An equilibrium-based formulation with nonlinear configuration dependent interpolation for geometrically exact 3D beams

Abstract

This article describes a novel equilibrium-based geometrically exact beam finite element formulation. First, the spatial position and rotation fields are interpolated by nonlinear configuration-dependent functions that enforce constant strains along the element axis, completely eliminating locking phenomena. Then, the resulting kinematic fields are used to interpolate the spatial sections force and moment fields in order to fulfill equilibrium exactly in the deformed configuration. The internal variables are explicitly solved at the element level and closed-form expressions for the internal force vector and tangent stiffness matrix are obtained, allowing for explicit computation, without numerical integration. The objectivity and absence of locking are verified and some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. The proposed formulation is successfully tested in several numerical application examples.