{"title":"On Some Approaches to the Study of Coefficient Inverse Problems of Mechanics with Variable Characteristics","authors":"A. O. Vatulyan","doi":"10.1134/S0025654424605767","DOIUrl":null,"url":null,"abstract":"<p>This paper covers some general aspects of studying coefficient inverse problems (CIP) for various models of mechanics, with the main attention paid to the class when the unknowns are functions of one variable included in the description of the differential operator (ordinary or in partial derivatives) characterizing the heterogeneity (functionally gradient materials, composites, biological tissues). Various types of statements of such IPs are discussed, a generalized reciprocity relation for various linear models of mechanics is formulated, weak and variational statements are given, some issues of constructing solutions are studied, iterative and effective computational schemes for solving direct and inverse problems are proposed; solutions to a number of CIPs in various statements are constructed, and the results of computational experiments are presented.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3417 - 3448"},"PeriodicalIF":0.6000,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654424605767","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper covers some general aspects of studying coefficient inverse problems (CIP) for various models of mechanics, with the main attention paid to the class when the unknowns are functions of one variable included in the description of the differential operator (ordinary or in partial derivatives) characterizing the heterogeneity (functionally gradient materials, composites, biological tissues). Various types of statements of such IPs are discussed, a generalized reciprocity relation for various linear models of mechanics is formulated, weak and variational statements are given, some issues of constructing solutions are studied, iterative and effective computational schemes for solving direct and inverse problems are proposed; solutions to a number of CIPs in various statements are constructed, and the results of computational experiments are presented.
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
