Stepanova N. Inverse problems of identification of force effects, inclusions and cuts in a thin plate

Stepanova N. Inverse problems of identification of force effects, inclusions and cuts in a thin plate. – Qualification scientific work presented as a manuscript. Thesis for Science Candidate Degree in Physics and Mathematics by specialty 01.02.04 – Mechanics of the Deformable Solids (Physics and Mathematics). – Oles Honchar Dnipro National University, Dnipro, 2019. This thesis is devoted to the development of the method of inverse problems for the identification of force influences and defects in a thin plate by the results of observation of its stress - strain state. The model of deformation of the observed thin plate by the presence of inclusions, sections, action of local forces under conditions of loads close to critical ones is constructed in the thesis. The variational approach is applied that based on the formulation of the full functional of the energy of the plate, to which an additional condition is attached, which determines the closeness of the real and observed states of the plate, and the unknown parameters of the model are described by means of characteristic functions. A numerical method is developed and an iterative algorithm for solving the identification problem combining finite element discretization of the plate model, linearization using the load parameter extension method, the theory of optimal partitioning of the sets and the Newton-Rafson method are developed. An approach has been developed to model a cut in a plate based on a solid plate model with a line along which the specified jumping of displacements and angles of rotation that determined by solving the inverse problem by satisfying the static conditions on the edges of the cut. With the developed approach, the tasks of identification of local power influences, rigid inclusions, longitudinal and cross cuts are solved. The effectiveness of the proposed approach is studied depending on the defect parameters. Keywords: thin plate, inverse problem, identification, inclusion, local force, crack, Lagrange function, finite element method.