Non-linear static and dynamic response of spherical shells

Abstract

In the present investigation an analytical technique using Chebyshev series expansion has been presented and used to study the non-linear transient behavior of shallow spherical shells with and without damping. The two coupled non-linear differential equation governing the shallow shell behavior are initially linearised using Taylor's series expansion. Results have been presented for three types of transient loadings, namely, step function, N-shaped pulse and sine wave pulse. It is shown that accurate results can be obtained using a five terms Chebyshev series expansion which is unlikely in the conventional methods.