Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics

Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambigu...
Ausführliche Beschreibung

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Autor*in:	Muhanna, Rafi L. [verfasserIn] Zhang, Hao [verfasserIn] Mullen, Robert L. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2006

Schlagwörter:	Interval Variable Interval Analysis Interval Arithmetic Lagrange Multiplier Method Interval Parameter

Übergeordnetes Werk:	Enthalten in: Reliable computing - [Lafayette, Louisiana] : [University of Louisiana at Lafayette], 1995, 13(2006), 2 vom: 20. Dez., Seite 173-194
Übergeordnetes Werk:	volume:13 ; year:2006 ; number:2 ; day:20 ; month:12 ; pages:173-194

Links:	Volltext

DOI / URN:	10.1007/s11155-006-9024-3

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allfields	10.1007/s11155-006-9024-3 doi (DE-627)SPR017161304 (SPR)s11155-006-9024-3-e DE-627 ger DE-627 rakwb eng 510 004 ASE 31.73 bkl Muhanna, Rafi L. verfasserin aut Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated. Interval Variable (dpeaa)DE-He213 Interval Analysis (dpeaa)DE-He213 Interval Arithmetic (dpeaa)DE-He213 Lagrange Multiplier Method (dpeaa)DE-He213 Interval Parameter (dpeaa)DE-He213 Zhang, Hao verfasserin aut Mullen, Robert L. verfasserin aut Enthalten in Reliable computing [Lafayette, Louisiana] : [University of Louisiana at Lafayette], 1995 13(2006), 2 vom: 20. Dez., Seite 173-194 (DE-627)320436284 (DE-600)2004383-1 1573-1340 nnns volume:13 year:2006 number:2 day:20 month:12 pages:173-194 https://dx.doi.org/10.1007/s11155-006-9024-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_100 GBV_ILN_101 GBV_ILN_110 GBV_ILN_120 GBV_ILN_161 GBV_ILN_285 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2048 GBV_ILN_2190 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 31.73 ASE AR 13 2006 2 20 12 173-194
spelling	10.1007/s11155-006-9024-3 doi (DE-627)SPR017161304 (SPR)s11155-006-9024-3-e DE-627 ger DE-627 rakwb eng 510 004 ASE 31.73 bkl Muhanna, Rafi L. verfasserin aut Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated. Interval Variable (dpeaa)DE-He213 Interval Analysis (dpeaa)DE-He213 Interval Arithmetic (dpeaa)DE-He213 Lagrange Multiplier Method (dpeaa)DE-He213 Interval Parameter (dpeaa)DE-He213 Zhang, Hao verfasserin aut Mullen, Robert L. verfasserin aut Enthalten in Reliable computing [Lafayette, Louisiana] : [University of Louisiana at Lafayette], 1995 13(2006), 2 vom: 20. Dez., Seite 173-194 (DE-627)320436284 (DE-600)2004383-1 1573-1340 nnns volume:13 year:2006 number:2 day:20 month:12 pages:173-194 https://dx.doi.org/10.1007/s11155-006-9024-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_100 GBV_ILN_101 GBV_ILN_110 GBV_ILN_120 GBV_ILN_161 GBV_ILN_285 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2048 GBV_ILN_2190 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 31.73 ASE AR 13 2006 2 20 12 173-194
allfields_unstemmed	10.1007/s11155-006-9024-3 doi (DE-627)SPR017161304 (SPR)s11155-006-9024-3-e DE-627 ger DE-627 rakwb eng 510 004 ASE 31.73 bkl Muhanna, Rafi L. verfasserin aut Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated. Interval Variable (dpeaa)DE-He213 Interval Analysis (dpeaa)DE-He213 Interval Arithmetic (dpeaa)DE-He213 Lagrange Multiplier Method (dpeaa)DE-He213 Interval Parameter (dpeaa)DE-He213 Zhang, Hao verfasserin aut Mullen, Robert L. verfasserin aut Enthalten in Reliable computing [Lafayette, Louisiana] : [University of Louisiana at Lafayette], 1995 13(2006), 2 vom: 20. Dez., Seite 173-194 (DE-627)320436284 (DE-600)2004383-1 1573-1340 nnns volume:13 year:2006 number:2 day:20 month:12 pages:173-194 https://dx.doi.org/10.1007/s11155-006-9024-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_100 GBV_ILN_101 GBV_ILN_110 GBV_ILN_120 GBV_ILN_161 GBV_ILN_285 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2048 GBV_ILN_2190 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 31.73 ASE AR 13 2006 2 20 12 173-194
allfieldsGer	10.1007/s11155-006-9024-3 doi (DE-627)SPR017161304 (SPR)s11155-006-9024-3-e DE-627 ger DE-627 rakwb eng 510 004 ASE 31.73 bkl Muhanna, Rafi L. verfasserin aut Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated. Interval Variable (dpeaa)DE-He213 Interval Analysis (dpeaa)DE-He213 Interval Arithmetic (dpeaa)DE-He213 Lagrange Multiplier Method (dpeaa)DE-He213 Interval Parameter (dpeaa)DE-He213 Zhang, Hao verfasserin aut Mullen, Robert L. verfasserin aut Enthalten in Reliable computing [Lafayette, Louisiana] : [University of Louisiana at Lafayette], 1995 13(2006), 2 vom: 20. Dez., Seite 173-194 (DE-627)320436284 (DE-600)2004383-1 1573-1340 nnns volume:13 year:2006 number:2 day:20 month:12 pages:173-194 https://dx.doi.org/10.1007/s11155-006-9024-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_100 GBV_ILN_101 GBV_ILN_110 GBV_ILN_120 GBV_ILN_161 GBV_ILN_285 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2048 GBV_ILN_2190 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 31.73 ASE AR 13 2006 2 20 12 173-194
allfieldsSound	10.1007/s11155-006-9024-3 doi (DE-627)SPR017161304 (SPR)s11155-006-9024-3-e DE-627 ger DE-627 rakwb eng 510 004 ASE 31.73 bkl Muhanna, Rafi L. verfasserin aut Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated. Interval Variable (dpeaa)DE-He213 Interval Analysis (dpeaa)DE-He213 Interval Arithmetic (dpeaa)DE-He213 Lagrange Multiplier Method (dpeaa)DE-He213 Interval Parameter (dpeaa)DE-He213 Zhang, Hao verfasserin aut Mullen, Robert L. verfasserin aut Enthalten in Reliable computing [Lafayette, Louisiana] : [University of Louisiana at Lafayette], 1995 13(2006), 2 vom: 20. Dez., Seite 173-194 (DE-627)320436284 (DE-600)2004383-1 1573-1340 nnns volume:13 year:2006 number:2 day:20 month:12 pages:173-194 https://dx.doi.org/10.1007/s11155-006-9024-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_63 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_100 GBV_ILN_101 GBV_ILN_110 GBV_ILN_120 GBV_ILN_161 GBV_ILN_285 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2048 GBV_ILN_2190 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4313 GBV_ILN_4328 GBV_ILN_4333 31.73 ASE AR 13 2006 2 20 12 173-194
language	English
source	Enthalten in Reliable computing 13(2006), 2 vom: 20. Dez., Seite 173-194 volume:13 year:2006 number:2 day:20 month:12 pages:173-194
sourceStr	Enthalten in Reliable computing 13(2006), 2 vom: 20. Dez., Seite 173-194 volume:13 year:2006 number:2 day:20 month:12 pages:173-194
format_phy_str_mv	Article
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topic_facet	Interval Variable Interval Analysis Interval Arithmetic Lagrange Multiplier Method Interval Parameter
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authorswithroles_txt_mv	Muhanna, Rafi L. @@aut@@ Zhang, Hao @@aut@@ Mullen, Robert L. @@aut@@
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author	Muhanna, Rafi L.
spellingShingle	Muhanna, Rafi L. ddc 510 bkl 31.73 misc Interval Variable misc Interval Analysis misc Interval Arithmetic misc Lagrange Multiplier Method misc Interval Parameter Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics
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topic_title	510 004 ASE 31.73 bkl Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics Interval Variable (dpeaa)DE-He213 Interval Analysis (dpeaa)DE-He213 Interval Arithmetic (dpeaa)DE-He213 Lagrange Multiplier Method (dpeaa)DE-He213 Interval Parameter (dpeaa)DE-He213
topic	ddc 510 bkl 31.73 misc Interval Variable misc Interval Analysis misc Interval Arithmetic misc Lagrange Multiplier Method misc Interval Parameter
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title	Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics
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title_full	Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics
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title_sort	interval finite elements as a basis for generalized models of uncertainty in engineering mechanics
title_auth	Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics
abstract	Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated.
abstractGer	Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated.
abstract_unstemmed	Abstract Latest scientific and engineering advances have started to recognize the need for defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [12], [47], [50]. Many interval-based uncertainty models have been developed to treat such situations. This paper presents an interval approach for the treatment of parameter uncertainty for linear static structural mechanics problems. Uncertain parameters are introduced in the form of unknown but bounded quantities (intervals). Interval analysis is applied to the Finite Element Method (FEM) to analyze the system response due to uncertain stiffness and loading. To avoid overestimation, the formulation is based on an element-by-element (EBE) technique. Element matrices are formulated, based on the physics of materials, and the Lagrange multiplier method is applied to impose the necessary constraints for compatibility and equilibrium. Earlier EBE formulation provided sharp bounds only on displacements [32]. Based on the developed formulation, the bounds on the system’s displacements and element forces are obtained simultaneously and have the same level of accuracy. Very sharp enclosures for the exact system responses are obtained. A number of numerical examples are introduced, and scalability is illustrated.
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title_short	Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics
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