Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks
The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdoma...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Torres, Diego Amadeu F. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015transfer abstract |
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| Schlagwörter: |
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| Umfang: |
37 |
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| Übergeordnetes Werk: |
Enthalten in: Does enhanced hydration have impact on autogenous deformation of internally cued mortar? - Zou, Dinghua ELSEVIER, 2019, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:283 ; year:2015 ; day:1 ; month:01 ; pages:243-279 ; extent:37 |
| Links: |
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| DOI / URN: |
10.1016/j.cma.2014.08.030 |
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ELV012692182 |
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| 245 | 1 | 0 | |a Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks |
| 264 | 1 | |c 2015transfer abstract | |
| 300 | |a 37 | ||
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| 520 | |a The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... | ||
| 520 | |a The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... | ||
| 650 | 7 | |a Crack modeling |2 Elsevier | |
| 650 | 7 | |a Mesh-based smooth partitions of unity |2 Elsevier | |
| 650 | 7 | |a Enrichment patterns |2 Elsevier | |
| 650 | 7 | |a Arbitrarily smooth GFEM/XFEM |2 Elsevier | |
| 650 | 7 | |a Singular stress fields |2 Elsevier | |
| 650 | 7 | |a Convergence analysis |2 Elsevier | |
| 700 | 1 | |a de Barcellos, Clovis S. |4 oth | |
| 700 | 1 | |a Mendonça, Paulo de Tarso R. |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier Science |a Zou, Dinghua ELSEVIER |t Does enhanced hydration have impact on autogenous deformation of internally cued mortar? |d 2019 |g Amsterdam [u.a.] |w (DE-627)ELV002113945 |
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10.1016/j.cma.2014.08.030 doi GBV00000000000221A.pica (DE-627)ELV012692182 (ELSEVIER)S0045-7825(14)00309-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 690 VZ 56.45 bkl Torres, Diego Amadeu F. verfasserin aut Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks 2015transfer abstract 37 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... Crack modeling Elsevier Mesh-based smooth partitions of unity Elsevier Enrichment patterns Elsevier Arbitrarily smooth GFEM/XFEM Elsevier Singular stress fields Elsevier Convergence analysis Elsevier de Barcellos, Clovis S. oth Mendonça, Paulo de Tarso R. oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:283 year:2015 day:1 month:01 pages:243-279 extent:37 https://doi.org/10.1016/j.cma.2014.08.030 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 283 2015 1 0101 243-279 37 045F 004 |
| spelling |
10.1016/j.cma.2014.08.030 doi GBV00000000000221A.pica (DE-627)ELV012692182 (ELSEVIER)S0045-7825(14)00309-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 690 VZ 56.45 bkl Torres, Diego Amadeu F. verfasserin aut Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks 2015transfer abstract 37 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... Crack modeling Elsevier Mesh-based smooth partitions of unity Elsevier Enrichment patterns Elsevier Arbitrarily smooth GFEM/XFEM Elsevier Singular stress fields Elsevier Convergence analysis Elsevier de Barcellos, Clovis S. oth Mendonça, Paulo de Tarso R. oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:283 year:2015 day:1 month:01 pages:243-279 extent:37 https://doi.org/10.1016/j.cma.2014.08.030 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 283 2015 1 0101 243-279 37 045F 004 |
| allfields_unstemmed |
10.1016/j.cma.2014.08.030 doi GBV00000000000221A.pica (DE-627)ELV012692182 (ELSEVIER)S0045-7825(14)00309-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 690 VZ 56.45 bkl Torres, Diego Amadeu F. verfasserin aut Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks 2015transfer abstract 37 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... Crack modeling Elsevier Mesh-based smooth partitions of unity Elsevier Enrichment patterns Elsevier Arbitrarily smooth GFEM/XFEM Elsevier Singular stress fields Elsevier Convergence analysis Elsevier de Barcellos, Clovis S. oth Mendonça, Paulo de Tarso R. oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:283 year:2015 day:1 month:01 pages:243-279 extent:37 https://doi.org/10.1016/j.cma.2014.08.030 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 283 2015 1 0101 243-279 37 045F 004 |
| allfieldsGer |
10.1016/j.cma.2014.08.030 doi GBV00000000000221A.pica (DE-627)ELV012692182 (ELSEVIER)S0045-7825(14)00309-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 690 VZ 56.45 bkl Torres, Diego Amadeu F. verfasserin aut Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks 2015transfer abstract 37 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... Crack modeling Elsevier Mesh-based smooth partitions of unity Elsevier Enrichment patterns Elsevier Arbitrarily smooth GFEM/XFEM Elsevier Singular stress fields Elsevier Convergence analysis Elsevier de Barcellos, Clovis S. oth Mendonça, Paulo de Tarso R. oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:283 year:2015 day:1 month:01 pages:243-279 extent:37 https://doi.org/10.1016/j.cma.2014.08.030 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 283 2015 1 0101 243-279 37 045F 004 |
| allfieldsSound |
10.1016/j.cma.2014.08.030 doi GBV00000000000221A.pica (DE-627)ELV012692182 (ELSEVIER)S0045-7825(14)00309-0 DE-627 ger DE-627 rakwb eng 004 004 DE-600 690 VZ 56.45 bkl Torres, Diego Amadeu F. verfasserin aut Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks 2015transfer abstract 37 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... Crack modeling Elsevier Mesh-based smooth partitions of unity Elsevier Enrichment patterns Elsevier Arbitrarily smooth GFEM/XFEM Elsevier Singular stress fields Elsevier Convergence analysis Elsevier de Barcellos, Clovis S. oth Mendonça, Paulo de Tarso R. oth Enthalten in Elsevier Science Zou, Dinghua ELSEVIER Does enhanced hydration have impact on autogenous deformation of internally cued mortar? 2019 Amsterdam [u.a.] (DE-627)ELV002113945 volume:283 year:2015 day:1 month:01 pages:243-279 extent:37 https://doi.org/10.1016/j.cma.2014.08.030 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 56.45 Baustoffkunde VZ AR 283 2015 1 0101 243-279 37 045F 004 |
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effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for gfem/xfem stress approximations around brittle cracks |
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Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks |
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The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... |
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The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... |
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The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular... |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV012692182</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625111110.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180602s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.cma.2014.08.030</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBV00000000000221A.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV012692182</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0045-7825(14)00309-0</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">004</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">690</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">56.45</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Torres, Diego Amadeu F.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">37</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular...</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called C k -GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C 0 -continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of C k -GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L 2 -norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C 0 counterparts built using conventional C 0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular...</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Crack modeling</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mesh-based smooth partitions of unity</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Enrichment patterns</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Arbitrarily smooth GFEM/XFEM</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Singular stress fields</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Convergence analysis</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">de Barcellos, Clovis S.</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mendonça, Paulo de Tarso R.</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier Science</subfield><subfield code="a">Zou, Dinghua ELSEVIER</subfield><subfield code="t">Does enhanced hydration have impact on autogenous deformation of internally cued mortar?</subfield><subfield code="d">2019</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV002113945</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:283</subfield><subfield code="g">year:2015</subfield><subfield code="g">day:1</subfield><subfield code="g">month:01</subfield><subfield code="g">pages:243-279</subfield><subfield code="g">extent:37</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.cma.2014.08.030</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">56.45</subfield><subfield code="j">Baustoffkunde</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">283</subfield><subfield code="j">2015</subfield><subfield code="b">1</subfield><subfield code="c">0101</subfield><subfield code="h">243-279</subfield><subfield code="g">37</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">004</subfield></datafield></record></collection>
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