The Schrodinger Equation of Thin Shell Theories

This work is the continuation of the discussions of [50] and [51]. In this paper:(A) The Love-Kirchhoff equation of small deflection problem for elastic thin shell with constant curvature are classified as the same several solutions of Schrödinger equation, and we show clearly that its form in axisymmetric problem;(B) For example for the small deflection problem, we extract me general solution of the vibration problem of thin spherical shell with equal thickness by the force in central surface and axisymmetric external field, that this is distinct from ref. [50] in variable. Today the variable is a space-place, and is not time;(C) The von Kármán-Vlasov equation of large deflection problem for shallow shell are classified as the solutions of AKNS equations and in it the one-dimensional problem is classified as the solution of simple Schrödinger equation for eigenvalues problem, and we transform the large deflection of shallow shell from nonlinear problem into soluble linear problem.