# Axisymmetric Buckling of Thin Shallow Circular
Spherical Shells under Uniform Pressure for Large
Values of Geometric Parameter Lambda

*Axisymmetric Buckling of Thin Shallow Circular
Spherical Shells under Uniform Pressure for Large
Values of Geometric Parameter Lambda*

Yeh, K., Song, W., and Cleghorn, W.L.

International Journal of Non-Linear Mechanics, Vol. 29, No. 4, pp. 603-611, 1994.

## Abstract

The problem of axisymmetrical buckling of thin shallow
circular spherical shells under uniform pressure with the
edge either rigidly clamped or simply supported is studied.
The Newton-spline function method is used to solve the
non-linear differential equations of thin shallow circular
spherical shells. Numerical results of upper and lower
critical loads for shells with the value of geometric
parameter lambda as great as 50 are obtained. The character
of prebuckling and postbuckling and the problem of finding
critical points is discussed. The problem is called the
very large geometric parameter lambda buckling problem of
a shallow circular spherical shell, whose results had been
predicted by Budiansky. Here we confirm his result as being
reasonable. Relations between the buckling model and the
geometric parameter lambda which improve Karman and Tsien's
suggestion are discussed.

Dimensions of a shallow circular spherical shell.

Deformed radial sections, rigidly clamped.