圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题(Ⅱ)

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The Problems of the Nonlinear Unsymmetrical Bending for Cylindrically Orthotropic Circular Plate(Ⅱ)

摘要: 本文利用“正则摄动法”^[2]研究文献[1]中由“两变量法”^[3]所得到的关于W_nm,nm,v_nm和ψ_nm(n=0.1.2...N:m=1.2...M)和的递推方程和递推边界条件的求解问题.求得了本问题的一致有效渐近解,最后作为实例,我们利用“混合摄动法”^[4]研究了轴对称线性弯曲问题,并将所得结果与文献[5]中给出的精确解相比较,两者基本上是一致的.
- 正交各向异性圆板 /
- 全核 /
- 摄动法
Abstract: In this Paper we study the recursive equations under the recursive boundary conditions for W_nm,nm,v_nm and ψ_nm(n=0.1.2...N:m=1.2...M.which derivedby the two-variable method ^[3] in the preceding paper^[1].We then solve these problems by using the method of regular perturbation^[2].and the uniformly valid asymptotic solution is obtained.Lastly we consider a particular example i.e the bending problems of the axisymmetrical circular plate by using the mixed perurbation method and compare our results with the exact solution found in Ret[5].They are similarly coincided.
- orthotropic circular plate /
- whole core /
- perturbation

[1]	秦圣立、黄家寅,国柱型正义各向异性圆形薄板的非线比非对称弯曲问题(I),应用数学和力学,15(8)(1994),779-796.
[2]	Jung Furu,On the boundary layer method,Alpliocl Mcrth.and Meth.(English Ed.),2,5(1981).461-473.
[3]	R.E.,O’Malley,Introduction to Singular Perturbations,Academic Press,New York(1974).
[4]	Qin Shengli.and Zheang Aishu.On the jumping problems of a circular thin plate with initial deflection,Appliesd Math and Meth.(English Ed.),8,5(1987).447-458.
[5]	Fan Fuqun and Dong Wanlin,Bending of circular plate of non-homogeneous cylindrically orthotropic composites,Aotcr Mechanica Sinica.17,5(1985),461-471.
[6]	A.H.Nayfeh,Introduction to Perturbation Technique John Wiley & Sons(1981).