Mathematical modelling of physically/geometrically non-linear micro-shells with account of coupling of temperature and deformation fields; Chaos, Solitons & Fractals; Vol. 104

Mathematical modelling of physically/geometrically non-linear micro-shells with account of coupling of temperature and deformation fields; Chaos, Solitons & Fractals; Vol. 104

Bibliografische gegevens
Parent link:Chaos, Solitons & Fractals: Scientific Journal
Vol. 104.— 2017.— [P. 635–654]
Coauteur: Национальный исследовательский Томский политехнический университет (ТПУ) Институт кибернетики (ИК) Кафедра инженерной графики и промышленного дизайна (ИГПД) Научно-учебная лаборатория 3D моделирования (НУЛ 3DМ)
Andere auteurs: Awrejcewicz J. Jan, Krysko V. A. Vadim, Sopenko A. A. Aleksandr Anatoljevich, Zhigalov M. V. Maksim, Kirichenko A. V. Anastasiya Valerjevna, Krysko A. V. Anton Vadimovich
Samenvatting:Title screen
A mathematical model of flexible physically non-linear micro-shells is presented in this paper, taking into account the coupling of temperature and deformation fields. The geometric non-linearity is introduced by means of the von Kбrmбn shell theory and the shells are assumed to be shallow. The Kirchhoff-Love hypothesis is employed, whereas the physical non-linearity is yielded by the theory of plastic deformations. The coupling of fields is governed by the variational Biot principle. The derived partial differential equations are reduced to ordinary differential equations by means of both the finite difference method of the second order and the Faedo-Galerkin method. The Cauchy problem is solved with methods of the Runge-Kutta type, i.e. the Runge-Kutta methods of the 4th (RK4) and the 2nd (RK2) order, the Runge-Kutta-Fehlberg method of the 4th order (rkf45), the Cash-Karp method of the 4th order (RKCK), the Runge-Kutta-Dormand-Prince (RKDP) method of the 8th order (rk8pd), the implicit 2nd-order (rk2imp) and 4th-order (rk4imp) methods. Each of the employed approaches is investigated with respect to time and spatial coordinates. Analysis of stability and nature (type) of vibrations is carried out with the help of the Largest Lyapunov Exponent (LLE) using the Wolf, Rosenstein and Kantz methods as well as the modified method of neural networks. The existence of a solution of the Faedo-Galerkin method for geometrically non-linear problems of thermoelasticity is formulated and proved. A priori estimates of the convergence of the Faedo-Galerkin method are reported. Examples of calculation of vibrations and loss of stability of square shells are illustrated and discussed.
Режим доступа: по договору с организацией-держателем ресурса
Taal:Engels
Gepubliceerd in: 2017
Onderwerpen:
электронный ресурс
труды учёных ТПУ
Online toegang:https://doi.org/10.1016/j.chaos.2017.09.008
Formaat: Elektronisch Hoofdstuk
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=666986

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