{"title":"Inverse Problem of Pure Bending of a Beam under Creep Conditions","authors":"S. V. Boyko, A. Yu. Larichkin","doi":"10.1134/S1990478923020047","DOIUrl":null,"url":null,"abstract":"<p> We propose an algorithm for solving the inverse problem of forming structural members\nunder creep conditions using the Nelder–Mead algorithm. The initial problem of finding the forces\nthat must be applied to obtain the desired curvature of a part is reduced to a sequence of\nauxiliary direct problems of modeling the stress-strain state of pure bending of rectangular beams.\nThis model, taking into account the difference in the properties of the material in tension and\ncompression as well as the presence of accumulated damage in the material during creep, was\nverified by numerical methods and implemented in the finite element program <span>MSC Marc</span>.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5800,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923020047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We propose an algorithm for solving the inverse problem of forming structural members
under creep conditions using the Nelder–Mead algorithm. The initial problem of finding the forces
that must be applied to obtain the desired curvature of a part is reduced to a sequence of
auxiliary direct problems of modeling the stress-strain state of pure bending of rectangular beams.
This model, taking into account the difference in the properties of the material in tension and
compression as well as the presence of accumulated damage in the material during creep, was
verified by numerical methods and implemented in the finite element program MSC Marc.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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