Geodesic
Non-standard problems of homogeneous structural elements with wedge shape features in the plane case
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2014), pp. 95-109
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new type of solid mechanics problems – non-standard ones – is distinguished. Their distinctive feature is the redundancy of restrictions on status parameters at at least one point on the body boundary. It is shown that the use of standard methods in solving non-standard problems does not guarantee the fulfillment of all specified conditions. The most important cases of nonstandard restrictions in flat homogeneous structural elements with singularities in the form of wedges are presented. Wedge side loading is studied in the following cases: free from stress, rigidly clamped, sliding without friction along a rigid surface, and surface power loaded. An iterative converging numerical-analytical method for studying problems of this type is proposed. At each step of the iterative process converging to the solution of the non-standard problem, the inverse problem in displacements is solved. An illustrative example shows the essential difference between the standard and iterative solutions of the non-standard problem in a vicinity of the wedge tip.
Keywords: non-standard problems, singular points, plane problem
Mots-clés : stress concentration. 
@article{VTGU_2014_1_a9,
     author = {V. M. Pestrenin and I. V. Pestrenina and L. V. Landik},
     title = {Non-standard problems of homogeneous structural elements with wedge shape features in the plane case},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {95--109},
     year = {2014},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2014_1_a9/}
}
TY  - JOUR
AU  - V. M. Pestrenin
AU  - I. V. Pestrenina
AU  - L. V. Landik
TI  - Non-standard problems of homogeneous structural elements with wedge shape features in the plane case
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2014
SP  - 95
EP  - 109
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VTGU_2014_1_a9/
LA  - ru
ID  - VTGU_2014_1_a9
ER  - 
%0 Journal Article
%A V. M. Pestrenin
%A I. V. Pestrenina
%A L. V. Landik
%T Non-standard problems of homogeneous structural elements with wedge shape features in the plane case
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2014
%P 95-109
%N 1
%U http://geodesic.mathdoc.fr/item/VTGU_2014_1_a9/
%G ru
%F VTGU_2014_1_a9
V. M. Pestrenin; I. V. Pestrenina; L. V. Landik. Non-standard problems of homogeneous structural elements with wedge shape features in the plane case. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2014), pp. 95-109. http://geodesic.mathdoc.fr/item/VTGU_2014_1_a9/

[1] Williams M. L., “Stress singularities resulting from various boundary conditions in angular corners in extension”, J. App. Mech., 19 (1952), 526–528

[2] Uflyand Ya. S., Integral'nye preobrazovaniya v zadachakh teorii uprugosti, Izd-vo AN SSSR, M.–L., 1967, 402 pp. (in Russian) | MR

[3] Bogy D. B., “Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading”, J. Appl. Mechanics, 35 (1968), 460–466 | DOI | Zbl

[4] Bogy D. B., “Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions”, Trans. ASME. Ser. E, 38:2 (1971), 87–96 | DOI

[5] Aksentyan O. K., “Osobennosti napryazhenno-deformirovannogo sostoyaniya plity v okrestnosti rebra”, Prikladnaya matematika i mekhanika, 1967, no. 1, 178–186 (in Russian) | Zbl

[6] Aksentyan O. K., Lushchik O. N., “Ob usloviyakh ogranichennosti napryazheniy u rebra sostavnogo klina”, Izv. AN SSSR. Mekhanika tverdogo tela, 1978, no. 5, 102–108 (in Russian)

[7] Aksentyan O. K., Lushchik O. N., “Napryazhenno-deformirovannoe sostoyanie v okrestnosti vershiny stykovogo soedineniya”, Prikladnaya mekhanika, 18:7 (1982), 66–73 (in Russian)

[8] Zadoyan M. A., “Prochnost' soedineniya sostavnykh plit”, Mekhanika tverdogo tela, 2003, no. 1, 111–122 (in Russian)

[9] Matveenko V. P., “Metod chislennogo analiza singulyarnosti napryazheniy v uglovykh tochkakh trekhmernykh tel”, Izv. RAN MTT, 1995, no. 5, 71–77 (in Russian)

[10] Matveenko V. P., Nakaryakova T. O., Sevodina N. V., Shardakov I. N., “Singulyarnost' napryazheniy v vershine odnorodnykh i sostavnykh konusov pri raznykh granichnykh usloviyakh”, Prikladnaya matematika i mekhanika, 72:3 (2008), 477–484 (in Russian) | MR

[11] Matveenko V. P., Fedorov A. Yu., “Optimizatsiya geometrii sostavnykh uprugikh tel kak osnova sovershenstvovaniya metodik ispytaniy na prochnost' kleevykh soedineniy”, Vychislitel'naya mekhanika sploshnykh sred, 4:4 (2011), 63–70 (in Russian)

[12] Sinclear G. B., “Stress singularities in classical elasticity – I: Removal, interpretation and analysis”, App. Mech. Rev., 57:4 (2004), 251–297 | DOI

[13] Sinclear G. B., “Stress singularities in classical elasticity – II: Asymptotic identification”, App. Mech. Rev., 57:4 (2004), 385–439 | DOI

[14] Chobanyan K. S., Napryazheniya v sostavnykh uprugikh telakh, Izd-vo AN ArmSSR, Erevan, 1987, 338 pp. (in Russian)

[15] Barut A., Guven I., Madenci E., “Analysis of singular stress fields at junctions of multiple dissimilar materials under mechanical and thermal loading”, Int. J. Solid and Structures, 38:50–51 (2001), 9077–9109 | DOI | Zbl

[16] Borzenkov S. M., Matveenko V. P., “Poluanaliticheskie singulyarnye elementy dlya ploskikh i prostranstvennykh zadach teorii uprugosti”, Izv. RAN MTT, 1995, no. 6, 48–61 (in Russian)

[17] Adams R. D., Atkins R. W., Harris J. A., Kinloch A. J., “Stress analysis and failure properties of carbon-fibre-reinforced-plastid steel double-lap joints”, J. Adhesion., 20 (1986), 29–53 | DOI

[18] Pestrenin V. M., Pestrenina I. V., Landik L. V., “Napryazhennoe sostoyanie vblizi osoboy tochki sostavnoy konstruktsii v ploskoy zadache”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2013, no. 4(24), 78–87 (in Russian)

[19] Pestrenin V. M., Pestrenina I. V., Landik L. V., Stepina E. V., “Temperaturnoe nagruzhenie sostavnoy konstruktsii v usloviyakh ploskoy zadachi”, Vestnik Permskogo universiteta. Matematika. Mekhanika. Informatika, 2013, no. 3(22), 66–71 (in Russian)

[20] Pestrenin V. M., Pestrenina I. V., Mekhanika kompozitnykh materialov i elementov konstruktsiy, Perm. un-t, Perm', 2005, 364 pp. (in Russian)