Perfect RigidPlastic Spreading of an Asymptotically Thin Cylindrical Layer

摘要

When constructing analytical solutions of the clas-sical Prandtl problem [1] and its numerous generaliza-tions [2–8] that simulate the technological process ofspreading a thin plastic layer, a series of kinematic and static hypotheses is conventionally accepted. Their use in fact means the semiregressive method of solution, and the validity is confirmed by the results, first of all by experimental ones. However, the question arises about the uniqueness of the solution of the nonlinear edge problem stated based on the assumptions on the form of the dependence of one or quantity or another on the coordinates. The asymptotic analysis for a thin layer, which is given below, allows us to investigate this question in detail.