The inverse non-stationary problem of identification of defects in an elastic rod

Abstract

Non-stationary inverse problems of deformed solid mechanics are among the most underexplored due to, inter alia, increasing dimension of non-stationary problems per unit as compared with stationary and static problems, as well as necessity to consider the initial conditions. In the context of the continuing progress of the aviation and aerospace industries, the question arises about technical condition monitoring of aircraft for the purposes of their safe operation. A large proportion of an aircraft structure consists of beam and rod elements exposed to various man-made and natural effects which cause defects inaccessible for visual inspection and required to be identified well in advance. It is well known that defects (such as cracks, cavities, rigid and elastic inclusions) are concentrators of stresses and largely cause processes, which lead to the destruction of elastic bodies. Therefore, the problem of identification of such defects and their parameters, i.e. the problem of identification, represents a great practical interest. Mathematically, the problem of identification represents a non-linear inverse problem. The development of methods of solving such problems is currently a live fundamental research issue.

Structural Design Method for Constructions: Simulation, Manufacturing and Experiment

“…In this case, the parameters vector consists of porosity (λ) and the ellipticity coefficient (β). To investigate the dependence between the stiffness tensor and the parameters vector, a representative elements method was used [31][32][33]. For this purpose, the parameterized finite element model of a cube with a spheroidal pore was implemented.…”

“…For approximation, a fourth-degree polynomial function was used with an approximation error threshold of about 0.9 [33][34][35][36]. In the calculations, some of the coefficients were equal to zero, so a common form of the final calculated polynomial was as follows:…”