Geodesic
Numerical simulation of nonlinear dynamics problems of elastic-plastic structures
Matematičeskoe modelirovanie, Tome 18 (2006) no. 1, pp. 10-16 
V. G. Bazhenov; V. K. Lomunov; D. T. Chekmarev. Numerical simulation of nonlinear dynamics problems of elastic-plastic structures. Matematičeskoe modelirovanie, Tome 18 (2006) no. 1, pp. 10-16. http://geodesic.mathdoc.fr/item/MM_2006_18_1_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The construction method of explicit-implicit schemes, proposed earlier by authous for unsteady dynamics of thin-walled structures in [1], [2], is developed. A theoretic feasibility of the method and its realization, based on continuum mechanics equations and shell theory is carried out. An example of non-linear solution of the rod dynamics problem, showing the method efficiency, is given.

[1] Bazhenov V. G., Chekmarev D. T., Variatsionno-raznostnye skhemy v nestatsionarnykh volnovykh zadachakh dinamiki plastin i obolochek, Izd-vo NNGU, N. Novgorod, 1992, 160 pp. | MR

[2] Bazhenov V. G., Pirogov S. A., Chekmarev D. T., “Yavnaya skhema so stabiliziruyuschim operatorom dlya resheniya nestatsionarnykh zadach dinamiki konstruktsii”, Izv. RAN, MTT, 2002, no. 5, 120–130

[3] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1989, 608 pp. | MR

[4] Bazhenov V. G., Chekmarev D. T., “Otsenki ustoichivosti yavnoi konechno-raznostnoi skhemy “krest” resheniya nestatsionarnykh zadach teorii uprugosti i teorii obolochek”, Prikladnye problemy prochnosti i plastichnosti. Algoritmizatsiya i avtomatizatsiya resheniya zadach uprugosti i plastichnosti, no. 28, izd-vo Gork. un-ta, Gorkii, 1984, 15–22

[5] Bazhenov V. G., Kibets A. I., Tulintsev O. V., “Primenenie momentnoi skhemy MKE dlya analiza nelineinykh trekhmernykh zadach dinamiki massivnykh i obolochechnykh elementov konstruktsii”, Prikladnye problemy prochnosti i plastichnosti. Metody resheniya, no. 47, izd-vo Nizhegor. un-ta, Nizhnii Novgorod, 1991, 46–53 | MR

[6] Bazhenov V. G., Lomunov V. K., “Metodika rascheta dinamicheskogo deformirovaniya geometricheski izmenyaemykh ploskikh sterzhnevykh sistem”, Problemy prochnosti i plastichnosti, Mezhvuz. sb., no. 64, 2002, 55–63

[7] Danilin A. N., Markov A. V., Modelirovanie dinamiki razvertyvaniya gibkikh sterzhnevykh sistem pri razlichnykh sposobakh izmeneniya ikh nachalnoi geometrii, Materialy VIII Mezhdunarodnogo simpoziuma “Dinamicheskie i tekhnologicheskie problemy mekhaniki konstruktsii i sploshnykh sred” (Yaropolets 11–15 fevralya 2002 g.), Moskva, 2002, 61 pp. | Zbl