Abstract:
The three-dimensional dynamical problem of the oblique impact of a rigid pellet on a deformable elastoplastic barrier is solved using a hybrid grid-characteristic scheme for the numerical solution of non-stationary systems of hyperbolic equations. Thegrid-characteristic hybrid scheme is adapted for the numerical solution of multidimensional non-stationary problems in the mechanics of deformable bodies.
Citation:
I. B. Petrov, I. G. Tormasov, A. S. Kholodov, “On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid”, Zh. Vychisl. Mat. Mat. Fiz., 30:8 (1990), 1237–1244; U.S.S.R. Comput. Math. Math. Phys., 30:4 (1990), 191–196
\Bibitem{PetTorKho90}
\by I.~B.~Petrov, I.~G.~Tormasov, A.~S.~Kholodov
\paper On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1990
\vol 30
\issue 8
\pages 1237--1244
\mathnet{http://mi.mathnet.ru/zvmmf3222}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1074168}
\zmath{https://zbmath.org/?q=an:0714.73091}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1990
\vol 30
\issue 4
\pages 191--196
\crossref{https://doi.org/10.1016/0041-5553(90)90062-W}
Linking options:
https://www.mathnet.ru/eng/zvmmf3222
https://www.mathnet.ru/eng/zvmmf/v30/i8/p1237
This publication is cited in the following 23 articles:
I. A. Mitskovets, N. I. Khokhlov, “Simulation of propagation of dynamic perturbations in porous media by the grid-characteristic method with explicit description of heterogeneities”, Comput. Math. Math. Phys., 63:10 (2023), 1904–1917
M. V. Muratov, D. I. Petrov, D. S. Konov, I. B. Petrov, “The Use of Convolutional Neural Networks to Search for Fractures in the Geological Media”, Lobachevskii J Math, 44:1 (2023), 394
A. V. Shevchenko, V. I. Golubev, “Boundary and contact conditions of higher order of accuracy for grid-characteristic schemes in acoustic problems”, Comput. Math. Math. Phys., 63:10 (2023), 1760–1772
Vasily Golubev, Ilia Nikitin, Anton Ekimenko, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2312, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2020, 050006
I. B. Petrov, M. V. Muratov, “The application of grid-characteristic method in solution of fractured formations exploration seismology direct problems (review article)”, Math. Models Comput. Simul., 11:6 (2019), 924–939
Igor B. Petrov, Smart Innovation, Systems and Technologies, 133, Smart Modeling for Engineering Systems, 2019, 8
A. I. Lobanov, “Nauchnye i pedagogicheskie shkoly Aleksandra Sergeevicha Kholodova”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 561–579
A. M. Ivanov, N. I. Khokhlov, “Parallelnaya realizatsiya setochno-kharakteristicheskogo metoda v sluchae yavnogo vydeleniya kontaktnykh granits”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 667–678
A. V. Favorskaya, I. B. Petrov, “The study of increased order grid-characteristic methods on unstructured grids”, Num. Anal. Appl., 9:2 (2016), 171–178
D. I. Petrov, I. B. Petrov, A. V. Favorskaya, N. I. Khokhlov, “Numerical solution of seismic exploration problems in the Arctic region by applying the grid-characteristic method”, Comput. Math. Math. Phys., 56:6 (2016), 1128–1141
V. I. Golubev, I. B. Petrov, N. I. Khokhlov, K. I. Shul'ts, “Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes”, Comput. Math. Math. Phys., 55:3 (2015), 509–518
V. A. Biryukov, M. V. Muratov, I. B. Petrov, A. V. Sannikov, A. V. Favorskaya, “Application of the grid-characteristic method on unstructured tetrahedral meshes to the solution of direct problems in seismic exploration of fractured layers”, Comput. Math. Math. Phys., 55:10 (2015), 1733–1742
M. V. Muratov, I. B. Petrov, A. V. Sannikov, A. V. Favorskaya, “Grid-characteristic method on unstructured tetrahedral meshes”, Comput. Math. Math. Phys., 54:5 (2014), 837–847
A. V. Vasyukov, A. S. Ermakov, I. B. Petrov, A. P. Potapov, A. V. Favorskaya, A. V. Shevtsov, “Combined grid-characteristic method for the numerical solution of three-dimensional dynamical elastoplastic problems”, Comput. Math. Math. Phys., 54:7 (2014), 1176–1189
Roiz S.I., Vlasov A.Yu., Petrov I.B., “Vizualizatsiya rezultatov chislennykh eksperimentov s pomoschyu sistemy \it{visualization toolkit}”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2011, no. 5, 122–126
A. P. Potapov, S. I. Roiz, I. B. Petrov, “Modelirovanie volnovykh protsessov metodom sglazhennykh chastits (SPH)”, Matem. modelirovanie, 21:7 (2009), 20–28
N. G. Matyushev, I. B. Petrov, “Mathematical simulation of deformation and wave processes in multilayered structures”, Comput. Math. Math. Phys., 49:9 (2009), 1615–1621
F. B. Chelnokov, “Yavnoe predstavlenie setochno-kharakteristicheskikh skhem dlya uravnenii uprugosti v dvumernom i trekhmernom prostranstvakh”, Matem. modelirovanie, 18:6 (2006), 96–108
I. B. Petrov, “Modelirovanie deformatsionnykh protsessov v slozhnykh konstruktsiyakh pri ikh intensivnom dinamicheskom nagruzhenii”, Matem. modelirovanie, 18:5 (2006), 91–110
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