Orthotropic Annular Shells on Elastic Foundations

Abstract

Theoretical nonlinear transient analysis of orthotropic annular shallow spherical shells interacting with Winkler‐Pasternak elastic subgrades is performed. The governing nonlinear equations of motion are derived and solved in space and time domains employing Chebyshev polynomials and implicit Houbolt time‐marching technique, respectively. The numerical results are obtained for both clamped and simply‐supported immovable outer edge conditions with free inner edge of the shell. The influence of foundation interaction, material orthotropy, and annular ratio on the response of spherical caps is determined. The results reveal that both foundation interaction and polar orthotropy play a significant role on the response characteristics of these shell structures.