受弯层合板边缘效应数值-摄动分析*
Numericai-Perturbation Analysis of Edge Effect in Bending Laminated Plate
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摘要: 本文将分析一个受弯复合材料层合板的计算模型.首先利用无量纲变量将层合板任一层的平衡方程变成以位移表示的摄动型微分方程式;然后利用合成展开法,将求解区域分成内部区域和边界层区域,并推导出求解外部解和内部解的数学模型.为突出边缘效应,最后用边界积分方程表示内部解.Abstract: In this paper, we consider a bending laminated plate. At first, the dimensionless variables are used to transform the equilibrium equations of any layer to perturbation differential equations. Secondly, the composite expansion is used and the solution domain is divided into interior and boundary layer regions and the mathematical models for the outer solution and the inner solution are yielded respectively. Then, the inner solution is expressed with the boundary intergral equation.
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[1] Pipes,R.B.and N.J.Pagano,Interlaminar stresses in composite laminates under uniform axial extension,J.Comp.Matherials.4(1970). [2] Wang,A.S.D.and F.W.Crossman,Some new results on edge effects in symmetric composite laminates,J.Comp.Materials,11(1977). [3] Pichas,R.Y.and T.H.H.Pian,Calculation of interlaminar stress concentration in composite laminates,J.Comp.Materials.15(1981). [4] Loo,Tsu-tao,On the nature of interlaminar edge stress in laminated composite structures,Proceedings of International Symposium on Composite Materials and Structures.Beijing,China.June(1986).10-13. [5] 叶碧泉、周焕文,层状复合材料结构边缘效应数值分析,应用数学和力学,9,5 (1988年),.403-410. [6] 周焕文,奇摄动在圆板大挠度问题中的应用,《奇异摄动理论及其在力学中的应用》(钱伟长主编),科学出版社(1981年). [7] 彭晓林、何广乾,广义函数法边界积分方程的建立,应用数学和力学,7,6 (1986年),497-504. [8] 齐民友编著,《线性偏微分算子引论》,科学出版社(1986年). -
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