合成展开法应用于球壳对称弯曲的边界层问题

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.

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

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.