Identification of the pulse axisymmetric load acting on a composite cylindrical shell, inhomogeneous in length, made of different materials

Abstract

The problem of identifying the load acting on the elements of structures belongs to the class of inverse problems of the mechanics of a deformable solid, which are often incorrect. Solving such problems is associated with the instability of the calculation results, which requires the development of special methods for their research. This predetermines the relevance of this study.The object of the study is a single-pass cylindrical shell consisting of two rigidly fastened butt-fastened sections made of different materials. Each of the shells is assumed to be elastic isotropic, having a cross-section of medium thickness. The equations of axisymmetric deformation of shells are used within the framework of Timoshenko hypotheses. An approach to solving direct and inverse problems for such discretely heterogeneous objects is proposed, which implies the conditional separation of a discretely heterogeneous cylindrical shell along the length, followed by the addition of functions of fictitious loads. The main analytical relationships for building a system of integral Volterra equations are given, for which an analytic-numerical solution is derived. The final ratios have been obtained, which make it possible to calculate the kinematic and force parameters of the study object in the process of non-stationary deformation. The inverse problem of identifying arbitrary loads acting on a shell that is heterogeneous in length is solved in a general form. An algorithm for the restoration of pulse loads has been developed, which is robust to errors in the initial data (about 5 %). The material related to solving direct and inverse problems for shells that are discretely heterogeneous in length can significantly advance the methodology for identifying pulse loads acting on structural elements.