Approximate Solutions to Nonlinear Problems of Solid Mechanics by Quasilinearization Method

Abstract

The approximate solution to the problem for an infinite plate with the circular hole under creep regime is obtained by the quasilinearization method. Four approximations of the solution for the nonlinear creep problem are found. It is shown that with increasing the number of approximations the solution converges to the limit numerical solution. It is worth to note that the tangential stress reaches its maximum value not at the circular hole but at the internal point of the plate. It is shown that quasilinearization method is the effective method for nonlinear problems. The model problem for steady state creep of a rotating disc is either considered. The high values of the creep exponent are analyzed and it is shown that the high values of the creep exponent require more iterations in the quasilinearization method.