A 2D field-consistent beam element for large displacement analysis using the total Lagrangian formulation

In this study, a new 2D Euler–Bernoulli beam element for large displacement analysis using the total Lagrangian formulation is proposed. In large displacement analysis, the beam kinematics written based on the total Lagrangian description is complicated. As a result, it is not easy to find suitable interpolations that are field consistent for beam elements developed in this description. For this reason, existing total Lagrangian beam elements generally employ field-inconsistent interpolations, which result in degradation of element performances. In this study, field-consistent interpolations for a 2D Euler–Bernoulli beam element are proposed. The field consistency is obtained by using a set of interpolations that satisfy a required relationship between relevant displacement fields. The construction of the interpolations is made possible by allowing the interpolations to be expressed as nonlinear functions of nodal degrees of freedom. The validity and efficiency of the proposed element are shown by solving various numerical examples found in the literature.