A 2D field-consistent beam element for large displacement analysis using a rational Bézier representation with varying weights

Abstract

This study develops a new 2D field-consistent Euler-Bernoulli beam element for the analysis of beam structures undergoing large displacements but small strains. The total Lagrangian description is considered in the derivation of finite element equations. Relationships between the cross-sectional rotation and displacements of the beam axis are derived, and consequently, the kinematics of the element are entirely described by the displacements of the beam axis. These relationships underlie the construction of field-consistent interpolations. Regarding geometric descriptions, the deformed configuration of an element is represented by a rational cubic Bézier curve. For better geometric representations of complex deformed configurations, some of the weights are treated as discrete unknowns. Several benchmark numerical examples are used to demonstrate the accuracy and robustness of the proposed beam element. The merits of considering weights as discrete unknowns are verified through comparisons between elements having varying weights and stationary weights. Furthermore, the proposed beam element is found to be naturally free from membrane locking, and thus, no additional efforts are required to handle the locking issues.