Analysis of a proposal for the simplified determination of critical loads of elastic shells

Abstract

Within the context of the stability analysis of the cryostat of a fusion reactor the question was raised whether the rather lengthy conventional stability analysis can be circumvented by applying a simplified strategy. This strategy requires the static linear deformation analysis of the structure with and without imperfections. The general assessment of its validity for thin shells under hydrostatic pressure involves two types of investigations: (i) a general stability analysis for thin shells; (ii) a general linear deformation analysis for thin imperfect shells and the definition of a suitable scalar parameter (β-parameter) which should represent the reciprocal of the critical load. For both problems approximate solutions are obtained based on the associated variational principles and a global Ritz formulation for the displacement components. The solution of the first problem is restricted to linear prebuckling deformations and is taken as reference solution. It is shown that the simplified strategy generally is not capable to predict the critical load of the reference solution exactly. This is in contrast to observations made for some simple stability problems where exact agreement with classical solutions had been obtained. Nevertheless, the results do not exclude the possibility that the proposed strategy will give reasonable approximate solutions at least for a restricted class of stability problems. This should be a subject of further analyses.