QUALITATIVE INVESTIGATION AND MONOTONIC ITERATIVE SOLUTIONS FOR NONLINEAR BENDING OF POLAR ORTHOTROPIC CIRCULAR PLATES  

作　　者：尚新春 程昌钧 

出　　处：《Applied Mathematics and Mechanics(English Edition)》1990年第12期1137-1154,共18页应用数学和力学（英文版）

摘　　要：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.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.

关 键 词：Mathematical Techniques Iterative Methods 

分 类 号：O3，O1[理学—力学]