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

Applied Mathematics and Mechanics (English Edition) ›› 1990, Vol. 11 ›› Issue (12): 1137-1154.

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

尚新春, 程昌钧

Department of Mechanics, Lanzhou University, Lanzhou

收稿日期:1990-04-26 出版日期:1990-12-18 发布日期:1990-12-18

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

Shang Xin-chun, Cheng Chang-jun

Department of Mechanics, Lanzhou University, Lanzhou

Received:1990-04-26 Online:1990-12-18 Published:1990-12-18

摘要/Abstract

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 oundary value problem reduces to the equivalent integral equations, and the so tions 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: nonlinear bending, qualitative analyses, monotonic iterative solu-tions, convergence criteria, global uniqueness, estimation of error

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 oundary value problem reduces to the equivalent integral equations, and the so tions 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.

Key words: nonlinear bending, qualitative analyses, monotonic iterative solu-tions, convergence criteria, global uniqueness, estimation of error

尚新春;程昌钧. QUALITATIVE INVESTIGATION AND MONOTONIC ITERATIVE SOLUTIONS FOR NONLINEAR BENDING OF POLAR ORTHOTROPIC CIRCULAR PLATES[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(12): 1137-1154.

Shang Xin-chun;Cheng Chang-jun. QUALITATIVE INVESTIGATION AND MONOTONIC ITERATIVE SOLUTIONS FOR NONLINEAR BENDING OF POLAR ORTHOTROPIC CIRCULAR PLATES[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(12): 1137-1154.

参考文献

[1] Nath, Y. and R. S. Alwar, Nonlinear dynamic analysis of orthotropic circular plates, Int. J.Solid Structures, 16 (1980), 433-443.
[2] Nowinisi, J., Cylindrically orthotropic circular plates, ZAMP, 11-(1960), 218-228.
[3] Gandhi, M. L., P. C. Dumir and Y. Nath, Nonlinear axisymmetric static analysis of orthotropic thin circular plates with elastically restrained edge, Computer Structures, 20(1985), 841-853.
[4] Shilkrut, D., Investigations of axisymmetric deformation of geometrically nonlinear,rotationally orthotropic, circular plates, Int. J. Non-Linear Mech., 18(1983), 95-118.
[5] Cheo, L. S. and E. L. Reiss, Unsymmetric wrinkling of circular plates, Q. App!. Math., 76(1973), 75-91.
[6] Yanowitch, M., Nonlinear buckling of circular plates,Comm. Pure Appl. Math., 9 (1956), 661.
[7] Vol'mir, A. S., Flexible Plates and Shells, Moscow (1956). (in Russian)
[8] Reiss, E. L., A uniqueness theorem for the nonlinear axisymmetric bending of circular plates,AIAA J., 1 (1963), 2650-2652.
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[10] Shang Xin-chun and Cheng Chang-jun, Qualitative analyses for nonlinear axisymmetric bending of circular plates (to appear). (in Chinese)
[11] Keller, H. B. and E. L. Reiss, Iterative solutions for the nonlinear bending of circular plates,Comm. Pure Appl. Math., 11 (1958), 273-298.
[12] Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Elastic Body，Holden-Bay Sense in Mathematical Physics, Julius J. Brandstaffer, Ed. (1963), 85.
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QUALITATIVE INVESTIGATION AND MONOTONIC ITERATIVE SOLUTIONS FOR NONLINEAR BENDING OF POLAR ORTHOTROPIC CIRCULAR PLATES

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

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