Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects
By the method of Hankel integral transformation, discontinuous solutions of equations of the axisymmetric elasticity theory are constructed for a piecewise homogeneous uniform layered space obtained by alternately joining two heterogeneous layers of equal thickness and whose junction contains a peri...
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Published in | Mechanics of composite materials Vol. 55; no. 1; pp. 13 - 28 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
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New York
Springer US
01.03.2019
Springer Springer Nature B.V |
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Abstract | By the method of Hankel integral transformation, discontinuous solutions of equations of the axisymmetric elasticity theory are constructed for a piecewise homogeneous uniform layered space obtained by alternately joining two heterogeneous layers of equal thickness and whose junction contains a periodic system of parallel circular disk-shaped defects. On the basis of the solutions found, as examples, the governing systems of integral equations with Weber–Sonin kernels are presented for two cases: with defects in the form of absolutely rigid disk-shape inclusions and circular cracks. Using rotation operators, the governing systems of equations, in both cases, are reduced to a singular integral equation of the second kind, which is solved by the method of mechanical quadratures. Simple formulas for determining the rigid-body displacement of inclusions and crack opening are obtained. |
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AbstractList | By the method of Hankel integral transformation, discontinuous solutions of equations of the axisymmetric elasticity theory are constructed for a piecewise homogeneous uniform layered space obtained by alternately joining two heterogeneous layers of equal thickness and whose junction contains a periodic system of parallel circular disk-shaped defects. On the basis of the solutions found, as examples, the governing systems of integral equations with Weber–Sonin kernels are presented for two cases: with defects in the form of absolutely rigid disk-shape inclusions and circular cracks. Using rotation operators, the governing systems of equations, in both cases, are reduced to a singular integral equation of the second kind, which is solved by the method of mechanical quadratures. Simple formulas for determining the rigid-body displacement of inclusions and crack opening are obtained. |
Audience | Academic |
Author | Hakobyan, L. V. Hakobyan, V. N. Dashtoyan, L. L. |
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Keywords | periodical mixed boundary-value problems disk-shape crack circular rigid inclusion |
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References | CR4 CR6 CR7 Amirjanyan, Sahakyan (CR15) 2017; 57 Erdogan (CR1) 1964; 32 CR12 Prudnikov, Brychkov, Marychev (CR17) 1981 CR11 CR10 Willis (CR3) 1972; 25 Mkhitaryan, Shekyan, Verlinski, Aidun, Marzocca (CR9) 2012; 35 Gakhov (CR14) 1977 Kassir, Bregman (CR18) 1972; 39 Mossakovskii, Rybka (CR2) 1964; 28 Korenev, Glaeske, Moiseev, Saigo (CR13) 2002 Gradshtein, Ryzhik (CR16) 1962 Hakobyan, Dashtoyan (CR5) 2006; 59 Hakobyan (CR8) 2014 FD Gakhov (9788_CR14) 1977 VI Mossakovskii (9788_CR2) 1964; 28 VN Hakobyan (9788_CR8) 2014 F Erdogan (9788_CR1) 1964; 32 SM Mkhitaryan (9788_CR9) 2012; 35 AA Amirjanyan (9788_CR15) 2017; 57 IS Gradshtein (9788_CR16) 1962 9788_CR10 MK Kassir (9788_CR18) 1972; 39 JR Willis (9788_CR3) 1972; 25 9788_CR6 9788_CR7 9788_CR4 B Korenev (9788_CR13) 2002 9788_CR11 9788_CR12 VN Hakobyan (9788_CR5) 2006; 59 AP Prudnikov (9788_CR17) 1981 |
References_xml | – volume: 57 start-page: 1285 issue: 8 year: 2017 end-page: 1293 ident: CR15 article-title: Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side publication-title: Comput. Math. and Math. Phys. doi: 10.1134/S0965542517080036 contributor: fullname: Sahakyan – year: 1977 ident: CR14 publication-title: Boundary-Value Problems [in Russian] contributor: fullname: Gakhov – year: 1962 ident: CR16 publication-title: Tables of Integrals, Sums, Series, and Products [in Russian] contributor: fullname: Ryzhik – ident: CR4 – year: 2014 ident: CR8 publication-title: Mixed Boundary-Value Problems on the Interaction of Continuous Deformable Bodies with Stress Concentrators of Various Types [in Russian] contributor: fullname: Hakobyan – volume: 28 start-page: 1061 issue: 6 year: 1964 end-page: 1069 ident: CR2 article-title: Generalization of the Griffith-Sneddon criterion for the case of a nonhomogeneous body publication-title: J. Appl. Math. and Mech. doi: 10.1016/0021-8928(64)90039-5 contributor: fullname: Rybka – ident: CR12 – ident: CR10 – ident: CR11 – year: 2002 ident: CR13 publication-title: Bessel Functions and Their Applications contributor: fullname: Saigo – year: 1981 ident: CR17 publication-title: Integrals and Series [in Russian] contributor: fullname: Marychev – ident: CR6 – volume: 59 start-page: 3 issue: 1 year: 2006 end-page: 10 ident: CR5 article-title: An axisymmetric problem for a compound space weakened by a semi-infinite ring-shaped crack publication-title: Izv. NAN RA, Mechanics contributor: fullname: Dashtoyan – ident: CR7 – volume: 25 start-page: 367 issue: 3 year: 1972 end-page: 385 ident: CR3 article-title: The penny-shaped crack on an interface publication-title: Quart J. Mech. and Appl. Math. doi: 10.1093/qjmam/25.3.367 contributor: fullname: Willis – volume: 35 start-page: 424 issue: 5 year: 2012 end-page: 447 ident: CR9 article-title: Stationary theory of heat-conductivity for an axi-symmetrical piecehomogeneous space with circular inclusion publication-title: J. Thermal Stresses doi: 10.1080/01495739.2012.663691 contributor: fullname: Marzocca – volume: 32 start-page: 829 issue: 4 year: 1964 end-page: 836 ident: CR1 article-title: Stress distribution in bonded dissimilar materials containing circular or ring-shaped cavities publication-title: Trans ASME. Ser. E. J. Appl. Mech. doi: 10.1115/1.3627323 contributor: fullname: Erdogan – volume: 39 start-page: 308 issue: 1 year: 1972 end-page: 310 ident: CR18 article-title: The stress-intensity factor for a penny-shaped crack between two dissimilar materials publication-title: Trans ASME. Ser. E. J. Appl. Mech. doi: 10.1115/1.3422648 contributor: fullname: Bregman – volume-title: Tables of Integrals, Sums, Series, and Products [in Russian] year: 1962 ident: 9788_CR16 contributor: fullname: IS Gradshtein – ident: 9788_CR12 – ident: 9788_CR10 – ident: 9788_CR11 – volume-title: Mixed Boundary-Value Problems on the Interaction of Continuous Deformable Bodies with Stress Concentrators of Various Types [in Russian] year: 2014 ident: 9788_CR8 contributor: fullname: VN Hakobyan – volume: 59 start-page: 3 issue: 1 year: 2006 ident: 9788_CR5 publication-title: Izv. NAN RA, Mechanics contributor: fullname: VN Hakobyan – volume: 25 start-page: 367 issue: 3 year: 1972 ident: 9788_CR3 publication-title: Quart J. Mech. and Appl. Math. doi: 10.1093/qjmam/25.3.367 contributor: fullname: JR Willis – volume-title: Integrals and Series [in Russian] year: 1981 ident: 9788_CR17 contributor: fullname: AP Prudnikov – volume: 39 start-page: 308 issue: 1 year: 1972 ident: 9788_CR18 publication-title: Trans ASME. Ser. E. J. Appl. Mech. doi: 10.1115/1.3422648 contributor: fullname: MK Kassir – ident: 9788_CR4 – volume-title: Bessel Functions and Their Applications year: 2002 ident: 9788_CR13 doi: 10.1201/b12551 contributor: fullname: B Korenev – volume: 57 start-page: 1285 issue: 8 year: 2017 ident: 9788_CR15 publication-title: Comput. Math. and Math. Phys. doi: 10.1134/S0965542517080036 contributor: fullname: AA Amirjanyan – volume: 32 start-page: 829 issue: 4 year: 1964 ident: 9788_CR1 publication-title: Trans ASME. Ser. E. J. Appl. Mech. doi: 10.1115/1.3627323 contributor: fullname: F Erdogan – volume: 28 start-page: 1061 issue: 6 year: 1964 ident: 9788_CR2 publication-title: J. Appl. Math. and Mech. doi: 10.1016/0021-8928(64)90039-5 contributor: fullname: VI Mossakovskii – volume: 35 start-page: 424 issue: 5 year: 2012 ident: 9788_CR9 publication-title: J. Thermal Stresses doi: 10.1080/01495739.2012.663691 contributor: fullname: SM Mkhitaryan – volume-title: Boundary-Value Problems [in Russian] year: 1977 ident: 9788_CR14 contributor: fullname: FD Gakhov – ident: 9788_CR6 – ident: 9788_CR7 |
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SubjectTerms | Ceramics Characterization and Evaluation of Materials Chemistry and Materials Science Classical Mechanics Composite materials Composites Cracks Defects Elasticity Glass Inclusions Integral transforms Materials Science Mathematical analysis Natural Materials Operators (mathematics) Periodicals Quadratures Singular integral equations Solid Mechanics Thickness |
Title | Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects |
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