Abstract
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 additional 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 von Karman plate theories are identified with respect to the large deformation bending of circular plates.
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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), and the Scientific and Technological Self-innovation Foundation of Huazhong Agricultural University (No. 52902-0900206074).
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Wang, X., Liu, X., Wang, J. et al. A Wavelet Method for Bending of Circular Plate with Large Deflection. Acta Mech. Solida Sin. 28, 83–90 (2015). https://doi.org/10.1016/S0894-9166(15)60018-0
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DOI: https://doi.org/10.1016/S0894-9166(15)60018-0