 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A.M. Simonyan and Yu.G. Sanoyan, "Investigation of the Plane Stress State of a Multilayer Structure under Heat Variations," Mech. Solids. 44 (5), 756-761 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
756-761 |
| DOI |
10.3103/S0025654409050124 |
| Title |
Investigation of the Plane Stress State of a Multilayer Structure under Heat Variations |
| Author(s) |
A.M. Simonyan (Institute of Mechanics, National Academy of Sciences of Republic of Armenia, Marshala Baghramian ave., 24B, Erevan, 375019, Republic of Armenia, aregsimonyan@mechins.sci.am)
Yu.G. Sanoyan (Institute of Mechanics, National Academy of Sciences of Republic of Armenia, Marshala Baghramian ave., 24B, Erevan, 375019, Republic of Armenia) |
| Abstract |
Now that composite materials are used in various fields of technology, their resistance to heat variations, which cause additional stresses because of noncoinciding layer thermal expansion coefficients, becomes increasingly topical.
Apparently, the first study in this field was performed in [1], where the stress state in beam-like thermostats was determined. In [2], it was shown that delamination moments arise at the ends of two-layer beams, and the possibility of their influence on the process of delamination of two-layer composites was considered. In [3], in a similar setting, delamination stresses in multilayer structures were considered. In [4-7], the stresses at the edges of two-layer beams were calculated. We note that in all these papers the main assumptions of beam theory were used, which were confirmed experimentally for the analysis of beams.
When studying the stress state near the ends of multilayer structures, the applicability of beam theory is doubtful, because the plane cross-section hypothesis, usually acceptable for beams, is justified only for the main part of the beam but not for areas near its ends, where the delamination process usually begins.
The paper [8] essentially deals with a problem for a rectangle whose short sides are free from external loads and whose long sides are free from normal pressures; some longitudinal displacements imitating the temperature strains from the neighboring rectangles are given on the long sides. In [9, 10], the same problem was solved with the use of different mathematical representations of the Airy function, but the obtained numerical results practically coincide. In the present paper, we consider a system consisting of infinitely many alternating isotropic elastic layers with repeated elastic and thermal characteristics; these layers are represented as rectangles connected along the long sides. |
| Keywords |
multilayer structure, heat variation, plane problem |
| References |
| 1. | S. P. Timoshenko,
"Analysis of Bi-Metal Thermostats,"
J. Opt. Soc. America
11 (9), 233-255 (1925). |
| 2. | T. D. Moore and J. L. Jarvis,
"Peeling in Bimaterial Beams: The Peeling Moment and Its Relation to the Differential Rigidity,"
Trans. ASME Appl. Mech.
71 (2), 290-292 (2004). |
| 3. | T. D. Moore,
"Thermomechanical Peeling in Multilayer Beams and Plates - a Solution from First Principles,"
Int. J. Solids Struct.
42 (1), 271-285 (2005). |
| 4. | E. Suhir,
"Stresses in Bi-Metal Thermostats,"
Trans. ASME Appl. Mech.
53 (3), 657-660 (1986). |
| 5. | E. Suhir,
"Interfacial Stresses in Bi-Metal Thermostats,"
Trans. ASME Appl. Mech.
56 (3), 595-600 (1989). |
| 6. | C. Q. Ru,
"Interfacial Thermal Stresses: Bimaterial Elastic Beams
in Modified Beams Models Revisited,"
Trans. ASME Electronic Packaging
124 (1), 141-146 (2002). |
| 7. | M. S. Hess,
"The End Problem for a Laminated Elastic Strip.
Differential Expansion Stresses,"
Compos. Mater.
3 (4), 630-641 (1969). |
| 8. | A. M. Simonyan and Yu. G. Sanoyan,
"Peculiarities of Temperature Resistance of Layered Composites,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 130-136 (2005)
[Mech. Solids (Engl. Transl.)
40 (6), 95-100 (2005)]. |
| 9. | A. M. Simonyan and Yu. G. Sanoyan,
"Influence of Heat Variations on the Stressed State of Multilayer Structures,"
in Problems of Dynamics of Deformable Media Interaction.
5th International Conference
(Goris, 2006),
pp. 329-333
[in Russian]. |
| 10. | A. M. Simonyan and Yu. G. Sanoyan,
"On the Temperature Problem for a Rectangle Fixed on Opposite Sides,"
in Problems of Mechanics of Deformable Bodies
(Gitutyun, Erevan, 2003),
pp. 324-330
[in Russian]. |
| 11. | K. S. Chobayan,
Stresses in Compound Elastic Bodies
(Izd-vo AN Arm. SSR, Erevan, 1987)
[in Russian]. |
| 12. | G. B. Kolchin,
Several Problems of Thermoelasticity for Rectangular Domains (Application of Special Orthogonal Polynomials to Solving Problems of Thermoelasticity)
(Shtiintsa, Kishinev, 1980)
[in Russian]. |
|
| Received |
24 January 2007 |
| Link to Fulltext |
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