Geodesic
Evolution of the wave pattern for piecewise linear uniaxial tension and compression of a heteromodulus elastic bar
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 54-70.

Voir la notice de l'article provenant de la source Math-Net.Ru

The process of changing the wave pattern in the problem of non-stationary deformation of a heteromodulus elastic bar under uniaxial piecewise linear tension and following compression is described as a connected sequence of local solutions on successive time intervals. All possible variants and results of collisions of primary and secondary strong discontinuities are indicated for a given piecewise linear function of boundary displacements. An efficient algorithm for solving one-dimensional boundary value problems of the dynamics of deformation of a heteromodular elastic medium under a piecewise linear boundary condition is proposed. The algorithm is based on finding a path in a local decision tree.
Keywords: heteromodular elasticity, piecewise-linear boundary condition, collision of strong discontinuities
Mots-clés : tension and compression of bar, exact solution on graph. . 
@article{SJIM_2022_25_4_a4,
     author = {O. V. Dudko and A. A. Lapteva and V. E. Ragozina},
     title = {Evolution of the wave pattern for piecewise linear uniaxial tension and compression of a heteromodulus elastic bar},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {54--70},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a4/}
}
TY  - JOUR
AU  - O. V. Dudko
AU  - A. A. Lapteva
AU  - V. E. Ragozina
TI  - Evolution of the wave pattern for piecewise linear uniaxial tension and compression of a heteromodulus elastic bar
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2022
SP  - 54
EP  - 70
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a4/
LA  - ru
ID  - SJIM_2022_25_4_a4
ER  - 
%0 Journal Article
%A O. V. Dudko
%A A. A. Lapteva
%A V. E. Ragozina
%T Evolution of the wave pattern for piecewise linear uniaxial tension and compression of a heteromodulus elastic bar
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2022
%P 54-70
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a4/
%G ru
%F SJIM_2022_25_4_a4
O. V. Dudko; A. A. Lapteva; V. E. Ragozina. Evolution of the wave pattern for piecewise linear uniaxial tension and compression of a heteromodulus elastic bar. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 54-70. http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a4/

[1] I. V. Baklashov, B. A. Kartoziya, Mekhanika gornykh porod, Nedra, M., 1975

[2] V. B. Zaalishvili, “Nelineinye svoistva gruntov”, Seismostoikoe stroitelstvo. Bezopasnost sooruzhenii, 2015, no. 4, 22–37

[3] E. V. Lomakin, B. N. Fedulov, “Nonlinear anisotropic elasticity for laminate composites”, Meccanica, 50:6 (2015), 1527–1535 | DOI | MR

[4] A. Yu. Ershova, M. I. Martirosov, “Eksperimentalnoe issledovanie raznomodulnykh polimernykh kompozitov s melkodispersnym napolnitelem”, Stroitelnaya mekhanika inzhenernykh konstruktsii i sooruzhenii, 2015, no. 5, 68–72

[5] M. Fouremeau, T. Borvik, A. Benallal, O. S. Hopperstad, “Anisotropic failure modes of high-strength aluminium alloy under various stress states”, Internat. J. Plasticity, 2013, no. 48, 34–53 | DOI

[6] A. I. Oleinikov, I. O. Ovcharov, “Opredelyayuschie uravneniya svyazi napryazhenii s deformatsiyami dlya chuguna”, Uchenye zapiski Komsomolsk. na-Amure gos. tekhn. un-ta, 1:3 (15) (2013), 42–46

[7] E. V. Lomakin, Yu. N. Rabotnov, “Sootnosheniya teorii uprugosti dlya izotropnogo raznomodulnogo tela”, Izv. AN SSSR. Mekhanika tverdogo tela, 1978, no. 6, 29–34

[8] S. A. Ambartsumyan, Raznomodulnaya teoriya uprugosti, Nauka, M., 1982 | MR

[9] V. A. Lyakhovskii, V. P. Myasnikov, “O povedenii uprugoi sredy s mikronarusheniyami”, Izv. AN SSSR. Fizika Zemli, 1984, no. 10, 71–75 | MR

[10] V. P. Myasnikov, A. I. Oleinikov, Osnovy mekhaniki geterogenno-soprotivlyayuschikhsya sred, Dalnauka, Vladivostok, 2007

[11] O. V. Sadovskaya, V. M. Sadovskii, Matematicheskoe modelirovanie v zadachakh mekhaniki sypuchikh sred, Fizmatlit, M., 2008

[12] O. V. Dudko, A. A. Lapteva, K. T. Semenov, “O rasprostranenii ploskikh odnomernykh voln i ikh vzaimodeistvii s pregradami v srede, po-raznomu soprotivlyayuscheisya rastyazheniyu i szhatiyu”, Dalnevostochnyi mat. zhurn., 6:1-2 (2005), 94–105

[13] O. V. Dudko, A. A. Lapteva, V. E. Ragozina, “Nestatsionarnye odnomernye dinamicheskie zadachi raznomodulnoi uprugosti s kusochno-lineinoi approksimatsiei kraevykh uslovii”, Vestn. Permskogo natsionalnogo issledovatelskogo politekh. un-ta. Mekhanika, 2019, no. 4, 37–47 | DOI | MR

[14] O. V. Dudko, A. A. Lapteva, V. E. Ragozina, “Solving nonstationary boundary value problem with piecewise linear boundary condition for one-dimensional dynamics of deformable heteromodular elastic solid”, AIP Conf. Proc., 2448:1 (2021), 020003 | DOI | MR

[15] S. N. Gavrilov, G. C. Herman, “Wave propagation in a semi-infinite heteromodular elastic bar subjected to a harmonic loading”, J. Sound and Vibration, 331:40 (2012), 4464–4480 | DOI

[16] M. Kuznetsova, M. Khudyakov, V. Sadovskii, “Wave propagation in continuous bimodular media”, Mech. Adv. Mater. Struct., 2021, April, 1–16 | DOI

[17] A. G. Kulikovskii, E. I. Sveshnikova, Nelineinye volny v uprugikh sredakh, Moskovskii litsei, M., 1998

[18] V. P. Maslov, P. P. Mosolov, “General theory of the solutions of the equations of motion of an elastic medium of different moduli”, J. Appl. Math. Mech., 49:3 (1985), 322–336 | DOI | MR