Complex variable methods for shape sensitivity of finite element models
Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape sensitivity analysis have some potential advantages over other methods. In particular, for first order sensitivities using the complex Taylor series...
Saved in:
| Published in: | Finite elements in analysis and design Vol. 47; no. 10; pp. 1146 - 1156 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
01.10.2011
Elsevier |
| Subjects: | |
| ISSN: | 0168-874X, 1872-6925 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape sensitivity analysis have some potential advantages over other methods. In particular, for first order sensitivities using the complex Taylor series expansion method (CTSE), the implementation is straightforward, only requiring a perturbation of the finite element mesh along the imaginary axis. That is, the real valued coordinates of the mesh are unaltered and no other modifications to the software are required. Fourier differentiation (FD) provides higher order sensitivities by conducting an FFT analysis of multiple complex variable analyses around a sampling radius in the complex plane. Implementation of complex variable sensitivity methods requires complex variable finite element software such that complex nodal coordinates can be used to implement a perturbation in the shape of interest in the complex domain. All resulting finite element outputs such as displacements, strains and stresses become complex and accurate derivatives of all finite element outputs with respect to the shape parameter of interest are available. The methodologies are demonstrated using two-dimensional finite element models of linear elasticity problems with known analytical solutions. It is found that the error in the sensitivities is primarily defined by the error in the finite element solution not the error in the sensitivity method. Hence, more accurate sensitivities can be obtained through mesh refinement. |
|---|---|
| AbstractList | Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape sensitivity analysis have some potential advantages over other methods. In particular, for first order sensitivities using the complex Taylor series expansion method (CTSE), the implementation is straightforward, only requiring a perturbation of the finite element mesh along the imaginary axis. That is, the real valued coordinates of the mesh are unaltered and no other modifications to the software are required. Fourier differentiation (FD) provides higher order sensitivities by conducting an FFT analysis of multiple complex variable analyses around a sampling radius in the complex plane. Implementation of complex variable sensitivity methods requires complex variable finite element software such that complex nodal coordinates can be used to implement a perturbation in the shape of interest in the complex domain. All resulting finite element outputs such as displacements, strains and stresses become complex and accurate derivatives of all finite element outputs with respect to the shape parameter of interest are available. The methodologies are demonstrated using two-dimensional finite element models of linear elasticity problems with known analytical solutions. It is found that the error in the sensitivities is primarily defined by the error in the finite element solution not the error in the sensitivity method. Hence, more accurate sensitivities can be obtained through mesh refinement. |
| Author | Millwater, Harry Bagley, Ronald Voorhees, Andrew |
| Author_xml | – sequence: 1 givenname: Andrew surname: Voorhees fullname: Voorhees, Andrew – sequence: 2 givenname: Harry surname: Millwater fullname: Millwater, Harry email: harry.millwater@utsa.edu – sequence: 3 givenname: Ronald surname: Bagley fullname: Bagley, Ronald |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24339701$$DView record in Pascal Francis |
| BookMark | eNqFkLFqHDEQQEWwIWc7X5Bmm5BqNyNpV7tbpAhH7AQMaRJIJ-a0I6xDK50l-Yj_PnLOuEiRVAPDezPwLthZiIEYe8uh48DVh31nXSDfCeC8g6EDkK_Yhk-jaNUshjO2qdTUTmP_8zW7yHkPAINQ_YbdbON68PSrOWJyuPPUrFTu4pIbG1OT7_BATaaQXXFHVx6baJv6yhVqyNNKoTRrXMjnK3Zu0Wd68zwv2Y_rz9-3X9rbbzdft59uWyPVUFraEc0A_cxBDnLZTeMOyYqBS2txHhauUC2oJglgoEeO_Yx1YyqvJiuUvGTvT3cPKd4_UC56ddmQ9xgoPmQ9zUqIEXpRyXfPJGaD3iYMxmV9SG7F9KhFL-U8Aq-cPHEmxZwT2ReEg36qq_f6T139VFfDoGvdas1_WcYVLC6GktD5_7gfT27tRkdHSWfjKBhaXCJT9BLdP_3f5nOZIg |
| CODEN | FEADEU |
| CitedBy_id | crossref_primary_10_1016_j_engfracmech_2013_07_012 crossref_primary_10_4028_www_scientific_net_AMR_891_892_1015 crossref_primary_10_1016_j_cma_2021_114195 crossref_primary_10_1016_j_ijfatigue_2019_05_036 crossref_primary_10_1016_j_cma_2023_116456 crossref_primary_10_1016_j_engfracmech_2016_04_002 crossref_primary_10_1016_j_ijfatigue_2012_01_016 crossref_primary_10_1177_0021998312460263 crossref_primary_10_1061__ASCE_EM_1943_7889_0000837 crossref_primary_10_1016_j_cma_2014_06_034 crossref_primary_10_3390_app13127125 crossref_primary_10_1016_j_advengsoft_2018_02_009 crossref_primary_10_1007_s00419_021_01996_0 crossref_primary_10_1016_j_jsv_2016_02_026 crossref_primary_10_1016_j_cam_2012_10_001 crossref_primary_10_2514_1_J057231 crossref_primary_10_1177_0954406212473391 crossref_primary_10_1007_s11433_013_5064_y crossref_primary_10_1007_s00707_015_1419_y crossref_primary_10_1016_j_engfracmech_2017_12_013 crossref_primary_10_1016_j_engfracmech_2021_107638 crossref_primary_10_1016_j_jcp_2019_07_030 crossref_primary_10_1016_j_finel_2025_104419 crossref_primary_10_1080_01495739_2016_1264871 crossref_primary_10_3390_app12052738 crossref_primary_10_1016_j_engfracmech_2012_02_006 crossref_primary_10_1016_j_ijpvp_2019_05_004 crossref_primary_10_1016_j_ijpvp_2015_05_006 crossref_primary_10_1007_s11075_024_01937_2 crossref_primary_10_1155_2013_515973 crossref_primary_10_1016_j_ijmecsci_2017_08_035 crossref_primary_10_1080_15397734_2025_2486397 crossref_primary_10_1145_3378538 crossref_primary_10_1134_S1064229318100101 crossref_primary_10_1016_j_finel_2017_07_001 crossref_primary_10_1016_j_orgel_2022_106734 crossref_primary_10_1016_j_cam_2018_03_005 crossref_primary_10_2514_1_J053282 |
| Cites_doi | 10.2514/1.19225 10.1109/99.537089 10.1016/j.enganabound.2005.03.001 10.1002/(SICI)1097-024X(199712)27:12<1427::AID-SPE138>3.0.CO;2-Q 10.1137/S003614459631241X 10.1016/j.finel.2008.06.011 10.2514/2.3131 10.1145/362759.362820 10.1016/S0168-874X(02)00073-2 10.1016/S0045-7930(01)00044-5 10.1145/838250.838251 10.1137/0704019 10.1007/s001580050183 10.1137/1021093 10.1061/(ASCE)0733-9399(2008)134:10(867) 10.1016/S0021-9991(03)00123-2 10.1016/j.automatica.2005.09.008 10.1090/S0025-5718-1968-0230468-5 10.2514/2.1270 10.2514/3.12257 |
| ContentType | Journal Article |
| Copyright | 2011 Elsevier B.V. 2015 INIST-CNRS |
| Copyright_xml | – notice: 2011 Elsevier B.V. – notice: 2015 INIST-CNRS |
| DBID | AAYXX CITATION IQODW 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1016/j.finel.2011.05.003 |
| DatabaseName | CrossRef Pascal-Francis Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Engineering Mathematics Physics |
| EISSN | 1872-6925 |
| EndPage | 1156 |
| ExternalDocumentID | 24339701 10_1016_j_finel_2011_05_003 S0168874X11000990 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1~. 1~5 29H 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABAOU ABBOA ABEFU ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACIWK ACNNM ACRLP ACZNC ADBBV ADEZE ADGUI ADJOM ADMUD ADTZH AEBSH AECPX AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AI. AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HLZ HVGLF HZ~ IHE J1W JJJVA KOM LX9 LY7 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 R2- RIG RNS ROL RPZ SBC SDF SDG SES SET SEW SPC SPCBC SST SSV SSW SSZ T5K T9H TN5 VH1 WUQ XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c365t-ebee9004910353db87baef2513ffa95d16a6da68300c04a1a49aa6dc91068f263 |
| ISICitedReferencesCount | 43 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000292035200003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0168-874X |
| IngestDate | Sun Nov 09 11:25:34 EST 2025 Mon Jul 21 09:14:49 EDT 2025 Tue Nov 18 22:28:23 EST 2025 Sat Nov 29 04:56:28 EST 2025 Fri Feb 23 02:34:33 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Keywords | Design sensitivities Complex Taylor series expansion (CTSE) Fourier differentiation Finite differencing Sensitivity methods Optimization Geometrical shape Sensitivity analysis Displacement(deformation) Taylor series Modeling Complex variable method Finite element method Complex method Linear elasticity Series expansion Structure modification Potential method Differentiation Mesh generation Structural analysis |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c365t-ebee9004910353db87baef2513ffa95d16a6da68300c04a1a49aa6dc91068f263 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 896227042 |
| PQPubID | 23500 |
| PageCount | 11 |
| ParticipantIDs | proquest_miscellaneous_896227042 pascalfrancis_primary_24339701 crossref_primary_10_1016_j_finel_2011_05_003 crossref_citationtrail_10_1016_j_finel_2011_05_003 elsevier_sciencedirect_doi_10_1016_j_finel_2011_05_003 |
| PublicationCentury | 2000 |
| PublicationDate | 2011-10-01 |
| PublicationDateYYYYMMDD | 2011-10-01 |
| PublicationDate_xml | – month: 10 year: 2011 text: 2011-10-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Finite elements in analysis and design |
| PublicationYear | 2011 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Haakus and Der Kiureghian (bib9) 2005 Chen, Choi (bib10) 1994; 32 Bischof, Khademi, Mauer, Carle (bib14) 1996; 3 Huebner, Dewhirst, Smith, Byrom (bib30) 2001 Henrici (bib27) 1979; 4 Bagley (bib28) 2006; 19 Bebamzadeh, Haukaas (bib11) 2008; 134 Gao, He (bib22) 2005; 29 Kim, Bates, Postlethwaite (bib23) 2006; 42 Martins, Sturdza, Alonso (bib5) 2003; 29 Reddy, Rao (bib6) 2008; 44 Lyness, Moler (bib15) 1967; 4 Newman, Whitfield, Anderson (bib31) 2003; 40 Choi (bib4) 2002; 39 Squire, Trapp (bib17) 1998; 40 Lyness (bib16) 1968; 22 Rightley, Henninger, Hanson (bib7) 1998 Bischof, Roh, Mauer-Oats (bib13) 1997; 27 Butuk, Pemba (bib25) 2003; 125 Sadd (bib29) 2005 Cervino, Bewley (bib21) 2003; 187 Choi, Kim (bib8) 2005; Volume 1 Anderson, Newman, Whitfield, Nielsen (bib18) 2001; 39 Lyness, Sande (bib26) 1971; 14 Madsen, Krenk, Lind (bib3) 2006 Wang, Apte (bib24) 2006; 44 Newman, Whitfield, Anderson, Step-size (bib19) 2003; 40 Burg, Newman (bib20) 2003; 32 Hansen, Liu, Olhoff (bib2) 2000; 21 M. Martinelli, Sensitivity Evaluation in Aerodynamic Optimal Design, Ph.D. Thesis, Scuola Normale Superiore di Pisa, 2007. Cook, Malkus, Plesha, Witt (bib1) 2002 Bagley (10.1016/j.finel.2011.05.003_bib28) 2006; 19 Choi (10.1016/j.finel.2011.05.003_bib4) 2002; 39 Rightley (10.1016/j.finel.2011.05.003_bib7) 1998 Huebner (10.1016/j.finel.2011.05.003_bib30) 2001 Newman (10.1016/j.finel.2011.05.003_bib19) 2003; 40 Martins (10.1016/j.finel.2011.05.003_bib5) 2003; 29 Lyness (10.1016/j.finel.2011.05.003_bib16) 1968; 22 Bischof (10.1016/j.finel.2011.05.003_bib13) 1997; 27 Cook (10.1016/j.finel.2011.05.003_bib1) 2002 Choi (10.1016/j.finel.2011.05.003_bib8) 2005; Volume 1 10.1016/j.finel.2011.05.003_bib12 Newman (10.1016/j.finel.2011.05.003_bib31) 2003; 40 Bebamzadeh (10.1016/j.finel.2011.05.003_bib11) 2008; 134 Burg (10.1016/j.finel.2011.05.003_bib20) 2003; 32 Lyness (10.1016/j.finel.2011.05.003_bib26) 1971; 14 Lyness (10.1016/j.finel.2011.05.003_bib15) 1967; 4 Sadd (10.1016/j.finel.2011.05.003_bib29) 2005 Squire (10.1016/j.finel.2011.05.003_bib17) 1998; 40 Cervino (10.1016/j.finel.2011.05.003_bib21) 2003; 187 Reddy (10.1016/j.finel.2011.05.003_bib6) 2008; 44 Bischof (10.1016/j.finel.2011.05.003_bib14) 1996; 3 Anderson (10.1016/j.finel.2011.05.003_bib18) 2001; 39 Butuk (10.1016/j.finel.2011.05.003_bib25) 2003; 125 Wang (10.1016/j.finel.2011.05.003_bib24) 2006; 44 Madsen (10.1016/j.finel.2011.05.003_bib3) 2006 Haakus and Der Kiureghian (10.1016/j.finel.2011.05.003_bib9) 2005 Henrici (10.1016/j.finel.2011.05.003_bib27) 1979; 4 Hansen (10.1016/j.finel.2011.05.003_bib2) 2000; 21 Chen (10.1016/j.finel.2011.05.003_bib10) 1994; 32 Gao (10.1016/j.finel.2011.05.003_bib22) 2005; 29 Kim (10.1016/j.finel.2011.05.003_bib23) 2006; 42 |
| References_xml | – year: 1998 ident: bib7 article-title: Adjoint Differentiation of Hydrodynamic Codes, CNLS Research Highlights – year: 2002 ident: bib1 article-title: Concepts and Applications of Finite Element Analysis – volume: 39 start-page: 119 year: 2002 end-page: 136 ident: bib4 article-title: Shape design sensitivity analysis and optimization of general plane arch structures publication-title: Finite Elements in Analysis and Design – volume: 40 start-page: 566 year: 2003 end-page: 573 ident: bib19 article-title: independent approach for multidisciplinary sensitivity analysis publication-title: Journal of Aircraft – volume: 21 start-page: 177 year: 2000 end-page: 195 ident: bib2 article-title: Shape sensitivity analysis using a fixed basis function finite element approach publication-title: Structural Multidisciplinary Optimization – volume: 134 start-page: 867 year: 2008 end-page: 880 ident: bib11 article-title: Second-order sensitivities of inelastic finite element response by direct differentiation publication-title: ASCE Journal of Engineering Mechanics – volume: 42 start-page: 177 year: 2006 end-page: 182 ident: bib23 article-title: Nonlinear robust performance analysis using complex-step gradient approximation publication-title: Automatica – volume: 29 start-page: 245 year: 2003 end-page: 263 ident: bib5 article-title: The complex-step derivative approximation publication-title: ACM Transactions on Mathematical Software – volume: 4 start-page: 202 year: 1967 end-page: 210 ident: bib15 article-title: Numerical differentiation of analytic functions publication-title: SIAM Journal of Numerical Analysis – volume: 14 start-page: 669 year: 1971 end-page: 675 ident: bib26 article-title: ENTCAF and ENTCRE: evaluation of normalized Taylor coefficients of an analytic function publication-title: Communications of the ACM – volume: 40 start-page: 110 year: 1998 end-page: 112 ident: bib17 article-title: Using complex variables to estimate derivatives of real functions publication-title: SIAM Review – volume: 44 start-page: 2958 year: 2006 end-page: 2961 ident: bib24 article-title: Complex variable method for eigensolution sensitivity analysis publication-title: AIAA Journal. – volume: 22 start-page: 352 year: 1968 end-page: 362 ident: bib16 article-title: Differentiation formulas for analytic functions publication-title: Mathematics of Computation – year: 2005 ident: bib29 article-title: Elasticity: Theory and Applications and Numerics – start-page: 1013 year: 2005 end-page: 1026 ident: bib9 article-title: Parameter sensitivity and importance measures in nonlinear finite element reliability analysis publication-title: Journal of Engineering Mechanics – volume: 40 start-page: 566 year: 2003 end-page: 573 ident: bib31 article-title: Step-size independent approach for multidisciplinary sensitivity analysis publication-title: Journal of Aircraft – volume: 125 start-page: 854 year: 2003 end-page: 858 ident: bib25 article-title: computing CHEMKIN sensitivities using complex variables publication-title: Transactions of the ASME – volume: 4 start-page: 481 year: 1979 end-page: 527 ident: bib27 article-title: Fast Fourier methods in computational complex analysis publication-title: SIAM Review – volume: Volume 1 year: 2005 ident: bib8 publication-title: Structural Sensitivity Analysis and Optimization: Linear Systems – volume: 32 start-page: 373 year: 2003 end-page: 383 ident: bib20 article-title: Computationally efficient, numerically exact design space derivatives via the complex Taylor's series expansion method publication-title: Computers and Fluids – volume: 32 start-page: 2099 year: 1994 end-page: 2107 ident: bib10 article-title: Continuum approach for second-order shape design sensitivity of three-dimensional elastic solids publication-title: AIAA Journal – year: 2006 ident: bib3 article-title: Methods of Structural Safety – volume: 27 start-page: 1427 year: 1997 end-page: 1456 ident: bib13 article-title: ADIC: an extensible automatic differentiation tool for ANSI-C publication-title: Software-Practice and Experience – volume: 39 start-page: 56 year: 2001 end-page: 63 ident: bib18 article-title: Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables publication-title: AIAA Journal – volume: 19 start-page: 255 year: 2006 end-page: 281 ident: bib28 article-title: On Fourier differentiation—a numerical tool for implicit functions publication-title: International Journal of Applied Mathematics – volume: 29 start-page: 788 year: 2005 end-page: 795 ident: bib22 article-title: A new inverse analysis for multi-region heat conduction BEM using complex-variable-differentiation method publication-title: Engineering Analysis with Boundary Elements – reference: M. Martinelli, Sensitivity Evaluation in Aerodynamic Optimal Design, Ph.D. Thesis, Scuola Normale Superiore di Pisa, 2007. – volume: 44 start-page: 875 year: 2008 end-page: 888 ident: bib6 article-title: Fractal finite element method based shape sensitivity analysis of mixed-mode fracture publication-title: Finite Elements in Analysis and Design – volume: 187 start-page: 544 year: 2003 end-page: 549 ident: bib21 article-title: On the extension of the complex-step derivative technique to pseudospectral algorithms publication-title: Journal of Computational Physics – year: 2001 ident: bib30 article-title: The Finite Element Method for Engineers – volume: 3 start-page: 18 year: 1996 end-page: 32 ident: bib14 article-title: Adifor 2.0: automatic differentiation of Fortran 77 programs publication-title: IEEE Computational Science and Engineering – volume: 44 start-page: 2958 year: 2006 ident: 10.1016/j.finel.2011.05.003_bib24 article-title: Complex variable method for eigensolution sensitivity analysis publication-title: AIAA Journal. doi: 10.2514/1.19225 – volume: 3 start-page: 18 year: 1996 ident: 10.1016/j.finel.2011.05.003_bib14 article-title: Adifor 2.0: automatic differentiation of Fortran 77 programs publication-title: IEEE Computational Science and Engineering doi: 10.1109/99.537089 – volume: 29 start-page: 788 year: 2005 ident: 10.1016/j.finel.2011.05.003_bib22 article-title: A new inverse analysis for multi-region heat conduction BEM using complex-variable-differentiation method publication-title: Engineering Analysis with Boundary Elements doi: 10.1016/j.enganabound.2005.03.001 – volume: 27 start-page: 1427 year: 1997 ident: 10.1016/j.finel.2011.05.003_bib13 article-title: ADIC: an extensible automatic differentiation tool for ANSI-C publication-title: Software-Practice and Experience doi: 10.1002/(SICI)1097-024X(199712)27:12<1427::AID-SPE138>3.0.CO;2-Q – volume: 40 start-page: 110 year: 1998 ident: 10.1016/j.finel.2011.05.003_bib17 article-title: Using complex variables to estimate derivatives of real functions publication-title: SIAM Review doi: 10.1137/S003614459631241X – year: 1998 ident: 10.1016/j.finel.2011.05.003_bib7 – volume: 44 start-page: 875 year: 2008 ident: 10.1016/j.finel.2011.05.003_bib6 article-title: Fractal finite element method based shape sensitivity analysis of mixed-mode fracture publication-title: Finite Elements in Analysis and Design doi: 10.1016/j.finel.2008.06.011 – ident: 10.1016/j.finel.2011.05.003_bib12 – volume: 40 start-page: 566 year: 2003 ident: 10.1016/j.finel.2011.05.003_bib19 article-title: independent approach for multidisciplinary sensitivity analysis publication-title: Journal of Aircraft doi: 10.2514/2.3131 – volume: 14 start-page: 669 year: 1971 ident: 10.1016/j.finel.2011.05.003_bib26 article-title: ENTCAF and ENTCRE: evaluation of normalized Taylor coefficients of an analytic function publication-title: Communications of the ACM doi: 10.1145/362759.362820 – volume: 39 start-page: 119 year: 2002 ident: 10.1016/j.finel.2011.05.003_bib4 article-title: Shape design sensitivity analysis and optimization of general plane arch structures publication-title: Finite Elements in Analysis and Design doi: 10.1016/S0168-874X(02)00073-2 – year: 2001 ident: 10.1016/j.finel.2011.05.003_bib30 – volume: 32 start-page: 373 year: 2003 ident: 10.1016/j.finel.2011.05.003_bib20 article-title: Computationally efficient, numerically exact design space derivatives via the complex Taylor's series expansion method publication-title: Computers and Fluids doi: 10.1016/S0045-7930(01)00044-5 – volume: 19 start-page: 255 year: 2006 ident: 10.1016/j.finel.2011.05.003_bib28 article-title: On Fourier differentiation—a numerical tool for implicit functions publication-title: International Journal of Applied Mathematics – year: 2005 ident: 10.1016/j.finel.2011.05.003_bib29 – volume: Volume 1 year: 2005 ident: 10.1016/j.finel.2011.05.003_bib8 – volume: 29 start-page: 245 year: 2003 ident: 10.1016/j.finel.2011.05.003_bib5 article-title: The complex-step derivative approximation publication-title: ACM Transactions on Mathematical Software doi: 10.1145/838250.838251 – volume: 4 start-page: 202 year: 1967 ident: 10.1016/j.finel.2011.05.003_bib15 article-title: Numerical differentiation of analytic functions publication-title: SIAM Journal of Numerical Analysis doi: 10.1137/0704019 – volume: 21 start-page: 177 year: 2000 ident: 10.1016/j.finel.2011.05.003_bib2 article-title: Shape sensitivity analysis using a fixed basis function finite element approach publication-title: Structural Multidisciplinary Optimization doi: 10.1007/s001580050183 – volume: 4 start-page: 481 year: 1979 ident: 10.1016/j.finel.2011.05.003_bib27 article-title: Fast Fourier methods in computational complex analysis publication-title: SIAM Review doi: 10.1137/1021093 – year: 2006 ident: 10.1016/j.finel.2011.05.003_bib3 – volume: 125 start-page: 854 year: 2003 ident: 10.1016/j.finel.2011.05.003_bib25 article-title: computing CHEMKIN sensitivities using complex variables publication-title: Transactions of the ASME – volume: 40 start-page: 566 year: 2003 ident: 10.1016/j.finel.2011.05.003_bib31 article-title: Step-size independent approach for multidisciplinary sensitivity analysis publication-title: Journal of Aircraft doi: 10.2514/2.3131 – year: 2002 ident: 10.1016/j.finel.2011.05.003_bib1 – volume: 134 start-page: 867 year: 2008 ident: 10.1016/j.finel.2011.05.003_bib11 article-title: Second-order sensitivities of inelastic finite element response by direct differentiation publication-title: ASCE Journal of Engineering Mechanics doi: 10.1061/(ASCE)0733-9399(2008)134:10(867) – volume: 187 start-page: 544 year: 2003 ident: 10.1016/j.finel.2011.05.003_bib21 article-title: On the extension of the complex-step derivative technique to pseudospectral algorithms publication-title: Journal of Computational Physics doi: 10.1016/S0021-9991(03)00123-2 – volume: 42 start-page: 177 year: 2006 ident: 10.1016/j.finel.2011.05.003_bib23 article-title: Nonlinear robust performance analysis using complex-step gradient approximation publication-title: Automatica doi: 10.1016/j.automatica.2005.09.008 – volume: 22 start-page: 352 year: 1968 ident: 10.1016/j.finel.2011.05.003_bib16 article-title: Differentiation formulas for analytic functions publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1968-0230468-5 – volume: 39 start-page: 56 year: 2001 ident: 10.1016/j.finel.2011.05.003_bib18 article-title: Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables publication-title: AIAA Journal doi: 10.2514/2.1270 – start-page: 1013 year: 2005 ident: 10.1016/j.finel.2011.05.003_bib9 article-title: Parameter sensitivity and importance measures in nonlinear finite element reliability analysis publication-title: Journal of Engineering Mechanics – volume: 32 start-page: 2099 year: 1994 ident: 10.1016/j.finel.2011.05.003_bib10 article-title: Continuum approach for second-order shape design sensitivity of three-dimensional elastic solids publication-title: AIAA Journal doi: 10.2514/3.12257 |
| SSID | ssj0005264 |
| Score | 2.1396458 |
| Snippet | Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1146 |
| SubjectTerms | Complex Taylor series expansion (CTSE) Complex variables Computer programs Design sensitivities Error detection Exact sciences and technology Finite differencing Finite element method Fourier differentiation Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis. Scientific computation Optimization Physics Sciences and techniques of general use Sensitivity analysis Sensitivity methods Software Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics |
| Title | Complex variable methods for shape sensitivity of finite element models |
| URI | https://dx.doi.org/10.1016/j.finel.2011.05.003 https://www.proquest.com/docview/896227042 |
| Volume | 47 |
| WOSCitedRecordID | wos000292035200003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-6925 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0005264 issn: 0168-874X databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lj9MwELagywGEeCwglsfKB8SlBOXpxMcFtSxoVRDqot4sN3bYXVVJabpLfz5je9ymqljgwCVKLOfl-Twej8fzEfKKyzLh01IGuWYqSLk2fS5TcAmjqa4US6vSkk3ko1ExmfAv6NBvLZ1AXtfFasXn_1XUUAbCNltn_0Hc64dCAZyD0OEIYofjXwne9PCZXvWvYBZs90U5kmibd6Hfnsm57rcmah1pI8BYrM6N4dnXLpLckeO0Xat1uFXBRtBKn8zEON7VVhjIt6ZZnGmnfjrxkrjx8KdEKpBjudiEIL-T39F5_tU6q7vOCIyGi7r-SVaAsF3QpVewLqWmB1LYUZeR9z9qvHRJxnfUuvMwXLyF9tAzzLtqfGHJZhTzK_ejz2J4enIixoPJ-PX8R2D4xcw6PJKt3CR7cZ7xokf2jj4OJp864UAM88C7H_AZqmws4M57f2fF3J3LFvpW5UhRdsZ3a7SMH5B7ONugRw4lD8kNXe-T-zjzoKjX231yp5OW8hH5gBCiHkIUIUQBQtRCiHYgRJuKOghRRAh1EHpMToeD8fvjAAk3gjJh2TKADq25mTNGYZIlalrkU6krsICTqpI8UxGTTElWJGFYhqmMZMollJRQnxVVzJInpFc3tX5KaKRUquEh2uwUgQaTqtS8VJnSXIb5NDogsW9AUWI2ekOKMhM-7PBC2FYXptVFmJkktgfkzfqmuUvGcn115iUj0J50dqIAXF1_4-GWHNcvi9ME7PcQvp56wQpQx2aNTda6uWxFwVkc5zASPvtzlefk9qYPvSC95eJSvyS3yqvlebs4RID-AtVCsG0 |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Complex+variable+methods+for+shape+sensitivity+of+finite+element+models&rft.jtitle=Finite+elements+in+analysis+and+design&rft.au=Voorhees%2C+Andrew&rft.au=Millwater%2C+Harry&rft.au=Bagley%2C+Ronald&rft.date=2011-10-01&rft.issn=0168-874X&rft.volume=47&rft.issue=10&rft.spage=1146&rft.epage=1156&rft_id=info:doi/10.1016%2Fj.finel.2011.05.003&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0168-874X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0168-874X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0168-874X&client=summon |