chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2024-25-4-213-227cheb-1859Research ArticleИстория математики и приложенийСomputer scienceРеализация и тестирование методов расчета напряженно-деформированного состояния упруго-пластических оболочек в CAE FidesysImplementation and testing of methods for calculating the stress-strain state of elasto-plastic shells in CAE FidesysЛевинВладимир АнатольевичLevinVladimir Anatolyevich

доктор физико-математических наук, профессор

doctor of physical and mathematical sciences, professor

v.a.levin@mail.ruКозловВиктор ВячеславовичKozlovVictor Vyacheslavovich

кандидат физико-математических наук

candidate of physical and mathematical sciences

vvkozlovtsu@mail.ruФилатоваАлександра ВячеславовнаFilatovaAlexandra Vyacheslavovna

магистр

master of sciences

filatovasasha-1@mail.ruХраименковАлександр ВладиславовичKhraimenkovAlexander Vladislavovich

магистр

master of sciences

hav.2000@mail.ruМосковский государственный университет им. М. В. ЛомоносоваРоссияLomonosov Moscow State UniversityRussian FederationТульский государственный университет; Московский государственный университет им. М. В. ЛомоносоваРоссияTula State University; Lomonosov Moscow State UniversityRussian FederationООО «Фидесис»РоссияFidesys LLCRussian Federation202420012025254213227Copyright © Левин В.А., Козлов В.В., Филатова А.В., Храименков А.В., 20252025Левин В.А., Козлов В.В., Филатова А.В., Храименков А.В.Levin V.A., Kozlov V.V., Filatova A.V., Khraimenkov A.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/1859

В статье приведена общая постановка краевых задач механики деформируемого твердого тела для упруго-пластических оболочек. Рассмотрен подход к численному моделированию оболочек в MITC формулировке при малых деформациях в рамках метода конечных элементов, который был реализован в отечественном пакете прочностного анализа CAE Fidesys. Особенностью разработки является учет эффектов пластического течения при расчете оболочек путем реализации алгоритмов интегрирования по толщине оболочки. Таким образом, появляется возможность использования напрямую критерия пластичности Губера-Мизеса в отличие от ряда исследований, в которых условие достижения пластичности записано в результантах. Для решения нелинейных систем уравнений применен метод Ньютона-Раффсона. В работе рассмотрен и приведен ряд ключевых аспектов соответствующей математической модели. Произведена оценка качества реализации алгоритмов посредством сравнения результатов, полученных в CAE Fidesys, с аналогичными результатами в других CAE пакетах для задач о нагружении упруго-пластических кольцевых пластин. В частности, рассмотрена задача, соответствующая задаче Ламе в условияхплоско-напряженного состояния, а также задача об изгибе пластинки.

In paper the general formulation of solid mechanics boundary problems for elasto-plastic shells is presented. The approach to numerical modeling of shells in the MITC formulation on small strains in the context of the finite element method, which was implemented inthe local strength analysis software CAE Fidesys, is considered. The development specific is to take into account the effects of plastic flow in the calculation of shells by implementing algorithms of integration over the thickness of the shell. Thus, it is possible to use the Huber-Mises yeld criterion directly in contrast to a number of studies, in which the condition for achieving plasticity is written in the resultants. The Newton-Raphson method was applied to solve nonlinear systems of equations. In paper the number of key aspects of the correspondingmathematical model is reviewed and presented. The algorithms implementation is evaluated by comparing the results obtained in the context of algorithms implementation in CAE Fidesys for elasto-plastic circular plate loading problems with similar results in other CAE programs. In particular, the problem which is appropriate to the Lame problem under plane-stress conditions and the plate bending problem are considered.

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The authors declare that there are no conflicts of interest present.