Inverse optimal control problems in creep theory
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 2, pp. 33-42.

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

We formulate inverse problems of the theory of quasi-static creep in the form of a variational principle and optimal control with constraints on the displacements and stresses and give necessary optimality conditions. In solving specific examples, we find a continuous function of optimal load that depends on two parameters. We construct and numerically implement the method for determining the parameters from given conditions of the problem.
Keywords: inverse creep problem, damagedness, multiobjective optimization problem, optimal control.
Mots-clés : variational principles
@article{SJIM_2012_15_2_a3,
     author = {K. S. Bormotin},
     title = {Inverse optimal control problems in creep theory},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {33--42},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_2_a3/}
}
TY  - JOUR
AU  - K. S. Bormotin
TI  - Inverse optimal control problems in creep theory
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2012
SP  - 33
EP  - 42
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2012_15_2_a3/
LA  - ru
ID  - SJIM_2012_15_2_a3
ER  - 
%0 Journal Article
%A K. S. Bormotin
%T Inverse optimal control problems in creep theory
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2012
%P 33-42
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2012_15_2_a3/
%G ru
%F SJIM_2012_15_2_a3
K. S. Bormotin. Inverse optimal control problems in creep theory. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 2, pp. 33-42. http://geodesic.mathdoc.fr/item/SJIM_2012_15_2_a3/

[1] Tsvelodub I. Yu., “Ob odnom klasse obratnykh zadach teorii polzuchesti”, Prikl. mekhanika i tekhn. fizika, 1989, no. 2, 163–173

[2] Vasidzu K., Variatsionnye metody v teorii uprugosti i plastichnosti, Mir, M., 1987

[3] Korobeinikov C. H., Nelineinoe deformirovanie tverdykh tel, Izd-vo SO RAN, Novosibirsk, 2000

[4] Banichuk N. V., Vvedenie v optimizatsiyu konstruktsii, Nauka, M., 1986 | MR

[5] Liu G. P., Yang J. B., Whidborne J. F., Multiobjective Optimisation and Control, Research Studies Press, Baldock–Hertfordshire, 2003

[6] Tsvelodub I. Yu., “Ob optimalnykh putyakh deformirovaniya v usloviyakh polzuchesti. Nekotorye prilozheniya k zadacham obrabotki materialov davleniem”, Izv. AN SSSR. Mekhanika tverdogo tela, 1987, no. 6, 128–136

[7] Tsvelodub I. Yu., Postulat ustoichivosti i ego prilozheniya v teorii polzuchesti metallicheskikh materialov, izd. IGiL SO AN SSSR, Novosibirsk, 1991

[8] Radchenko V. P., Eremin Yu. A., Reologicheskoe deformirovanie i razrushenie materialov i elementov konstruktsii, Mashinostroenie, M., 2004

[9] Gorev B. V., Rubanov V. V., Sosnin O. V., “O polzuchestimaterialov s raznymi svoistvami pri rastyazhenii i szhatii”, Problemy prochnosti, 1979, no. 7, 62–67

[10] Chernorutskii I. G., Metody optimizatsii i prinyatiya reshenii, Lan, SPb., 2001

[11] Chernousko F. L., Banichuk N. V., Variatsionnye zadachi mekhaniki i upravleniya (chislennye metody), Nauka, M., 1973

[12] Malinin N. N., Prikladnaya teoriya plastichnosti i polzuchesti, Mashinostroenie, M., 1975

[13] Annin B. D., Oleinikov A. I., Bormotin K. S., “Modelirovanie protsessov formoobrazovaniya panelei kryla samoleta SSJ-100”, Prikl. mekhanika i tekhn. fizika, 51:4 (2010), 155–165