Qualitative investigation and monotonic iterative solutions for nonlinear bending of polar orthotropic circular plates

Abstract

This paper presents a systematical investigation of the nonlinear bending of polar orthotropic circular plates under arbitrarily axisymmetric loads and a variety of boundary conditions. Firstly, the boundary value problem reduces to the equivalent integral equations, and the solutions to the linearized problem are given by means of generalized functions. Secondly, the general properties of the solutions of the nonlinear integral equations are investigated in detail, such as, wrinkling, non-negativity, and singularity etc. Then, the monotonic iterative solutions are formally given and the convergence criteria and the global uniqueness of the solutions are discussed. The error estimate of the iterative process is obtained. Finally, a special example is discussed which shows that the conclusions and methods of this paper are valid. Several results in the paper are presented for the first time.