Stress state of flexible plates with a hole that are subject to bending

This paper proposes and mathematically proves a method to regularize singular iterations used to solve geometrically nonlinear problems of bending of thin plates with a hole. It is established that the new approximations for deflections and stress functions satisfy the boundary conditions exactly and Karman’s equations asymptotically exactly. The regularization method and the approximations for solutions are based on new methods of summing functional series and sequences __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 1, pp. 100–116, January 2007.