Згин зварної пластинчастої конструкції за контакту берегів колового міжфазного розрізу

Abstract

Наведено методику розрахунку кусково-однорідної зварної пластинчастої конструкції, що містить нескінченну ізотропну пластинку з круговим отвором і пружний круглий диск з розрізом на ділянці сполучення, береги якого контактують за дії згинальних навантажень. Моментні напруження на контурах пластинки і диска визначаються із системи сингулярних інтегральних рівнянь, наближений розв’язок якої побудовано методами механічних квадратур і колокації. Досліджено вплив на напружений стан складеної пластинки і величини зони контакту відносної жорсткості зварювального шва та величини розрізу.

Mixed contact problem of the interaction of the infinity isotropic plate with the circular hole of single radius and the circular elastic disk through the open welded seam of constant rigidity in tension (compression) and bending, is considered. Under bending load, the cut edges between the plate and the disk contact partly or along the whole length in one of the common base of the composite plate. The solving of the problem includes the determination of the stress state components at the interface of the materials of the plate and the disk as well as in the welded seam.

General state of stress in the lamellar construction is presented as the superposition of the two-dimensional stress states: generalized two-dimensional stress state and bending in the technical theory of the bending plates. The boundary conditions on the smooth contact zone are formulated as the equality of the normal displacements and rotation angles of the normal line to the mean plane in the contour points. As the perfect mechanical contact exists in the zone of soldered joint so the boundary conditions are written as equality of displacements, rotation angles and deformations between the plate, welded seam and the disk. The system of singular integral-differential equations for the determination of contact stresses in the zone of soldered joint and in the contact zone is built through modeling welded seam as the elastic line which coincides with the splice lines of the plate and the disk, and, using the integral relations between the vector displacement components and the rotation angle of normal line in the contour points of the plate (disk) and the contour stress. The finding functions structure in the ends of these zones is determined. The approximate solution of the problem is built by the method of mechanical quadrature and collocation which is used to analyze the influence upon the relative rigidity of welded seam and the cut size on the composite plate stress state and the size of contact zone. The numerical example is considered.