Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity
Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Ra...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ioakimidis, N. I. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1993 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 1993 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mechanica - Springer-Verlag, 1965, 98(1993), 1-4 vom: März, Seite 99-106 |
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| Übergeordnetes Werk: |
volume:98 ; year:1993 ; number:1-4 ; month:03 ; pages:99-106 |
| Links: |
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| DOI / URN: |
10.1007/BF01174296 |
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| Katalog-ID: |
OLC2030114367 |
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| 520 | |a Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. | ||
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10.1007/BF01174296 doi (DE-627)OLC2030114367 (DE-He213)BF01174296-p DE-627 ger DE-627 rakwb eng 530 VZ Ioakimidis, N. I. verfasserin aut Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity 1993 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1993 Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. Dynamical System Fluid Dynamics Stress Intensity Intensity Factor Stress Intensity Factor Anastasselou, E. G. aut Enthalten in Acta mechanica Springer-Verlag, 1965 98(1993), 1-4 vom: März, Seite 99-106 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:98 year:1993 number:1-4 month:03 pages:99-106 https://doi.org/10.1007/BF01174296 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 98 1993 1-4 03 99-106 |
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10.1007/BF01174296 doi (DE-627)OLC2030114367 (DE-He213)BF01174296-p DE-627 ger DE-627 rakwb eng 530 VZ Ioakimidis, N. I. verfasserin aut Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity 1993 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1993 Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. Dynamical System Fluid Dynamics Stress Intensity Intensity Factor Stress Intensity Factor Anastasselou, E. G. aut Enthalten in Acta mechanica Springer-Verlag, 1965 98(1993), 1-4 vom: März, Seite 99-106 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:98 year:1993 number:1-4 month:03 pages:99-106 https://doi.org/10.1007/BF01174296 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 98 1993 1-4 03 99-106 |
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10.1007/BF01174296 doi (DE-627)OLC2030114367 (DE-He213)BF01174296-p DE-627 ger DE-627 rakwb eng 530 VZ Ioakimidis, N. I. verfasserin aut Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity 1993 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1993 Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. Dynamical System Fluid Dynamics Stress Intensity Intensity Factor Stress Intensity Factor Anastasselou, E. G. aut Enthalten in Acta mechanica Springer-Verlag, 1965 98(1993), 1-4 vom: März, Seite 99-106 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:98 year:1993 number:1-4 month:03 pages:99-106 https://doi.org/10.1007/BF01174296 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 98 1993 1-4 03 99-106 |
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10.1007/BF01174296 doi (DE-627)OLC2030114367 (DE-He213)BF01174296-p DE-627 ger DE-627 rakwb eng 530 VZ Ioakimidis, N. I. verfasserin aut Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity 1993 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1993 Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. Dynamical System Fluid Dynamics Stress Intensity Intensity Factor Stress Intensity Factor Anastasselou, E. G. aut Enthalten in Acta mechanica Springer-Verlag, 1965 98(1993), 1-4 vom: März, Seite 99-106 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:98 year:1993 number:1-4 month:03 pages:99-106 https://doi.org/10.1007/BF01174296 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 98 1993 1-4 03 99-106 |
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10.1007/BF01174296 doi (DE-627)OLC2030114367 (DE-He213)BF01174296-p DE-627 ger DE-627 rakwb eng 530 VZ Ioakimidis, N. I. verfasserin aut Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity 1993 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1993 Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. Dynamical System Fluid Dynamics Stress Intensity Intensity Factor Stress Intensity Factor Anastasselou, E. G. aut Enthalten in Acta mechanica Springer-Verlag, 1965 98(1993), 1-4 vom: März, Seite 99-106 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:98 year:1993 number:1-4 month:03 pages:99-106 https://doi.org/10.1007/BF01174296 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_59 GBV_ILN_63 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2057 GBV_ILN_4046 GBV_ILN_4313 GBV_ILN_4316 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 98 1993 1-4 03 99-106 |
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Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity |
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Ioakimidis, N. I. |
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Acta mechanica |
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Acta mechanica |
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eng |
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500 - Science |
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1993 |
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txt |
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99 |
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Ioakimidis, N. I. Anastasselou, E. G. |
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98 |
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530 VZ |
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Ioakimidis, N. I. |
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10.1007/BF01174296 |
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530 |
| title_sort |
application of the green and the rayleigh-green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity |
| title_auth |
Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity |
| abstract |
Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. © Springer-Verlag 1993 |
| abstractGer |
Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. © Springer-Verlag 1993 |
| abstract_unstemmed |
Summary An elementary but quite general method for the construction of path-independent integrals in plane and three-dimensional elasticity is suggested. This approach consists simply in using the classical Green formula in its reciprocal form for harmonic functions and, further, the more general Rayleigh-Green formula also in its reciprocal form, but for biharmonic functions. A large number of harmonic and biharmonic functions appears in a natural way in the theory of elasticity. Therefore, the construction of path-independent integrals (or, probably better, surface-independent integrals in the three-dimensional case) becomes really a trivial task. An application to the determination of stress intensity factors at crack tips is considered in detail and only the sum of the principal stress components is used in the path-independent integral. Further applications of the method are easily possible. © Springer-Verlag 1993 |
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| title_short |
Application of the Green and the Rayleigh-Green reciprocal identities to path-independent integrals in two- and three-dimensional elasticity |
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https://doi.org/10.1007/BF01174296 |
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Anastasselou, E. G. |
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