四边固定正交各向异性矩形板的非线性弯曲问题
The Proplems of Nonliear Bending for Orthotropic Rectangular Plate with Four Clamped Edges
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摘要: 本文利用“两变量法”[1]和“混和摄动法”[2]研究了正交各向异性矩形板在非均布横向载荷作用下的非线性弯曲问题,在四边固定条件下,得到了一致有效渐近解.Abstract: In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using"the method of twovariable"[1] and "the method of mixing perturbation"[2].The uniformly valid asymptotic solutions of Nth-order for ε1 and Mth-order for ε2 for ortholropic rectangular plale with four clamped edges are oblained.
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[1] 江福汝,关于边界层方法,应用数学和力学,2(5)(1981),461-473. [2] 秦圣立、张爱椒,关于具有初始挤度阿圆形薄板的跳跃问题,应用数学和力学.8(5)(1987),447-458. [3] W.Z.Chien(钱伟长),Asymptotic behavior of a thin clampod circular plate under uniform normal pressure at very large defleetion,Sci.Rep.Nat.Tsing Hua Univ,Ser,A(5)(1984),71-94. [4] 江福汝,环形和圆形薄板在各种支承条件下的非对称弯曲(Ⅰ),应用数学和力学,3(5)(1982),6 29-640. [5] 江福汝,环形和圆形薄板在各种支承条件下的非对称弯曲,应用数学和力学,5(2)(1984),191-203. [6] 秦圣立、黄家寅,圆柱型正交各向异险圆形薄板的非对称弯曲问题(Ⅰ).应甲数学和力学,15(8)(1994,8),741-757. [7] 周次青,正交各向异性矩形薄板的非线性弯曲,应用数学和力学.5(3)(1984).419-436. [8] R.E.O'Mally.,Introduction to Singular Perturbation,Academic Press(1974). -
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