不对称的各向异性叠层矩形板的非线性弯曲(Ⅰ)
Nonlinear Bendings of Unsymmetrically Layered Anisotropic Rectangular Plates
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摘要: 本文研究了不对称的各向异性叠层矩形板在多种支承条件下的非线性弯曲,利用文[1]中提出的奇异摄动方法,导出了板在横向载荷和边缘拉力的联合作用下,其挠度和应力函数的一致有效的N阶渐近解。因此,本文的研究对于这样一个复杂的问题提供了一个简单而又有效的方法。Abstract: An analysis for the nonlinear bendings of unsymmetrically layered anisotropic rectangular plates subjected to combined edge tensions and lateral loading under venous supports is presented. The uniformly valid N-order asymptotic solutions of the transverse deflection and stress function are derived by the singular perturbation method offered in [1]. The present investigation may provide a simple and convenient method for such a complex problem.
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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,3,6(1982), 629-640. [3] Ashton and Whitney,Approximate solutions for unsymmetrically laminated plates,Journal of Composite Materials,3,Jan.(1969),189-191. [4] Zaghloul,S.A.and J.B.Kennedy,Nonlinear analysis of unsymmetrically laminated plates,Proc.ASCE.J.of Eng.Mech.Div.101,EM3. (1975),169-186. [5] Prabhakara,M.K.and C.Y.Chia,Nonlinear analysis of laminated cross-ply plates,Journal of Eng.Mech.Div.ASCE.103,EMA.(1977),749-753. [6] Giri,J.and G.J.Simitses,Deflection response of general laminated composite plates to inplane and transverse load,Fibre Science and Technology,13,3(1980),225-242. [7] Jones,R.M.,Mechanics of Composite Materials,Scripta Book Co.,Washington,D.C.,McGraw-Hill,New York(1975). [8] S.铁摩辛柯,S.沃诺斯基,《板壳理论》,科学出版社(1977). [9] 周次青,正交异性矩形薄板在各种支承条件下的非线性弯曲,应用数学和力学,5, 3 (1984),419-436. [10] 周次青,对称正交铺设矩形叠层板的非线性弯曲,应用数学和力学,8, 9 (1985), 819-832. [11] 周次青,对称的各向异性叠层矩板板的非线性弯曲(待发表). [12] Whitney,J.M.and A.W.Leissa,Analysis of heterogeneous anisotropic plates,J.Appl.Mech.,36(1969),261. [13] Stavsky,Y.,On the general theory of heterogeneous aeolotropic plates,Aeronautical Quarterly,15(1964),29-38.
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