Configuration-dependent interpolation in higher-order 2D beam finite elements

•We propose a configuration-dependent interpolation for 2D non-linear beams.•We establish a connection between this interpolation and linked interpolation in linear analysis.•The results obtained show good performance regardless of the integration order.

In this paper we discuss interpolation functions for the field variables and their variations in relation to geometrically non-linear planar beam finite elements of Reissner's type within the context of a non-standard, configuration-dependent interpolational setting.We derive the new configuration-dependent interpolation functions as an extension of the helicoidal interpolation to higher-order elements. In linear analysis, the new interpolation coincides with the higher-order linked interpolation, which is known to produce exact results for polynomial loading.The numerical analysis performed on representative examples illustrates the performance of the configuration-dependent interpolation compared to the Lagrangian interpolation.