Abstract
In this paper the thin plate bending problem of residual stress which is generated due to the change of loading after the partial displacement constraint is given under a loading is analyzed. Then the crack initiation due to the residual stress and the change of loading is investigated. The rational mapping function and the complex variable method are used. The solution of residual stress is obtained by superposing the solution of uniform bending of an external force boundary value problem and that of uniform bending of a mixed boundary value problem under partial displacement constraint. Clamped supported and simple support boundaries are treated as the displacement constraint. Stress distributions before and after the crack is initiated by residual stress from an end of the displacement constraint are investigated. Occurrence of a crack and its direction are investigated using the energy release rate of crack initiation under the initial loading and that after the crack initiates.
