Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia (RUDN University)10880Research ArticleMATHEMATICAL MODEL OF THE STRESS-STRAIN STATE OF A BEAM WITH A VARIABLE SECTION WITH AN EFFECT OF "BOUNDARY LAYER"FirsanovVal Vk906@mai.ruMAI, Moscow150620156636912092016Copyright © 2016, Structural Mechanics of Engineering Constructions and Buildings2016The essence of this mathematical model consist in construction of the basic stress-strain state which is based on a new hypothesis of a vertical element and an additional stress-strain state of the regional flat deformation arising of close rigidly jammed edge. It gives the chance more exactly to estimate the strength of aircraft structures near to irregularities of type of con- nections, join elements (spars) with variation in wall thickness, of the slender swept-delta wings, empennage, and rocket stabilizes. The method of asymptotic integration of the differential equations of a three-dimensional theory of elasticity is applied. By means of special oblique-angled system of the coordinates relationship for the two of fringe problem was derived. The problems of additional, stress- strain state of the frige flat deformation was solved by the variational method of Vlasov- Kantorovich. On the example of the calculation of the beam with constant thickness, it is shown that the considerable contribution to the general stress state is brought by the transverse normal and shearing stresses, which in the classical theory of bars and shells are neglected.beam of variable cross-sectionisothotropic materialvariational method of Vlasov - Kantorovitchstress-strain stateaviation structuresarbitrary system of coordi- nateasymptotic integrationбалка переменного сеченияизотропный материалвариа- ционный метод Власова- Канторовичанапряженно-деформированное состояниеавиа- ционные конструкциикосоугольная система координатлонжеронасимптотическое интегрирование