合成展开法应用于球壳对称弯曲的边界层问题

周焕文

合成展开法应用于球壳对称弯曲的边界层问题

周焕文

武汉大学

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出版历程
- 收稿日期: 1983-01-20
- 刊出日期: 1983-12-15

The Method of Composite Expansions Applied to Boundary Layer Problems in Symmetric Bending of the Spherical Shells

Zhou Huan-wen

Wuhan University, Wuhan

摘要

摘要: 本文推广钱伟长在[5]中提出的合成展开法分析双参数边界层问题. 对于受均布荷载作用的球壳对称变形问题,其非线性平衡方程可以写成(2.3a),(2.3b):式中ε与δ是待定参数.当δ=1,ε是小参数时,这是第一边界层问题:当δ与ε都县小参数时.这是第二边界层问题. 对于上述问题,我们假定ε,δ和p满足ε³pδ=1-ε在这个条件下,应用推广的合成展开法,求出上述问题具有固定边界条件情况的渐近解.

Abstract: In this paper,the method of composite expansions, which was proposed by W. Z. Chien (1948,[5]), is extended to investigate two-parameter boundary layer problems.For the problems of symmetric deformations of the spherical shells under the action of uniformly distribution load q, its nonlinear equilibrium equations can be written as follows(2.3a)、(2.3b): where ε and δ are undetermined parameters.If δ=1 and ε is a small parameter, the above-mentioned problem is called first boundary layer problem; if ε is a small parameter, and δ is a small parameter, too, the above-mentioned problem is called second boundary layer problem.For the above problems, however, we assume that the constants ε, δ and p satisfy the following equation: ε³pδ=1-ε In the defining of this condition, using the extended method of composite expansions, we find out the asymptotic solution of the above problems with the clamped boundary condition.

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参考文献(13)

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