Coupling finite element and reliability analysis through proper generalized decomposition model reduction
SUMMARYThe FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite...
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| Vydané v: | International journal for numerical methods in engineering Ročník 95; číslo 13; s. 1079 - 1093 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Chichester
Blackwell Publishing Ltd
28.09.2013
Wiley Wiley Subscription Services, Inc |
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | SUMMARYThe FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi‐material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi‐material model. This parametrized solution is used in conjunction with a first‐order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two‐dimensional plane elasticity are presented.Copyright © 2013 John Wiley & Sons, Ltd. |
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| AbstractList | The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi‐material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi‐material model. This parametrized solution is used in conjunction with a first‐order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two‐dimensional plane elasticity are presented.Copyright © 2013 John Wiley & Sons, Ltd. SUMMARY The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi-material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi-material model. This parametrized solution is used in conjunction with a first-order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two-dimensional plane elasticity are presented.Copyright [copy 2013 John Wiley & Sons, Ltd. SUMMARY The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi-material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi-material model. This parametrized solution is used in conjunction with a first-order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two-dimensional plane elasticity are presented.Copyright © 2013 John Wiley & Sons, Ltd. [PUBLICATION ABSTRACT] SUMMARYThe FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi‐material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi‐material model. This parametrized solution is used in conjunction with a first‐order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two‐dimensional plane elasticity are presented.Copyright © 2013 John Wiley & Sons, Ltd. |
| Author | Polit, O. Gallimard, L. Vidal, P. |
| Author_xml | – sequence: 1 givenname: L. surname: Gallimard fullname: Gallimard, L. email: Correspondence to: L. Gallimard, Université Paris Ouest, 50 rue de Sèvres 92410 Ville d'Avray, France., laurent.gallimard@u-paris10.fr organization: LEME, Université Paris Ouest Nanterre La Défense, 50 rue de Sèvres 92410 Ville d'Avray, France – sequence: 2 givenname: P. surname: Vidal fullname: Vidal, P. organization: LEME, Université Paris Ouest Nanterre La Défense, 50 rue de Sèvres 92410 Ville d'Avray, France – sequence: 3 givenname: O. surname: Polit fullname: Polit, O. organization: LEME, Université Paris Ouest Nanterre La Défense, 50 rue de Sèvres 92410 Ville d'Avray, France |
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| Cites_doi | 10.1016/j.jnnfm.2010.12.012 10.1061/(ASCE)0733-9399(1986)112:1(85) 10.1016/j.na.2006.02.001 10.1016/S0167-4730(97)00026-X 10.1016/S0951-8320(00)00043-0 10.1016/S0045-7825(02)00211-6 10.1002/nme.3136 10.1016/j.cma.2010.01.009 10.1016/j.compstruct.2011.12.016 10.1016/j.probengmech.2005.07.005 10.1007/978-94-011-5614-1_14 10.1016/j.jnnfm.2006.07.007 10.1007/978-1-4612-1432-8 10.1016/S0029-5493(98)00184-8 |
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| Keywords | Stratified material Solid solid interface Rupture Structural reliability model reduction finite element analysis Modeling FORM approximation Finite element method Reduction method Uncertain system Proper generalized decomposition Plane elasticity System reduction Mechanical system Reduced order systems Simulation model Reduced order model Algorithm analysis Structural analysis structural reliability proper generalized decomposition finite element analysis |
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| References | Shi ZJ, Shen J. Convergence of the Polak Ribière Polyak conjugate gradient method. Nonlinear Analysis: Theory, Methods and Applications 2007; 66(6):1428-1441. Pendola M, Mohamed A, Lemaire M, Hornet P. Combination of finite element and reliability methods in nonlinear fracture mechanics. Reliability Engineering and System Safety 2000; 70:15-27. Der Kiureghian A, de Stefano M. Efficients algorithms for second order reliability analysis. Journal of Engineering Mechanics 1991; 117(12):37-49. Allix O, Vidal P. A new multi-solution approach suitable for structural identification problems. Computer Methods in Applied Mechanics and Engineering 2002; 191(25-26):2727-2758. Nouy A. A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Computer Methods in Applied Mechanics and Engineering 2010; 199(23-24):1603-1626. Der Kiureghian A, Dakessian T. Multiple design points in first and second-order reliability. Structural Safety 1998; 20:37-49. Ladevèze P. Nonlinear Computational Structural Mechanics - New Approaches and Non-incremental Methods of Calculation. Springer-Verlag: New York, 1999. Rackwitz R, Fiessler B. Structural reliability under random load sequences. Computer and Structures 1979; 9(5):484-494. Chinesta F, Ammar A, Leygue A, Keunings R. An overview of the proper generalized decomposition with applications in computational rheology. Journal of Non-Newtonian Fluid Mechanics 2011; 166(11):578-592. Ammar A, Mokdada B, Chinesta F, Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Journal of Non-Newtonian Fluid Mechanics 2011; 139:153-176. Gallimard L. Errors bounds for the reliability index in finite element reliability analysis. International Journal for Numerical Methods in Engineering 2011; 87:781-994. Haukaas T, Der Kiureghian A. Strategies for finding the design point in non-linear finite element reliability analysis. Probabilistic Engineering Mechanics 2006; 21:133-147. Ditlevsen O, Madsen HO. Structural Reliability Methods. Wiley: New York, 1996. Hasofer AM, Lind NC. An exact and invariant first order reliability format. Journal of Engineering Mechanics, ASCE 1974; 100(EM1):111-121. Mohamed A, Lemaire M, Mitteau JC, Meister E. Finite element and reliability: a method for compound variables - application on a cracked heating system. Nuclear Engineering and Design 1998; 185:185-202. Lemaire M. Fiabilité des structures. Hermes: Paris, 2005. Vidal P, Gallimard L, Polit O. Assessment of a composite beam finite element based on the proper generalized decomposition. Composite Structures 2012; 94:1900-1910. Der Kiureghian A, Liu PL. Structural reliability under incomplete probability information. Journal of Engineering Mechanics 1986; 112(1):85-104. 2012; 94 2002; 191 2011; 139 2006; 21 1986; 112 1997 2010; 199 1996 2000; 70 2011; 87 2005 1994 1991; 117 1974; 100 2007; 66 1998; 20 1979; 9 2011; 166 1999 1998; 185 Hasofer AM (e_1_2_9_4_1) 1974; 100 e_1_2_9_20_1 Ditlevsen O (e_1_2_9_2_1) 1996 e_1_2_9_11_1 Zhang Y (e_1_2_9_7_1) 1994 e_1_2_9_10_1 e_1_2_9_21_1 e_1_2_9_13_1 e_1_2_9_12_1 e_1_2_9_8_1 Lemaire M (e_1_2_9_3_1) 2005 e_1_2_9_9_1 e_1_2_9_15_1 e_1_2_9_14_1 Rackwitz R (e_1_2_9_5_1) 1979; 9 e_1_2_9_17_1 e_1_2_9_16_1 e_1_2_9_19_1 Der Kiureghian A (e_1_2_9_6_1) 1991; 117 e_1_2_9_18_1 |
| References_xml | – reference: Chinesta F, Ammar A, Leygue A, Keunings R. An overview of the proper generalized decomposition with applications in computational rheology. Journal of Non-Newtonian Fluid Mechanics 2011; 166(11):578-592. – reference: Lemaire M. Fiabilité des structures. Hermes: Paris, 2005. – reference: Ammar A, Mokdada B, Chinesta F, Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Journal of Non-Newtonian Fluid Mechanics 2011; 139:153-176. – reference: Gallimard L. Errors bounds for the reliability index in finite element reliability analysis. International Journal for Numerical Methods in Engineering 2011; 87:781-994. – reference: Ladevèze P. Nonlinear Computational Structural Mechanics - New Approaches and Non-incremental Methods of Calculation. Springer-Verlag: New York, 1999. – reference: Der Kiureghian A, Dakessian T. Multiple design points in first and second-order reliability. Structural Safety 1998; 20:37-49. – reference: Allix O, Vidal P. A new multi-solution approach suitable for structural identification problems. Computer Methods in Applied Mechanics and Engineering 2002; 191(25-26):2727-2758. – reference: Nouy A. A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Computer Methods in Applied Mechanics and Engineering 2010; 199(23-24):1603-1626. – reference: Vidal P, Gallimard L, Polit O. Assessment of a composite beam finite element based on the proper generalized decomposition. Composite Structures 2012; 94:1900-1910. – reference: Der Kiureghian A, de Stefano M. Efficients algorithms for second order reliability analysis. Journal of Engineering Mechanics 1991; 117(12):37-49. – reference: Mohamed A, Lemaire M, Mitteau JC, Meister E. Finite element and reliability: a method for compound variables - application on a cracked heating system. Nuclear Engineering and Design 1998; 185:185-202. – reference: Ditlevsen O, Madsen HO. Structural Reliability Methods. Wiley: New York, 1996. – reference: Shi ZJ, Shen J. Convergence of the Polak Ribière Polyak conjugate gradient method. Nonlinear Analysis: Theory, Methods and Applications 2007; 66(6):1428-1441. – reference: Hasofer AM, Lind NC. An exact and invariant first order reliability format. Journal of Engineering Mechanics, ASCE 1974; 100(EM1):111-121. – reference: Der Kiureghian A, Liu PL. Structural reliability under incomplete probability information. Journal of Engineering Mechanics 1986; 112(1):85-104. – reference: Pendola M, Mohamed A, Lemaire M, Hornet P. Combination of finite element and reliability methods in nonlinear fracture mechanics. Reliability Engineering and System Safety 2000; 70:15-27. – reference: Rackwitz R, Fiessler B. Structural reliability under random load sequences. Computer and Structures 1979; 9(5):484-494. – reference: Haukaas T, Der Kiureghian A. Strategies for finding the design point in non-linear finite element reliability analysis. 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article-title: A priori model reduction through proper generalized decomposition for solving time‐dependent partial differential equations publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 20 start-page: 37 year: 1998 end-page: 49 article-title: Multiple design points in first and second‐order reliability publication-title: Structural Safety – volume: 94 start-page: 1900 year: 2012 end-page: 1910 article-title: Assessment of a composite beam finite element based on the proper generalized decomposition publication-title: Composite Structures – volume: 9 start-page: 484 issue: 5 year: 1979 end-page: 494 article-title: Structural reliability under random load sequences publication-title: Computer and Structures – volume: 66 start-page: 1428 issue: 6 year: 2007 end-page: 1441 article-title: Convergence of the Polak Ribière Polyak conjugate gradient method publication-title: Nonlinear Analysis: Theory, Methods and Applications – volume: 185 start-page: 185 year: 1998 end-page: 202 article-title: Finite element and reliability: a method for compound variables ‐ application on a cracked heating system publication-title: Nuclear Engineering and Design – volume: 87 start-page: 781 year: 2011 end-page: 994 article-title: Errors bounds for the reliability index in finite element reliability analysis publication-title: International Journal for Numerical Methods in Engineering – year: 1999 – start-page: 297 volume-title: Proceedings of the 6th IFIP WG7.5 Reliability and Optimization of Structural System year: 1994 ident: e_1_2_9_7_1 – ident: e_1_2_9_16_1 doi: 10.1016/j.jnnfm.2010.12.012 – ident: e_1_2_9_19_1 doi: 10.1061/(ASCE)0733-9399(1986)112:1(85) – ident: e_1_2_9_21_1 doi: 10.1016/j.na.2006.02.001 – volume: 117 start-page: 37 issue: 12 year: 1991 ident: e_1_2_9_6_1 article-title: Efficients algorithms for second order reliability analysis publication-title: Journal of Engineering Mechanics – ident: e_1_2_9_20_1 doi: 10.1016/S0167-4730(97)00026-X – volume-title: Fiabilité des structures year: 2005 ident: e_1_2_9_3_1 – ident: e_1_2_9_11_1 doi: 10.1016/S0951-8320(00)00043-0 – ident: e_1_2_9_14_1 doi: 10.1016/S0045-7825(02)00211-6 – ident: e_1_2_9_9_1 doi: 10.1002/nme.3136 – ident: e_1_2_9_15_1 doi: 10.1016/j.cma.2010.01.009 – ident: e_1_2_9_17_1 doi: 10.1016/j.compstruct.2011.12.016 – ident: e_1_2_9_8_1 doi: 10.1016/j.probengmech.2005.07.005 – volume-title: Structural Reliability Methods year: 1996 ident: e_1_2_9_2_1 – ident: e_1_2_9_10_1 doi: 10.1007/978-94-011-5614-1_14 – ident: e_1_2_9_12_1 doi: 10.1016/j.jnnfm.2006.07.007 – volume: 9 start-page: 484 issue: 5 year: 1979 ident: e_1_2_9_5_1 article-title: Structural reliability under random load sequences publication-title: Computer and Structures – volume: 100 start-page: 111 issue: 1 year: 1974 ident: e_1_2_9_4_1 article-title: An exact and invariant first order reliability format publication-title: Journal of Engineering Mechanics, ASCE – ident: e_1_2_9_13_1 doi: 10.1007/978-1-4612-1432-8 – ident: e_1_2_9_18_1 doi: 10.1016/S0029-5493(98)00184-8 |
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| Snippet | SUMMARYThe FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM... The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with... SUMMARY The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM... |
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| SubjectTerms | Algorithms Computer simulation Engineering Sciences Exact sciences and technology Failure finite element analysis Finite element method FORM approximation Fracture mechanics (crack, fatigue, damage...) Fundamental areas of phenomenology (including applications) Joining Mathematical analysis Mathematical models Mathematics Mechanics Mechanics of materials model reduction Numerical analysis Numerical analysis. Scientific computation Partial differential equations, initial value problems and time-dependant initial-boundary value problems Physics proper generalized decomposition Reliability analysis Sciences and techniques of general use Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics structural reliability |
| Title | Coupling finite element and reliability analysis through proper generalized decomposition model reduction |
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| Volume | 95 |
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