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.