Stochastic finite cell method for structural mechanics
Finite cell method is known as a combination of finite element method and fictitious domain approach in order to reduce the difficulties associated with mesh generation so that it can successfully handle complex geometries. This study proposes a stochastic extension of finite cell method, as a novel...
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| Published in | Computational mechanics Vol. 68; no. 1; pp. 185 - 210 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2021
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0178-7675 1432-0924 |
| DOI | 10.1007/s00466-021-02026-0 |
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| Abstract | Finite cell method is known as a combination of finite element method and fictitious domain approach in order to reduce the difficulties associated with mesh generation so that it can successfully handle complex geometries. This study proposes a stochastic extension of finite cell method, as a novel computational framework, for uncertainty quantification of structures. For this purpose, stochastic finite cell method (SFCM) is developed as a new efficient method, including the features of finite cell method, for computational stochastic mechanics considering complicated geometries arising from computer-aided design (CAD). Firstly, finite cell method is formulated for solving the Fredholm integral equation of the second kind used for Karhunen-Loève expansion in order to decompose the random field within a physical domain having arbitrary boundaries. Then, the SFCM is formulated based on Karhunen-Loève and polynomial chaos expansions for the stochastic analysis. Several numerical examples consisting of benchmark problems are provided to demonstrate the efficiency, accuracy and capability of the proposed SFCM. |
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| AbstractList | Finite cell method is known as a combination of finite element method and fictitious domain approach in order to reduce the difficulties associated with mesh generation so that it can successfully handle complex geometries. This study proposes a stochastic extension of finite cell method, as a novel computational framework, for uncertainty quantification of structures. For this purpose, stochastic finite cell method (SFCM) is developed as a new efficient method, including the features of finite cell method, for computational stochastic mechanics considering complicated geometries arising from computer-aided design (CAD). Firstly, finite cell method is formulated for solving the Fredholm integral equation of the second kind used for Karhunen-Loève expansion in order to decompose the random field within a physical domain having arbitrary boundaries. Then, the SFCM is formulated based on Karhunen-Loève and polynomial chaos expansions for the stochastic analysis. Several numerical examples consisting of benchmark problems are provided to demonstrate the efficiency, accuracy and capability of the proposed SFCM. |
| Audience | Academic |
| Author | Zakian, Pooya |
| Author_xml | – sequence: 1 givenname: Pooya orcidid: 0000-0002-7252-9531 surname: Zakian fullname: Zakian, Pooya email: p-zakian@araku.ac.ir organization: Department of Civil Engineering, Faculty of Engineering, Arak University |
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| Cites_doi | 10.1002/9781118481844 10.1061/(ASCE)0733-9399(1989)115:5(1035) 10.1007/s11012-015-0242-9 10.1002/9780470033326 10.1007/978-3-7091-1565-7 10.1002/9781118443378 10.1080/15376494.2016.1202359 10.1243/09544119jeim739 10.1007/s11831-014-9139-3 10.1016/j.apm.2018.06.027 10.1046/j.1365-246x.1999.00967.x 10.1016/j.probengmech.2006.11.004 10.1016/j.finel.2012.10.001 10.1007/s00466-019-01692-5 10.1016/j.cma.2019.03.008 10.1061/AJRUA6.0001040 10.1007/s00466-007-0173-y 10.2307/j.ctv7h0skv 10.1016/j.compstruc.2017.03.008 10.1007/978-90-481-3520-2 10.1016/j.cma.2008.11.007 10.1016/j.compstruc.2016.10.009 10.1016/j.cma.2004.10.008 10.1016/j.cma.2017.12.012 10.1023/A:1006514109327 10.1016/j.cam.2013.08.016 10.1016/S0045-7825(96)01078-X 10.1002/nme.3289 10.1002/(sici)1097-0207(19990730)45:9<1139::aid-nme617>3.0.co;2-t 10.1016/j.jcp.2016.02.014 10.1002/nme.165 10.1016/j.compstruc.2019.05.012 10.1007/s10237-011-0322-2 10.1002/nme.4663 10.1007/s00466-014-1019-z |
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| Keywords | Karhunen-Loève expansion Finite cell method Polynomial chaos expansion Fredholm integral equation Stochastic finite cell method Computational stochastic mechanics |
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| References | MaitreOLKnioOMSpectral methods for uncertainty quantification: with applications to computational fluid dynamics2010NetherlandsSpringer10.1007/978-90-481-3520-2 JoulaianMDuczekSGabbertUDüsterAFinite and spectral cell method for wave propagation in heterogeneous materialsComput Mech201454661675324691210.1007/s00466-014-1019-z1311.74056 Liu GR (2009) Mesh free methods: moving beyond the finite element method. 2nd Edition, CRC Press, Boca Raton LazPJBrowneMA review of probabilistic analysis in orthopaedic biomechanicsProc Inst Mech Eng [H]201022492794310.1243/09544119jeim739 DuczekSJoulaianMDüsterAGabbertUNumerical analysis of Lamb waves using the finite and spectral cell methodsInt J Numer Meth Eng2014992653322644510.1002/nme.46631352.74144 Ghanem RG, Spanos PD (2003) Stochastic Finite elements: a spectral approach. Courier Dover Publications, Mineola KhajiNZakianPUncertainty analysis of elastostatic problems incorporating a new hybrid stochastic-spectral finite element methodMech Adv Mater Struct2017241030104210.1080/15376494.2016.1202359 MishraSSchwabCŠukysJMulti-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered mediumJ Comput Phys2016312192217347117510.1016/j.jcp.2016.02.0141351.76117 ZhangLBatheKJOverlapping finite elements for a new paradigm of solutionComput Struct2017187647610.1016/j.compstruc.2017.03.008 Bathe KJ (1996) Finite element procedures, 1st edn. Prentice Hall; 2nd ed KJ Bathe, Watertown, MA, 2014 ZakianPKhajiNA novel stochastic-spectral finite element method for analysis of elastodynamic problems in the time domainMeccanica201651893920347671710.1007/s11012-015-0242-91338.74110 ShangSYunGJStochastic finite element with material uncertainties: implementation in a general purpose simulation programFinite Elem Anal Des2013646578300239410.1016/j.finel.2012.10.0011282.76125 KavehAOptimal structural analysis20062ChichesterWiley1138.74002 SchillingerDDüsterARankEThe hp-d-adaptive finite cell method for geometrically nonlinear problems of solid mechanicsInt J Numer Meth Eng20128911711202289690310.1002/nme.32891242.74161 Arregui-MenaJDMargettsLMummeryPMPractical application of the stochastic finite element methodArchives Comput Methods Eng201623171190344951510.1007/s11831-014-9139-31348.65160 ZakianPKhajiNA stochastic spectral finite element method for wave propagation analyses with medium uncertaintiesAppl Math Model20186384108384428410.1016/j.apm.2018.06.02707182990 OliveiraSPAzevedoJSSpectral element approximation of Fredholm integral eigenvalue problemsJ Comput Appl Math20142574656310740510.1016/j.cam.2013.08.0161294.65115 LiKGaoWWuDSongCChenTSpectral stochastic isogeometric analysis of linear elasticityComput Methods Appl Mech Eng2018332157190376442310.1016/j.cma.2017.12.0121439.74441 MohammadiSXFEM fracture analysis of composites2012HobokenWiley10.1002/9781118443378 StefanouGThe stochastic finite element method: past, present and futureComput Methods Appl Mech Eng20091981031105110.1016/j.cma.2008.11.0071229.74140 PokusińskiBKamińskiMLattice domes reliability by the perturbation-based approaches vs. semi-analytical methodComput Struct201922117919210.1016/j.compstruc.2019.05.012 KaminskiMThe stochastic perturbation method for computational mechanics2013HobokenWiley10.1002/9781118481844 ParvizianJDüsterARankEFinite cell methodComput Mech200741121133237780210.1007/s00466-007-0173-y1162.74506 KomatitschDTrompJIntroduction to the spectral element method for three-dimensional seismic wave propagationGeophys J Int199913980682210.1046/j.1365-246x.1999.00967.x HughesTJRCottrellJABazilevsYIsogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinementComput Methods Appl Mech Eng200519441354195215238210.1016/j.cma.2004.10.0081151.74419 SzafranJJuszczykKKamińskiMReliability assessment of steel lattice tower subjected to random wind load by the stochastic finite-element methodASCE-ASME J Risk Uncertain Eng Syst Part A: Civil Eng202060402000310.1061/AJRUA6.0001040 KavehAOptimal analysis of structures by concepts of symmetry and regularity2013ViennaSpringer10.1007/978-3-7091-1565-7 SpanosPDGhanemRStochastic finite element expansion for random mediaJ Eng Mech19891151035105310.1061/(ASCE)0733-9399(1989)115:5(1035) GhanemRDhamSStochastic finite element analysis for multiphase flow in heterogeneous porous mediaTransp Porous Media199832239262177649510.1023/A:1006514109327 BelytschkoTKrongauzYOrganDFlemingMKryslPMeshless methods: an overview and recent developmentsComput Methods Appl Mech Eng199613934710.1016/S0045-7825(96)01078-X0891.73075 AndersMHoriMThree-dimensional stochastic finite element method for elasto-plastic bodiesInt J Numer Meth Eng200151449478183031810.1002/nme.1651015.74055 RuessMTalDTrabelsiNYosibashZRankEThe finite cell method for bone simulations: verification and validationBiomech Model Mechanobiol20121142543710.1007/s10237-011-0322-2 LiKWuDGaoWSongCSpectral stochastic isogeometric analysis of free vibrationComput Methods Appl Mech Eng2019350127392502910.1016/j.cma.2019.03.0081441.74258 ZakianPKhajiNA stochastic spectral finite element method for solution of faulting-induced wave propagation in materially random continua without explicitly modeled discontinuitiesComput Mech20196410171048400367810.1007/s00466-019-01692-507119150 KomatitschDVilotteJ-PVaiRCastillo-CovarrubiasJMSánchez-SesmaFJThe spectral element method for elastic wave equations—application to 2-D and 3-D seismic problemsInt J Numer Meth Eng1999451139116410.1002/(sici)1097-0207(19990730)45:9<1139::aid-nme617>3.0.co;2-t0947.74074 KavehAComputational structural analysis and finite element methods2013SwitzerlandSpringer1282.65002 Xiu D (2010) Numerical methods for stochastic computations: a spectral method approach. Princeton University Press, New Jersey ZakianPKhajiNKavehAGraph theoretical methods for efficient stochastic finite element analysis of structuresComput Struct2017178294610.1016/j.compstruc.2016.10.009 HuangSMahadevanSRebbaRCollocation-based stochastic finite element analysis for random field problemsProbab Eng Mech20072219420510.1016/j.probengmech.2006.11.004 A Kaveh (2026_CR21) 2013 2026_CR25 P Zakian (2026_CR19) 2017; 178 OL Maitre (2026_CR13) 2010 A Kaveh (2026_CR22) 2006 2026_CR20 S Huang (2026_CR39) 2007; 22 D Komatitsch (2026_CR17) 1999; 139 K Li (2026_CR34) 2019; 350 S Duczek (2026_CR31) 2014; 99 N Khaji (2026_CR9) 2017; 24 J Szafran (2026_CR11) 2020; 6 M Kaminski (2026_CR3) 2013 M Anders (2026_CR4) 2001; 51 P Zakian (2026_CR6) 2018; 63 S Mishra (2026_CR5) 2016; 312 T Belytschko (2026_CR24) 1996; 139 PJ Laz (2026_CR14) 2010; 224 D Schillinger (2026_CR30) 2012; 89 D Komatitsch (2026_CR18) 1999; 45 G Stefanou (2026_CR2) 2009; 198 S Shang (2026_CR8) 2013; 64 J Parvizian (2026_CR27) 2007; 41 L Zhang (2026_CR28) 2017; 187 TJR Hughes (2026_CR26) 2005; 194 PD Spanos (2026_CR36) 1989; 115 JD Arregui-Mena (2026_CR15) 2016; 23 P Zakian (2026_CR7) 2019; 64 R Ghanem (2026_CR12) 1998; 32 M Joulaian (2026_CR32) 2014; 54 K Li (2026_CR33) 2018; 332 S Mohammadi (2026_CR35) 2012 SP Oliveira (2026_CR37) 2014; 257 B Pokusiński (2026_CR10) 2019; 221 M Ruess (2026_CR29) 2012; 11 2026_CR1 P Zakian (2026_CR16) 2016; 51 A Kaveh (2026_CR23) 2013 2026_CR38 |
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