Stability analysis of shells of revolution on nonlinear elastic foundations

Abstract

In many practical applications, thin shells are in contact with soils or other solids. Such situations arise in cylindrical bulk solid storage silos, above-ground and underground liquid storage tanks, underground pipelines, ballistic missiles filled with solid propellants, and concrete-filled steel tubular columns. As a result, many studies have been carried out on the analysis and behavior of shells on elastic foundations. However, little has been done on shells on nonlinear elastic foundations, despite the fact that foundation behavior is generally nonlinear. This paper presents a finite element formulation for the buckling analysis of shells of revolution on nonlinear elastic foundations. To achieve a versatile foundation model, the foundation reaction-displacement relationship is represented by a number of discrete data points (referred to as the Discrete-Point or DP Model in this paper). Any specific nonlinear functions such as polynomials can be treated as special cases of this model and accurately represented by a sufficiently large number of data points. The validity and capability of the present analysis are demonstrated through numerical comparisons. The paper also presents the first set of verified numerical results for buckling of shells on nonlinear elastic foundations, which can be used to benchmark results from other sources in the future.