Abstract:
The aim of this paper is applying of Discontinuous Galerkin Method to deformation and destruction problems of elastoplastic bodies as well as to hydroelastic problems. Two-sided crack model for destruction, Prandtl–Reuss elastoplastic model, dynamic contact of bodies, wave propagation through coupled elastic-acoustic media for marine seismology, comparison of reflected waves in fluid-filled and infinite thin crack models and underwater objects detection are described. Method was implemented for HPC infrastructure.
Keywords:
Discontinuous Galerkin Method, mechanics of deformable solids, HPC, wave problems in coupled elastic-acoustic media, marine seismology, fluid-filled crack, dynamic contact of bodies, destruction.
Citation:
V. A. Miryaha, A. V. Sannikov, I. B. Petrov, “Discontinuous Galerkin method for numerical simulation of dynamic processes in solids”, Mat. Model., 27:3 (2015), 96–108; Math. Models Comput. Simul., 7:5 (2015), 446–455
This publication is cited in the following 20 articles:
Vladimir Lapshin, “A Study of the Effect of Impact Speed on the Dynamics of Mechanical Interactions of Bodies”, KEM, 910 (2022), 663
Favorskaya V A., Petrov I.B., “Combination of Grid-Characteristic Method on Regular Computational Meshes With Discontinuous Galerkin Method For Simulation of Elastic Wave Propagation”, Lobachevskii J. Math., 42:7, SI (2021), 1652–1660
Katerina A. Beklemysheva, Igor B. Petrov, Smart Innovation, Systems and Technologies, 214, Smart Modelling For Engineering Systems, 2021, 287
Andrey Stankevich, Alexey Vasyukov, Igor Petrov, 2021 Ivannikov Memorial Workshop (IVMEM), 2021, 76
Andrey S. Stankevich, Igor B. Petrov, Alexey V. Vasyukov, Smart Innovation, Systems and Technologies, 215, Smart Modelling for Engineering Systems, 2021, 235
V L Lapshin, E V Zenkov, V P Yashenko, “A three-mass viscoelastic plastic model used for studying mechanics and dynamics of shock interaction of solid bodies in determining the mechanical characteristics of building materials”, IOP Conf. Ser.: Earth Environ. Sci., 751:1 (2021), 012103
V. L. Lapshin, E. V. Zenkov, “Control algorithm for an elastic-viscoplastic model to study processes of shock interaction of bodies”, Advanced Engineering Research, 21:2 (2021), 191
N. Khokhlov, P. Stognii, “Novel approach to modeling the seismicwaves in the areas with complex fractured geological structures”, Minerals, 10:2 (2020), 122
I. B. Petrov, “Mathematical modeling of natural and anthropogenic processes in the arctic zone”, Lobachevskii J. Math., 41:4, SI (2020), 552–560
Lapshin V., Kobzov D., International Conference on Modern Trends in Manufacturing Technologies and Equipment (Icmtmte) 2020, IOP Conference Series-Materials Science and Engineering, 971, IOP Publishing Ltd, 2020
V. A. Miryaha, A. V. Sannikov, V. A. Biryukov, I. B. Petrov, “Discontinuous Galerkin method for ice strength investigation”, Math. Models Comput. Simul., 10:5 (2018), 609–615
I. B. Petrov, “Problems of simulation of natural and anthropogenous processes in the Arctic zone of the Russian Federation”, Math. Models Comput. Simul., 11:2 (2019), 226–246
V. A. Miryaha, I. B. Petrov, “Discontinuous Galerkin method for simulation of ice flow impact on vertical cylinder offshore structure”, Math. Models Comput. Simul., 11:3 (2019), 400–414
M. A. Zaitsev, S. A. Karabasov, “Skhema Kabare dlya chislennogo resheniya zadach deformirovaniya uprugoplasticheskikh tel”, Matem. modelirovanie, 29:11 (2017), 53–70
O. O'Reilly, E. M. Dunham, J. Nordstrom, “Simulation of wave propagation along fluid-filled cracks using high-order summation-by-parts operators and implicit-explicit time stepping”, SIAM J. Sci. Comput., 39:4 (2017), B675–B702
V. A. Biryukov, V. A. Miryakha, I. B. Petrov, “Analysis of the dependence of the global load on the mechanical parameters of ice under interaction between an ice field and construction”, Dokl. Phys., 62:6 (2017), 328–331
V. Biryukov, V. Miryakha, I. Petrov, “ANALIZ ZAVISIMOSTI GLOBALNOI NAGRUZKI OT MEKhANIChESKIKh PARAMETROV LDA PRI VZAIMODEISTVII LEDYaNOGO POLYa S KONSTRUKTsIEI”, Doklady Akademii nauk, 2017, no. 6, 696
V. A. Biryukov, V. A. Miryaha, I. B. Petrov, N. I. Khokhlov, “Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods”, Comput. Math. Math. Phys., 56:6 (2016), 1086–1095
Voroshchuk D.N. Miryaha V.A. Petrov I.B. Sannikov A.V., “Discontinuous Galerkin Method For Wave Propagation in Elastic Media With Inhomogeneous Inclusions”, Russ. J. Numer. Anal. Math. Model, 31:1 (2016), 41–50
A. V. Favorskaya, I. B. Petrov, D. I. Petrov, N. I. Khokhlov, “Numerical modeling of wave processes in layered media in the Arctic”, Math. Models Comput. Simul., 8:4 (2016), 348–357
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