Згин зосередженою силою тонкої пластини, розташованої на пружній основі та послабленої контактною тріщиною

Abstract

The paper considers the two-dimensional formulation of the problem of the contact interaction of the crack edges in a plate bent by the concentrated force on the elastic Winkler foundation. The crack closure is described using the model of contact along a line in one of the plate surfaces. Within the framework of this model, the boundary value problem is formulated for the equations of the classical theories of plate bending on the elastic foundation and a plane stress state with interrelated tension and bending conditions on the crack line. The obtained boundary value problem has been solved using singular integral equations method. Based on numerical solutions of the integral equation the dependences of forces and moments intensity factors in the vicinity of the defect tips and distribution of contact forces along the crack line on the parameters of elastic foundation stiffness and the coordinate of the application point of the load have been investigated. The effect of crack closure and influence of the elastic foundation stiffness on the limit equilibrium of the plate, depending on the coordinate of the point of application of the concentrated force, has been evaluated. The area of the correctness of the problem statement when the crack closure occurs throughout its length has been established. It was found that the crack closure leads to the appearance of nonzero forces intensity factor, reduction of the moments intensity factor and increase of the limit load. The dependences of the forces and moments intensity factors and the limit load on the dimensionless coordinate of the point of application of the concentrated force are nonmonotonic. Numerical analysis showed that increasing the elastic foundation stiffness, as well as the displacement of the point of application of the force from the center of the cut, increase the limit load and weaken the contact reaction.