Hybrid Analysis of Shallow Spherical Shells

Abstract

The exact solution of shallow spherical shells subjected to apex loads contains arbitrary constants that appear in the stress and normal displacement functions. In general, these constants are obtained from the conditions of regularity, transition and boundary. For large “characteristic” length, the relations between the arbitrary constants become clumsy and complicated. Considering hinged boundary conditions uncovers inherent difficulties to the formulation of these relations. This paper is concerned with the experimental determination of the arbitrary constants. A thin‐walled model of a shallow spherical shell subjected to uniform distributed load over a small area at the apex, having hinged supports, is prepared and tested thoroughly. The surface stresses are formulated in terms of the arbitrary constants. Based on the experimentally recorded strains (stresses), in on‐line interaction, model, and personal computer, the significant constants are determined. The results might be normalized and made applicable to other shells of similar geometric proportions. The present approach provides the basic idea for developing a new transducer.