Scherbina I. Application of asymptotic method to the decision of contact tasks of flat theory of resiliency for orthotropic environments

О The object is the tense state of orthotropic semibar or rectangle, which are under act of hard stamp. The aim - research of the tensely-deformed state of rectangular resilient plate which is under act of hard stamp with flat foundation.Methods - asymptotic, methods of theory of functions of complex variable. The decision of regional task of theory of resiliency is taken to the successive decision of tasks of theory of potential. Analytical expressions for basic functions, characterizing the tensely-deformed state of the system of contacting bodies, are got. Possible maximum transitions are conducted, the conduct of functions is considered in neighbouring of the special points.The analytical decisions of new intricate problems are first got: about pressing of hard stamp with flat foundation in the free verge of resilient ortotropnoy semibar and rectangle taking into account forces of friction; with a friction and coupling;Melan’s task for orthotropic rectangle. Results of work can be used in the calculation and planning organizations, which сonnect with creation of constructions, functioning in the conditions of contact co-operation, and also in educational process.