Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Mechanics of Composite Materials
Published in: Mechanics of Composite Materials 1/2019

01-04-2019

Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects

Authors: V. N. Hakobyan, L. V. Hakobyan, L. L. Dashtoyan

Published in: Mechanics of Composite Materials | Issue 1/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.
previous article Asymptotic Solution of the First 3D Dynamic Elasticity Theory Problem on Forced Vibrations of a Three-Layer Plate with an Asymmetric Structure
next article Numerical Modeling of the Casting Process and Impact Loading of a Steel-Fiber-Reinforced High-Performance Self-Compacting Concrete

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
F. Erdogan, “Stress distribution in bonded dissimilar materials containing circular or ring-shaped cavities,” Trans ASME. Ser. E. J. Appl. Mech., 32, No. 4, 829-836 (1964).CrossRef
2.
V. I. Mossakovskii and M. T. Rybka, “Generalization of the Griffith-Sneddon criterion for the case of a nonhomogeneous body,” J. Appl. Math. and Mech., 28, No. 6, 1061-1069 (1964).CrossRef
3.
J. R. Willis, “The penny-shaped crack on an interface,” Quart J. Mech. and Appl. Math., 25, No. 3, 367-385 (1972).CrossRef
4.
G. Ya. Popov, “About concentration of elastic stresses near thin delaminated inclusion,” Modern Problems of Mechanics and Aviation, 156-162 (1980).
5.
V. N. Hakobyan and L. L. Dashtoyan, “An axisymmetric problem for a compound space weakened by a semi-infinite ring-shaped crack,” Izv. NAN RA, Mechanics, 59, No. 1, 3-10 (2006).
6.
V. N. Hakobyan, “Stresses near an absolutely rigid penny-shaped inclusion in a piecewise homogeneous space,” Proc. of Int. Conf. “Topical Problems of the Mechanics of Continuous Media,” devoted to the 95th anniversary of birth of N. Kh. Arutyunyan, Yerevan, 45-51 (2007).
7.
V. N. Hakobyan, S. E. Mirzoyan, and L. L. Dashtoyan, “Axisymmetric mixed problem for a compound space with a penny-shaped crack,” Bulletin of MGTU named by N. E. Bauman. Series Natural Sci., No. 3, 31-46 (2015).
8.
V. N. Hakobyan, Mixed Boundary-Value Problems on the Interaction of Continuous Deformable Bodies with Stress Concentrators of Various Types [in Russian], Izd. Gitutyun NAN RA, Yerevan (2014).
9.
S. M. Mkhitaryan, L. A. Shekyan, S. V. Verlinski, D. Aidun, and P. Marzocca, “Stationary theory of heat-conductivity for an axi-symmetrical piecehomogeneous space with circular inclusion,” J. Thermal Stresses, 35, No. 5, 424-447 (2012).CrossRef
10.
G. Ya. Popov, Selected Works [in Russian], Vol. 1, Izd. Tipogr. “VBV” (2007).
11.
G. Ya. Popov, Selected Works [in Russian], Vol. 2, Izd. “VBV” (2007).
12.
V. N. Hakobyan, “Axisymmetric stress state of piecewise-homogeneous layered space with parallel penny-shaped cracks,” Proc. of XVIII Int. Conf. “Modern Problems of Mechanics of Continuous Media,” Rostov-on-Don, Vol. 1, 35-39 (2016).
13.
B. Korenev, H. J. Glaeske, E. Moiseev, and M. Saigo, Bessel Functions and Their Applications, CRC Press, London, (2002).
14.
F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).
15.
A. A. Amirjanyan and A. V. Sahakyan, “Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side,” Comput. Math. and Math. Phys., 57, No. 8, 1285-1293 (2017).CrossRef
16.
I. S. Gradshtein, and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow (1962).
17.
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marychev, Integrals and Series [in Russian], Nauka, Moscow (1981).
18.
M. K. Kassir and A. M. Bregman, “The stress-intensity factor for a penny-shaped crack between two dissimilar materials,” Trans ASME. Ser. E. J. Appl. Mech., 39, No. 1, 308-310 (1972).CrossRef
Metadata
Title
Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects
Authors
V. N. Hakobyan
L. V. Hakobyan
L. L. Dashtoyan
Publication date
01-04-2019
Publisher
Springer US
Published in
Mechanics of Composite Materials / Issue 1/2019
Print ISSN: 0191-5665
Electronic ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-019-09788-y

Other articles of this Issue 1/2019

Mechanics of Composite Materials 1/2019 Go to the issue

OriginalPaper

Structure and Mechanical Properties of a Dispersedly Filled Transparent Polycarbonate

OriginalPaper

Crashworthiness Experiment and Simulation Analysis of Composite Thin-Walled Circular Tubes Under Axial Crushing

OriginalPaper

Predicting the Elastic Properties of 3D N-Directional Braided Composites Via a Theoretical Method

OriginalPaper

Review of Basalt-Fiber-Reinforced Cement-based Composites in China: Their Dynamic Mechanical Properties and Durability

Announcement

Notes for Contributors

OriginalPaper

Experimental Verification of the Theory of Structural-Mechanical Behavior of a Filled 3D Cross-Linked Elastomer

Premium Partners

    Image Credits