The Second Mixed Boundary Value Problem of Thin Plate Bending and Its Application.

Abstract

A solution to the second mixed boundary value problem for thin plate bending is derived under the following loading conditions: two components of the external force are applied on two parts of the boundary, and equivalent shearing forces and an angle of deflection in the y-direction are applied at the remaining two parts of the boundary which are straight. To obtain the solution, complex stress functions and a rational mapping function are used. The half-plane with surface and subsurface cracks under uniform bending moment has been considered as an example. The geometry of the body is symmetric about the crack line and is a doubly connected region. The distributions of stress and stress intensity factors are obtained and presented graphically.