About systems of integral equations of logitudinally and transversely reinforced slabs with meromorphic symbol

Abstract

The problem of the study is a stress-strain state of the elastic layer reinforced on the surface with longitudinally and transversely arranged plates of finite width. Boundary problems for such a block structure have not previously been studied analytically due to the lack of the appropriate mathematical apparatus. In a number of works the object of study are the cases of reinforcement with longitudinally and transversely directed cylindrical armature. However, these problems have limited range of application: just as the building constructions, while the problems studied in this paper have a much wider range of applications. In particular in the study of underground structures’ strength, where for secure fastening longitudinally and transversely extended supports are necessary. It is the study with the defectoscopy method of the state of inaccessible lower support according to the characteristics of the upper support fields. It is of interest to study the behavior of such a block structure with different locations of armatures and their different mechanical characteristics. The question of the wave fields excited in such constructions also has not been studied yet. The study of such problems has been made possible thanks to the development by the authors of the solution method for integral equations’ systems with meromorphic symbol. The paper presents various settings of boundary problems for block structures representing linearly deformable layer having longitudinally and transversely located surface reinforcing elements modeled by heterogeneous plates in the form of different sized strips with different mechanical properties.