On Some Approaches to the Study of Coefficient Inverse Problems of Mechanics with Variable Characteristics

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.