Регуляризирующий алгоритм А. Н. Тихонова в некорректных задачах нестационарной динамики упругих элементов конструкции

Abstract

Tikhonov’s regularization algorithm and its application to solving the ill-posed problems in deformable solid mechanics are considered. Some problems of nonstationary deforming of elastic structural elements can be reduced to the Volterra integral equations. Ill-posed problems arise in the study of the Volterra integral equations. Finite-dimensional approximation of the ill-posed problem and the smoothing functional is carried out within the bounds of the regularization algorithm. The inverse identification problem for the unknown disturbing force applied to a rectangular plate is given as an example of an ill-posed problem. The solution of this ill-posed problem is obtained using Tikhonov’s regularization algorithm. Special attention is paid to choosing the regularization parameter. Functional diagrams for the regularization parameter are shown. The significant influence of the priory information on the solution of the ill-posed problems is noted in conclusion.