{"title":"On the Existence of Solutions of Nonlinear Boundary Value Problems for Nonshallow Timoshenko-Type Shells with Free Edges","authors":"S. N. Timergaliev","doi":"10.1134/S1990478923040154","DOIUrl":null,"url":null,"abstract":"<p> We study the existence of solutions of a boundary value problem for a system of nonlinear\nsecond-order partial differential equations for the generalized displacements under given nonlinear\nboundary conditions that describes the equilibrium state of elastic nonshallow isotropic\ninhomogeneous shells of zero Gaussian curvature with free edges in the framework of the\nTimoshenko shear model. The research method is based on integral representations for generalized\ndisplacements containing arbitrary functions that allow the original boundary value problem to be\nreduced to a nonlinear operator equation for generalized displacements in the Sobolev space. The\nsolvability of the operator equation is established using the contraction mapping principle.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"874 - 891"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","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/S1990478923040154","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 study the existence of solutions of a boundary value problem for a system of nonlinear
second-order partial differential equations for the generalized displacements under given nonlinear
boundary conditions that describes the equilibrium state of elastic nonshallow isotropic
inhomogeneous shells of zero Gaussian curvature with free edges in the framework of the
Timoshenko shear model. The research method is based on integral representations for generalized
displacements containing arbitrary functions that allow the original boundary value problem to be
reduced to a nonlinear operator equation for generalized displacements in the Sobolev space. The
solvability of the operator equation is established using the contraction mapping principle.
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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