Jordan form asymptotic solutions near the tip of a V-shaped notch in Reissner plate

The expressions for the first two order solutions of the asymptotic near-tip fields for V-shaped notch in Reissner plate have been given by the eigenfunction expansion method in the open literature. However, the eigenfunction expansion solutions are incomplete due to the absence of the asymptotic solution corresponding to a crucial eigenvalue. In this paper the asymptotic solution has been derived as a supplement to previous work. Moreover, it is found that the asymptotic solution for the displacement distribution in the plate becomes infinite for some special vertex angles of the notch, this is a paradox. The cases of the paradox are studied, and the corresponding bounded solutions are found to be explained by the Jordan form solution according to the methods of mathematical physics. In another case, Jordan form asymptotic solution also arises where an eigenvalue becomes a double root. By virtue of the methods of mathematical physics, the Jordan form asymptotic solutions for these special cases are derived making use of a rational procedure and specified in explicit form. A numerical example is given in order to prove the validity of the present study and also to discuss the importance of the completeness of the eigenfunction expansion solutions.