对称铺设各向异性叠层矩形板的非线性弯曲
Nonlinear Bendings of Symmetrically Layered Anisotropic Rectangular Plates
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摘要: 本文研究了对称铺设各向异性矩形叠层板在各种支承条件下的非线性弯曲.应用奇异摄动方法导出了挠度和应力函数的一致有效的N阶渐近解.对承受边缘张力和侧向载荷的简支矩形叠层板应用奇摄动方法和改进了的迦辽金方法(一种加权残数法)进行了分析和计算.Abstract: This paper has studied the nonlinear bendings of symmetrically layered anisotropic rectangular plates under various supports.The uniformly valid N-order asymptotic solutions of the deflection and stress function are derived by the singular perturbation method offered in [1].The analysis and calculations are given for simply and clamped supported,rectangular plates subjected to combined edge tensions and lateral loading in conjunction with the modified Galerkin procedure(a method of weighted residuals).
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[1] 江福汝,关于椭圆型方程的奇摄动,复旦学报,自然科学版,2 (1978),29-37. [2] 江福汝,环形和圆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). [3] 周次青,对称正交铺设矩形叠层板在各种支承条件下的非线性弯曲,应用数学和力学,6,9(1985). [4] Whitney,J.M.and A.W.Leissa,Analysis of a simply supported laminated anisotropic rectangular plate,American Institute of Aeronautics and Astronautics Journal,8,1(1970),28-33. [5] Zaghloul S.A.and J.B.Kennedy,Nonlinear behaviour of symmetrically laminated plates,J.Appl.Mech.,42,1(1975),234-236. [6] Prabnakara M.K.and C.Y.Chia,Nonlinear analysis of laminated cross-ply plates,J.of Eng Mech.Div.,101,EM 3(1975),749-753. [7] Jones,R.M.,Mechanics of Composite Materials,Scripta Book Co.,Washington D.C.,McGraw-Hill,New York(1975). [8] Timoshenko S.and S.Woinowsky-Krieger,Theory of Plates and Shells(1959). [9] 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. -
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