A neural network based closed-form solution for the distortional buckling of elliptical tubes

Following the Eurocode 3 philosophy, it is expected that the design of elliptical hollow section (EHS) tubes will be based on the slenderness concept, which requires the calculation of the EHS critical stress. The critical stress of an EHS tube under compression may be associated with local buckling, distortional buckling or flexural buckling. The complexity in deriving analytical expressions for distortional critical stress from classical shell theories, led us to apply Artificial Neural Networks (ANN). This paper presents closed-form expressions to calculate the distortional critical stress and half-wave length of EHS tubes under compression, using ANN. Almost 400 EHS geometries are used and based solely on three parameters: the outer EHS dimensions (A and B) and its thickness (t). Two architectures are shown to be successful. They are tested for several statistical parameters and proven to be very well behaved. Finally, some simple illustrative examples are shown and final remarks are drawn concerning the accuracy of the closed-formed formulas.

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► EHS tubes under compression may buckle in either local or distortional modes.
► Analytical formulas exist for local buckling of EHS tubes but they are missing for distortional buckling of EHS tubes, due to inherent complexity of distortional mechanics.
► Artificial Neural Networks (ANN) are used to develop closed-form expressions for the calculation of the distortional critical stress and half-wave length of EHS tubes under compression.
► They are tested for several statistical parameters and proven to be very well behaved.