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.