A WAVELET METHOD FOR BENDING OF CIRCULAR PLATE WITH LARGE DEFLECTION  

作　　者：Xiaomin Wang Xiao jing Liu Jizeng Wang Youhe Zhou 

机构地区：[1]College of Engineering, Huazhong Agricultural University [2]Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education of China, and College of Civil Engineering and Mechanics, Lanzhou University

出　　处：《Acta Mechanica Solida Sinica》2015年第1期83-90,共8页固体力学学报（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11472119,11032006 and 11121202);the National Key Project of Magneto-Constrained Fusion Energy Development Program(No.2013GB110002);the Scientific and Technological Self-innovation Foundation of Huazhong Agricultural University(No.52902-0900206074)

摘　　要：A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.

关 键 词：large deformation bending problem circular plate wavelet method 

分 类 号：O344.1[理学—固体力学]