engleski

Configuration-dependent interpolation in non-linear 2D beam finite elements

Configuration-dependent interpolation in 3D beam theory is a powerful tool, which may be used to provide a result invariant to the choice of a beam reference axis or invariant to a rigid-body rotation. In this paper, 2D beam elements only are analysed in order to eliminate the second of these issues, which is inherently spatial in nature. The configuration-dependent interpolation constructed in this way contributes to accuracy of the solution considerably and as a result completely eliminates the problem of shear locking. In linear analysis, this interpolation also gives the theoretical solution for the Timoshenko beam element. Nevertheless, all of this has been proven for two-noded beam elements only and the question naturally arises as to how this idea can be generalised to higher-order elements. In this work, we present different approaches to this problem and analyse their outcomes and practicality. We find out that the results obtained from the assumption that the standard Reissner strain measures should be constant correspond to the helicoidal interpolation of Borri and Bottasso. When this methodology is applied to a linear distribution of strain measures, the derivation complicates considerably. The development of higher-order non-linear interpolation, however, is still possible by requesting equivalence between the linear limit of the configuration-dependent interpolation sought and the standard linked interpolation of a particular order.

configuration-dependent interpolation; non-linear beam element

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