对称正交铺设矩形叠层板的非线性弯曲
Nonlinear Bendings of Rectangular Symmetrically Laminated Cross-Ply Plates under Various Supports
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摘要: 本文应用[1]中提出的奇异摄动方法,在[3]的基础上,研究了在各种支承条件下承受均布载荷的对称正交铺设矩形叠层板的非线性弯曲问题,导出了挠度和应力函数的一致有效的N阶形式渐近解.对承受均布压力,边界位移为零的简支矩形板进行了分析、计算.Abstract: This paper studies the nonlinear bendings of rectangular symmetrically laminated cross-ply plates subjected to uniform pressure under various supports on the basis of[3] by the singular perturbation method offered in[1]. The uniformly valid N-order asymptotic solutions of the deflection and stress function are derived. Analyses and numerical solutions are given for simply supported rectangular laminates, whase edge displacement is vanished.
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[1] 江福汝,关于椭圆型方程的奇摄动,复旦学报(自然科学报),2(1978), 29-37. [2] 江福汝,环形和回形薄板在各种支承条件下的非对称非线性弯曲问题,应用数学和力学,3,5.(1982),629-640. [3] 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. [4] Levy, Samuel, Large deflection theory for rectangular plates, Proc.Symposia Appl.Math., 1(1949), 197. [5] Zaghloul S.A.and J.B.Kennedy, Nonlinear behaviour of symmetrically laminated plates, J Appl.Mech, 42, 1(1975), 234-236. [6] Timoshenko, S and S.Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill Book Company.Inc.(1959). [7] Jones.R.M., Mechanics of Composite Materials, Scripta Book Co., Washington, D.C., McGraw-Hill, New York, (1975). -
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