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)
The Problems of the Nonlinear Unsymmetrical Bending for Cylindrically Orthotropic Circular Plate(Ⅱ)
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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Wnm,nm,vnm和ψnm(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.Abstract: In this Paper we study the recursive equations under the recursive boundary conditions for Wnm,nm,vnm and ψnm(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.
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Key words:
- orthotropic circular plate /
- whole core /
- perturbation
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[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). -
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