur M, Albelda J, Nadal E, Ródenas J J (2014) Imposing dirichlet boundary conditions in hierarchical cartesian meshes by means of stabilized lagrange multipliers. Int J Numer Methods Eng 98(6):399–417

Tur M, Albelda J, Marco O, Ródenas J J (2015) Stabilized Method to Impose Dirichlet Boundary Conditions using a Smooth Stress Field. Comput Methods Appl Mech Eng 296:352–375

Yao T, Choi KK (1989) 3-d shape optimal design and automatic finite element regridding. Int J Numer Methods Eng 28(2):369–384

Zhang L, Gerstenberger A, Wang X, Liu W K (2004) Immersed Finite Element Method. Comput Methods Appl Mech Eng 293(21):2051–2067

Zhang Y, Wang W, Hughes T J R (2013) Conformal Solid T-spline Construction from Boundary T-spline Representations. Comput Mech 6(51):1051–1059

Zienkiewicz O C, Zhu J Z (1987) A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis. Int J Numer Methods Eng 24(2):337–357

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