Evolution of the wave pattern for piecewise linear uniaxial tension and compression of a heteromodulus elastic bar. (Russian. English summary) Zbl 1543.74059
Sib. Zh. Ind. Mat. 25, No. 4, 54-70 (2022); translation in J. Appl. Ind. Math. 16, No. 4, 645-658 (2022).
MSC:
| 74J40 | Shocks and related discontinuities in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74S99 | Numerical and other methods in solid mechanics |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
heteromodular elasticity; piecewise-linear boundary condition; strong discontinuity collision; graph-assisted solution; computer algebra Maxima 5.45.1References:
| [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 · Zbl 1329.74040 · doi:10.1007/s11012-015-0104-5 |
| [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:10.1016/j.ijplas.2013.02.004 |
| [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 · Zbl 0599.73019 |
| [9] | V. A. Lyakhovskii, V. P. Myasnikov, “O povedenii uprugoi sredy s mikronarusheniyami”, Izv. AN SSSR. Fizika Zemli, 1984, no. 10, 71-75 |
| [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 · Zbl 1145.76003 |
| [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:10.15593/perm.mech/2019.4.04 |
| [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:10.1063/5.0073464 |
| [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:10.1016/j.jsv.2012.05.022 |
| [16] | M. Kuznetsova, M. Khudyakov, V. Sadovskii, “Wave propagation in continuous bimodular media”, Mech. Adv. Mater. Struct., 2021, April, 1-16 · doi:10.1080/15376494.2021.1889725 |
| [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 · Zbl 0608.73034 · doi:10.1016/0021-8928(85)90031-0 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
