Stress concentration around irregular holes using complex variable method
Engineering materials are vulnerable targets for damage by chemical agents. This results in various types of irregular cavities which may subsequently change their shape under the combined action of loads and chemical attack. Such shape evolutions are subject to certain constraints. This paper explo...
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| Veröffentlicht in: | Sadhana (Bangalore) Jg. 23; H. 4; S. 393 - 412 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Springer Nature B.V
01.08.1998
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| ISSN: | 0256-2499, 0973-7677 |
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| Abstract | Engineering materials are vulnerable targets for damage by chemical agents. This results in various types of irregular cavities which may subsequently change their shape under the combined action of loads and chemical attack. Such shape evolutions are subject to certain constraints. This paper explores the evolution in stresses as a result of an evolution in the shape of an isolated irregular hole in an infinite elastic plate subjected to remote uniform stress. The constraint employed here is a fixed area for the irregular hole with variable perimeter as a result of the evolution. Increase in perimeter implies decrease in strain energy on account of increased surface energy. Such phenomena could also occur in polymeric sheets on account of viscoelasticity even in the absence of chemical agents. This paper presents the evolution in boundary stresses as the cavity evolves to take different shapes. Complex variable methods are developed to tackle three cases of remote loading: (a) hydrostatic tension, (b) uniaxial tension, and (c) pure shear state. Of the above three cases, the first case of hydrostatic loading leads to a remarkably simple result for the boundary stress as shown in this paper. The last case is obtained by superposing a uniaxial tension and uniaxial compression along orthogonal directions. |
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| AbstractList | Engineering materials are vulnerable targets for damage by chemical agents. This results in various types of irregular cavities which may subsequently change their shape under the combined action of loads and chemical attack. Such shape evolutions are subject to certain constraints. This paper explores the evolution in stresses as a result of an evolution in the shape of an isolated irregular hole in an infinite elastic plate subjected to remote uniform stress. The constraint employed here is a fixed area for the irregular hole with variable perimeter as a result of the evolution. Increase in perimeter implies decrease in strain energy on account of increased surface energy. Such phenomena could also occur in polymeric sheets on account of viscoelasticity even in the absence of chemical agents. This paper presents the evolution in boundary stresses as the cavity evolves to take different shapes. Complex variable methods are developed to tackle three cases of remote loading: (a) hydrostatic tension, (b) uniaxial tension, and (c) pure shear state. Of the above three cases, the first case of hydrostatic loading leads to a remarkably simple result for the boundary stress as shown in this paper. The last case is obtained by superposing a uniaxial tension and uniaxial compression along orthogonal directions. |
| Author | Simha, K R Y Mohapatra, S S |
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| References | G F Carrier (BF02745750_CR1) 1966 A H England (BF02745750_CR3) 1971 D Vandembroucq (BF02745750_CR8) 1997; E-55 D Vandembroucq (BF02745750_CR9) 1997; E-55 D Givoli (BF02745750_CR4) 1992; 59 G S Savin (BF02745750_CR6) 1962 R V Churchill (BF02745750_CR2) 1960 H Kober (BF02745750_CR5) 1952 S Timoshenko (BF02745750_CR7) 1970 |
| References_xml | – volume-title: Stress concentration around holes year: 1962 ident: BF02745750_CR6 – volume: E-55 start-page: 6186 year: 1997 ident: BF02745750_CR9 publication-title: Phys. Rev. – volume: E-55 start-page: 6171 year: 1997 ident: BF02745750_CR8 publication-title: Phys. Rev. – volume-title: Introduction to complex variables year: 1960 ident: BF02745750_CR2 – volume-title: Theory of elasticity year: 1970 ident: BF02745750_CR7 – volume-title: Functions of a complex variable year: 1966 ident: BF02745750_CR1 – volume-title: Dictionary of conformal representations year: 1952 ident: BF02745750_CR5 – volume-title: Complex variable methods in elasticity year: 1971 ident: BF02745750_CR3 – volume: 59 start-page: S65 year: 1992 ident: BF02745750_CR4 publication-title: Trans. ASME: J. Appl. Mech. doi: 10.1115/1.2899509 |
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| SubjectTerms | Chemical damage Complex variables Elastic plates Evolution Holes Strain energy Stress concentration Surface energy Viscoelasticity |
| Title | Stress concentration around irregular holes using complex variable method |
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