Approximated-asymptotic solution of the complex variable equation of toroidal shells under axial symmetric loads

Abstract

The series-approach and the asymptotic-approach are usually used to solve the complex variable equation of the toroidal shells under axial symmetric loads. As is known, the convergence of the series-solution is good only for small values of\(\mu = \sqrt {12(1 - v^2 )} a^2 /(r_0 h)\). On the other hand, the convergence of the asymptotic solution is good only for large values of μ. In this paper, based on an earlier work[1], a new approach which may be called the approximated-asymptotic solution has been developed and it is valid for both small and large values of μ. It is shown that the results of the approximated-asymptotic solution for toroidal shell with μ=0.5 coincide very well with those of the series-solution, while the results of the asymptotic solution for this value of μ are not as good, and the results of the approximated-asymptotic solution for μ=15 agree with those of the asymptotic solution.